• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Fuzzy Articles
 

Fuzzy Articles

on

  • 15,613 views

This file contains 89 abstracts on Fuzzy Systems and its applications on the variety of subjects. ...

This file contains 89 abstracts on Fuzzy Systems and its applications on the variety of subjects.
List of Abstracts :
1. A Novel Unsupervised Neuro-Fuzzy System Applied to Circuit Analysis
2. A Numerical Approach Based on Neuro-Fuzzy Systems for Obtaining Functional Inverse
3. Improved Genetic Algorithm-Based Optimization of Fuzzy Logic Controllers
4. FUZZY REAL NUMBERS AND THEIR RELATION TO THE TOPOLOGICAL VECTOR SPACE
5. Fuzzy Seminormed Linear Space
6. A Novel Algorithm for Tuning of the Type-2 Fuzzy System
7. Fuzzy Um-set in Sostak sense
8. Velocity Control of an Electro Hydraulic Servosystem by Sliding Mamdani
9. An On-line Fuzzy Backstepping Controller for Rotary Inverted Pendulum System
10. Optimal Design of Type_1 TSK Fuzzy Controller Using GRLA
11. System of linear fuzzy differential equations
12. A method for fully fuzzy linear system of equations
13. Full fuzzy linear systems of the form Ax+b=Cx+d
14. Solving fuzzy polynomial equation by ranking method
15. Stabilization of Autonomous Bicycle by an Intelligent Controller
16. Solving fuzzy linear programming problems with piecewise linear membership functions by the determination of a crisp maximizing decision
17. Fuzzy Convex Subalgebras of Residuated Lattice
18. Algebraic Fuzzy Subsets of Non-commutative Join Spaces
19. An Ant Based Algorithm Approach to Vehicle Navigation
20. Novel ranking method of fuzzy numbers
21. A Trapezoidal Membership Function Block for Fuzzy Applications
22. Ranking Fuzzy Numbers by Sign Length
23. Ranking of fuzzy numbers by left and right ranking Functions
24. An Application of Possibility Goal Programming to the Time-Cost Trade off Problem
25. A Multi Hybrid Genetic Algorithm for the Quadratic Assignment Problem
26. Implementation of Evolutionary Algorithm and Fuzzy Sets for Reliability Optimization of Engineering Systems
27. One-sided Process Capability Indices and Fuzzy lower Confidence Bounds for them
28. Fuzzy Confidence regions for the Taguchi Index in Fuzzy Process
29. A Method of Generating a Random Sample From a Fuzzy Distribution Function
30. Fuzzy linear regression analysis with trapezoidal coefficients
31. Probability on balanced lattices
32. Dpq-DISTANCE AND THE STRONG LAWOF LARGE NUMBER FOR NEGATIVELY DEPENDENT FUZZY RANDOM VARIABLES
33. Reducible Fuzzy Markov Chain and Fuzzy Absorption Probability
34. Fuzzy Traffic Rate Controller (FTRC) for Mobile Ad hoc Network Routers
35. A Fuzzy Routing Algorithm for Low Earth Satellite Networks
36. A metaheuristic Algorithm for New Models of Fuzzy Bus Terminal Location Problem with a Certain Ranking Function
37. Finding the Inversion of a Square Matrix and Pseudo-inverse of a Non-square Matrix by Hebbian Learning Rule
38. Solving Fuzzy Integral equations by Differential Transformation Method
39. FUZZY TOPOLOGICAL SPACES
40. COMMON FIXED POINT THEOREM IN COMPLETE FUZZY METRIC SPACES
41. Extension Principle for Vauge Sets
42. Signed Decomposition of Fully Fuzzy Linear Systems
43. Iteration approach of solving interval and fuzzy linear system of equations
44. FUZZY BANACH ALGEBRA
45. Some Properties of Zariski Topology on the Spectrum of Prime Fuzzy Submodules
46. A NEURAL NETWORK MODEL FOR SOLVING STOCHASTIC FUZZY MULTIOBJECTIVE LINEAR FRACTIONAL PROGRAMS
47. Application of a hybrid GA-BP optimized neural network for springback estimation in sheet metal forming process
48. Vehicle Type Recognition Using Probabilistic Constraint Support Vector Machine
49. On-line Identification and Prediction of Lorenz's Chaotic System Using Chebyshev Neural Networks
50. A Novel Hybrid Structure and Criteria in Modeling and Identification
51. Design of a VLSI Hamming Neural Network For arrhythmia classification
52. Designing an optimal PID controller using Imperialist Competitive Algorithm
53. Fractional PID Controller Design based on Evolutionary Algorithms for Robust two-inertia Speed Control
54. Neural Networks for Fault Detection and Isolation of

Statistics

Views

Total Views
15,613
Views on SlideShare
15,610
Embed Views
3

Actions

Likes
1
Downloads
674
Comments
2

3 Embeds 3

http://www.lmodules.com 1
http://virtualcampus.pupr.edu 1
http://alef.fiit.stuba.sk 1

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel

12 of 2 previous next

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Fuzzy Articles Fuzzy Articles Document Transcript

    • ! "
    •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
    •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
    • 45 1 1 # 1 C = !" 47 $ / / !- 1 @ ! 'B+ 1 & # 48 - "I 2 1 #@ / / !- #$ # 59 2 #& # 5 #& # @ 6! 5 $ # @ -! ' # D ' E 5% 0# + ' @1 @ - = 5( 0# H' @1 @ B -! - - + & . 53 - @ -! # & 54 0 " + " ! @ 6 55 / I / 6 # /@ ' 6 + " - 57 #, @ #- 1 + " 58 - ' 6 + " 79 & 1 #H . - # ! @ 6 + " 7 & # ! 1 " 1 @ 7 + @ # . " # + # 7% " ,,& 1 7( + # # ' # 73 @- . $2 $ # %. 2 # 74 . # 2- + 75 ' # - ! 77 & + # 0 ' #& 78 + . 0# + $ # #/ = 1 @ 6
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Novel Unsupervised Neuro-Fuzzy System Applied to Circuit Analysis Hadi Sadoghi Yazdi Seyed Ebrahim Hosseini Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran E-mail: {sadoghi, ehosseini}@sttu.ac.ir Abstract: In this paper, for the first time, unsupervised neuro-fuzzy system is presented and is applied in circuit analysis. Usually Neuro-fuzzy systems have a learning phase in which the system is trained with input data. But if the training set is unavailable, conventional procedures encounter serious problem. Due to unsupervised character, no learning data is needed. To investigate the method, linear circuit is analyzed. Results are compared with the exact solution. Keywords: Unsupervised neuro-fuzzy system, Circuit analysis. Where ψ (x ) denotes the solution, G is the functional 1. Introduction defining the structure of the differential equation, and Artificial neural networks (ANN), as intelligent ∇ is some differential operator. The basic idea, called computational tools have been used for modeling and collocation method, is to discretize the domain D over optimization of analog circuit design [1]. For example a finite set of points D . Thus (1) becomes a system of optimization of high-speed very large scale integration equations. Suppose an approximation of the solution (VLSI) interconnects [2], global modeling [3, 4] and ψ(x) is given by the trail solution ψt(x). As a measure circuit synthesis [5]. for the degree of fulfillment of the original differential Numerous problems in science and engineering can be equation (1), an error function similar to the mean converted to a set of differential equations. Basic squared error is defined: numerical methods can be used to solve differential E= 1 [( )] ∑ G xi ,ψ t , ∇ψ t , ∇ 2ψ t ,... . D xt ∈D 2 (2) equations such as the finite difference method, the finite element method, the finite volume method and the boundary element method. Therefore, finding an approximation of the solution Neural networks (NNs) are used to approximate of (1) is equal to finding a function that minimizes the stochastically unknown functions and relations. This error E . It is well known that a multilayer feed forward approximation is a kind of implicit model of the neural network is a universal approximator [7], unknown dependencies. In contrast, differential therefore the trail solution ψt(x) can be represented by equations are used to model explicitly all relations. such an artificial neural network. In case of a given Solving ordinary and partial differential equations can network architecture the problem is reduced to finding be learned to a good degree by an artificial neural a configuration of weights that minimizes (2). As E is network. The basic ideas were presented by Lagaris, differentiable with respect to the weights for most Likas, and Fotiadis [6]. Let the differential equation to differential equations, efficient gradient-based learning be solved be given by: G (x,ψ ( x ), ∇ψ (x ), ∇ 2ψ ( x ),...) = 0 x ∈ D ⊆ R n , algorithms for artificial neural networks can be (1) employed for minimizing (2). 1 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Numerical Approach Based on Neuro-Fuzzy Systems for Obtaining Functional Inverse Hadi Sadoghi Yazdi1, Sohrab Effati2 1-Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran 2-Department of Mathematics, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran Abstract: In this paper, a new and easy available numerical method is presented in calculation of functional inverse. As for ANFIS (Adaptive Network based Fuzzy Inference System) model is available without great difficulty in MATLAB software also due to important of obtaining functional inverse in wide range applications, we present ANFIS-based approach for the first time for obtaining inverse of mathematical functions. The proposed approach includes two main stages, in the first step; some limited points are sampled from desired function using Monte Carlo simulation and second step contains training of ANFIS system that input system is output points of function and ANFIS desired values are input values to function. One of notes in the proposed approach is calculation of inverse of time varying functions only with tuning of generated fuzzy model with the least square and the back propagation (BP) algorithms to form of hybrid learning algorithm which able into tracking of time varying functions. Experimental results over many functions show superiority of the proposed method relative MATLAB software. Keywords: Functional inverse; Adaptive Network based Fuzzy Inference System; Monte Carlo method; Hybrid learning; MATLAB software. 1. Introduction resolution image which is as close as possible to the Functional inverse not only is used in mathematics original high resolution image subject to certain but also have many applications in engineering and constraints [4]. sciences. Finding sources from measured data is a common problem in a real world. From the Inverse learning in signal processing: mathematic point of view, solving the equation obtain The developments of inverse learning was initiated inverse of function or an iterative approach give us from adaptive signal processing and control of linear functional inverse. If f is a continuous function systems approach [2, 3] and due to its potential [ ] applicability, until now several modifications and defined in interval a, b , g is inverse of f if applications are still being developed in the literature. ( f o g )(x ) = x or f (g (x )) = x ; so −1 g is f or is a In data communications, receiver equalization has become an essential building block to mitigate the functional inverse. Functional inverse can study from inter-symbol interference problem, which is due to different views: limited bandwidth of low cost channel materials. Several equalization methods have been developed Finding source of generated data: which are types of functional inverse [5]. The inverse problem of finding the source from the data is other form of functional inverse. In practice a Constructing inverse signal: process has two elements, the physical process and Creating of inverse signal for reducing of the measurement. In the measurement procedure undesirable signal is another view of functional noise is inserted to data. So it is needed a smoother is inverse. Active noise control systems are based on the selected for noise reduction then backward mapping principle of superposition: an unwanted noise is is required for finding source [1]. cancelled out by the action of a secondary noise that In the field of image processing, finding main generates a sound wave of equal amplitude and image from degraded image is based on dealing with opposite phase [6]. This idea has evolved and new the problem as an inverse problem. Based on the applications have been developed in which the observation model, our objective is to obtain a high 15 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Improved Genetic Algorithm-Based Optimization of Fuzzy Logic Controllers Amin Chegeni, Abdollah Khoei, Khayrollah Hadidi Microelectronics Research Laboratory Urmia University st_a.chegeni@urmia.ac.ir a.khoei@urmia.ac.ir kh.hadidi@urmia.ac.ir Abstract: This paper presents a new method to degree of freedom and degrades the performance. improve genetic algorithm-based optimization of fuzzy Second, since the plant is nonlinear, as we will logic controllers considering both membership explain in this paper, if the FLC is optimized for a functions and rules. We indicate that eliminating the special input signal, the system may be unstable limitation on symmetric membership functions and for other inputs. Thus, optimizing the FLC for rules results better optimization. Furthermore, we only one special input is a faulty optimization. optimize fuzzy logic controller using genetic algorithm In this paper, we indicate that eliminating the considering whole of system states, which cause the reliability of the controller to improve significantly. mentioned limitation on symmetric MFs and rule table results in more degree of freedom and consequently better optimization. Furthermore, we Keywords: Fuzzy logic controller, genetic analyze the effect of optimizing FLC for different algorithm, optimization. states of the system, and show that the reliability of the controller improves significantly when 1 Introduction involving more states of the system in the optimization. In the last decade, many researches have focused This paper is organized as follows. In section II, a on the learning and tuning algorithms for both brief description of GA is presented. Optimization model based and model-free design of fuzzy logic mechanism will be presented in section III, and in controllers (FLCs). The literature report successful section IV, two well-known examples along with applications of methods based on fuzzy clustering, their simulation results will be presented to verify neural networks (NNs), reinforcement learning, the feasibility and advantage of this method. and genetic algorithms (Gas) for the most widely Section V concludes this work. adopted techniques. In many researches, only membership functions (MFs) are used in the 2 Genetic Algorithms (GA’s) optimization process, and in some of them, both MFs and rules are optimized. However, two GA’s are search algorithms modeled after the important points usually are not considered in the mechanics of natural genetics [8]. They are useful practical optimization. First, in almost all articles, approaches to problems requiring effective and the resulted MFs and/or rule-table are constrained efficient searching, and their use is widespread in to be symmetrical [1, 3, 4, 5]. Considering that the applications to business, scientific, and plant controlled by FLC is generally nonlinear, the engineering fields. In an optimally designed optimal MFs and rule table are not necessarily application, GA’s can be used to obtain an symmetrical; therefore, restricting the approximate solution for single variable or optimization to symmetric results decreases the multivariable optimal problems. Before a GA is 25 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran FUZZY REAL NUMBERS AND THEIR RELATION TO THE TOPOLOGICAL VECTOR SPACE I. SADEQI AND M. SALEHI esadeqi@sut.ac.ir Abstract: : In this paper first we show that the fuzzy normed spaces (FNS) constructed by fuzzy real numbers are topological vector space, and then we prove that the definition of fuzzy continuity and topological continuity are equivalent. By using that we can easily establish all results in the topological vector spaces for the fuzzy normed spaces.. Keywords: Fuzzy real number, Fuzzy norm, Fuzzy bounded operator, topological vector space. 1 Introduction Felbin [1] put forward the concept of a fuzzy We denote the origin of a linear space by θ; and the normed linear space (briefly , FNS) by applying set of all fuzzy real number by F. If h∈ F and h(t) the notion of fuzzy distance to the linear space. It = 0 whenever t < 0, then h is called an non- is more natural and practical that the norm of a negative fuzzy real number and by F+ we mean the point is a fuzzy number rather than a real number. set of all non-negative fuzzy real number. The Xiao and Zhu [2] investigated the linear number 0 stands for the fuzzy number satisfying topological structure and some basis properties of FNS under the condition of weaker right norm and 0 (t) = 1 and 0 (t) = 1 if t ≠0 clearly, 0 ∈ F+. The left norm. We will show that a fuzzy normed space set of all real numbers can be embedded in F is also a topological vector space and we will because if r ∈ (-∞ , ∞), then r ∈ F satisfies r (t) = prove that the fuzzy continuity and topological continuity (fuzzy boundedness and topological 0 (t - r). For h ∈ F , r ∈ (0,∞) and α∈ (0,1], r • h boundedness) are equivalent. So all results and is defined as (r • h)(t) = h(t/r) and 0 • h is defined theorems in the topological vector spaces hold for the fuzzy normed spaces in general. There are to be 0 ; the α-level set [h]α = {t : h(t) ≥ α} is a − + many important known theorems in the topological closed interval and we denote it by [h]α= [h α ,h α ]. vector spaces; among them are Uniform Definition 2.1. Let X be a linear space over real boundedness, Open mapping theorem, Closed number field; L and R (respectively, left norm and Graph theorem, Han-Banach theorem,... which right norm) be symmetric and non decreasing remain true for fuzzy normed spaces. Therefore as mapping from [0, 1] × [0, 1] into [0,1] satisfying it is cited above already proven in classical analysis, for fuzzy normed spaces. The only L(0,0) = 0 , R(1,1) = 1. Then ∥ .∥ is called a fuzzy problem remain is that we investigate the norm and (X, ∥ .∥ , L , R ) a fuzzy normed space properties in fuzzy normed spaces which does not hold in classical analysis. (abbreviated to FNS). If the mapping ∥ .∥ from X into F+ satisfies the following axioms where − + 2 preliminaries [∥ x∥ ]α = [∥ x∥ α ,∥ x∥ α ] for x∈ X and Our notation and definition follow [2]. α∈ (0,1] ) 45 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Seminormed Linear Space I . Sadeqi and F. Solaty kia esadeqi@sut.ac.ir Abstract: In this note we introduce and study the notion of fuzzy seminorm and we get some new results. Finally we give an example of a fuzzy seminorm space which is fuzzy normable but is not classical normable. Keywords: fuzzy normed space, fuzzy seminorm, Minkowski functional, fuzzy metric. (N5) N( x , . ) is a non -decreasing function on 1 Introduction ℜ , and lim N(x, t)=1 as t → ∞ . The pair (X, N) is said to be a fuzzy normed In 1984, Kastaras [3] first introduced the idea of space. fuzzy norm on a linear space. In 1992, Felbin [4] introduced an idea of a fuzzy norm on a linear 2 Fuzzy seminorm space whose associated metric is Kaleva [5] type. In 1994, S.C.Chang and J.N.Mordeson [6] Definition: A fuzzy seminorm on a vector space introduced an idea of a fuzzy norm on a linear X is a function on X × ℜ such that space whose associated metric is Kramosil and P1) ∀ t ∈ ℜ with t ≤ 0, ρ (x, t) =0; Michalek type [7]. Following Chang and P2) ∀ t ∈ ℜ with t > 0, ρ (cx, t) = ρ (x, t/|c|) Mordeson, In 2003, T.Bag and S.K.Samanta introduced in [1] a definition of fuzzy norm and if c ≠ 0 proved the decomposition theorem of fuzzy norm P3) ∀ t, s ∈ ℜ , x, u ∈ X , ρ (x+u, t+s) ≥ min to a family of crisp norms. We introduce the fuzzy { ρ (x, t), ρ (u, s) } seminorm and study some of it's properties, then P4) ρ ( x , . ) is a non-decreasing function of ℜ by an example we will show that a family of fuzzy and lim ρ (x, t)=1 as t → ∞ seminorm implies a fuzzy norm on C ( Ω ) space but it is not true in classical case. Note : A fuzzy seminorm ρ is a fuzzy norm N if Preliminary it satisfies ; ρ (x, t)= 1 ∀ t ∈ ℜ with t > 0 then x = 0. Definition: [1] Let X be a vector space. A fuzzy subset N of X × ℜ is called a fuzzy norm on Definition: A family P of fuzzy seminorms on X X if the following condition, are satisfied for all is said to be separating if to each x ≠ 0 x, y ∈ X and c ∈ ℜ : corresponds at least one ρ ∈ P and t ∈ ℜ such (N1) N(x, t) = 0 ; ∀ t ∈ ℜ with t ≤ 0 that ρ (x, t) ≠ 1. (N2) N(x, t) = 1 ; ∀ t ∈ ℜ , t > 0 iff x=0 (N3) N(c x, t) = N(x, t/|c|), ∀ t ∈ ℜ , t >0 and Theorem: Let ρ is a fuzzy seminorm on a vector c ≠ 0 space X. Define ρ α (x) = inf { t : ρ (x ,t) ≥ α }, (N4) N(x + y, t +s) ≥ min {N(x, s), N( y, t)}, for all x ,y ∈ X , s ,t ∈ ℜ α ∈ (0,1). Then {ρ α : α ∈ (0,1)} an ascending 51 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Novel Algorithm for Tuning of the Type-2 Fuzzy System Sayed Mohammad Ali Mohammadi1 Ali Akbar gharaveisi1 Mashaalah Mashinchi2 s_m_ali_mohammadi@yahoo.com a_gharaveisi@yahoo.com mmachinci@yahoo.com 1. Department of Electrical Engineering, Shahi Bahonar University of Kerman-Iran 2. Department of Mathematic, Shahi Bahonar University of Kerman –Iran Abstract- Type-2 fuzzy logic systems (FLSs) let uncertainties that occur in rule-based FLSs be modeled using the new third dimension of type-2 fuzzy sets. Although a complete theory of type-2 FLSs exists for general type-2 fuzzy sets, it is only for interval type-2 fuzzy sets that type-2 FLSs are practical. Type 2 fuzzy sets allow for linguistic grades of membership. A type-2 fuzzy inferencing systems uses type-2 fuzzy sets to represent uncertainty in both the representation and inferencing. However; as with type-l fuzzy systems there is till an issue with regard to the design of the appropriate membership functions. One of the best performance the fuzzy inference system is optimized by the least square and numerical method .The key advantages of the least square method are the efficient use of samples and the simplicity of the implementation but it can be take long time for convergence. This paper presents a novel type-2 adaptive system for learning the membership grades of type-2 fuzzy sets which can be important. The results from the application problems lead us to believe that this approach offers the capability to allow linguistic descriptors to be learnt by an adaptive network and we can use some new algorithm same as Reinforcement Learning Methods for adaptation. Key word: Fuzzy Decision, Type 2 Fuzzy Sets, Adaptive Fuzzy Systems, FOU . I. Introduction 1- The meanings of the words that are used in One possible approach to deal with the vague the antecedents and consequents of rules concepts is fuzzy logic systems, which are can be uncertain (words mean different based on the fuzzy set theory, formulated and things to different people). developed by Zadeh [1]. Fuzzy set theory is a 2-Consequents rnay have a histogram of generalization of classical set theory that values associated with them, especially provides a way to absorb the uncertainty when knowledge is extracted from a group inherent to phenomena whose information is of experts who do not all agree. vague and supplies a strict mathematical 3-Measurements that activate a FLS may be framework, which allows its study with some noisy and therefore uncertain. precision and accuracy. A fuzzy logic system 4-The data that are used to tune the (FLS) can deal with the vagueness and parameters of a FLS may also be noisy. uncertainty residing in the knowledge All of’ these uncertainties translate into possessed by human beings or implicated in uncertainties about fuzzy set membership the numerical data, and it allows us to functions. Traditional type-I fuzzy sets are not represent the system parameters with linguistic able to directly model such uncertainties terms[2]. Since the introduction of the basic because their membership functions are totally conceptions of the fuzzy set theory, FLS have crisp. On the other hand, type-2 fuzzy sets are been studied for more than 30 years. The able to model such uncertainties because their success of their applications is in various membership functions are themselves fuzzy. fields. They can be very helpful to achieve classification tasks, offline process simulation and diagnosis, decision support tools, and process control [3]. Fuzzy rules and membership functions have been used as a key tool to express knowledge. There are (at least) four sources of uncertainties associated with fuzzy logic systems (FLSs) which can be listed as follows: Figure.1-Structure of a Type-2 FLS 63 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Fuzzy Um-set in Sostak sense Intelligent Systems Scientific Society of Iran Mohsen Alimohammady and Mehdi Roohi Department of Mathematics, Faculty of Basic Sciences University of Mazandaran, Babolsar 47416–1468, Iran, amohsen@umz.ac.ir, mehdi.roohi@gmail.com Abstract. This paper is devoted to extending the notion of fuzzy minimal space in Sostak sense. The concepts of fuzzy Um -set, (U, m)-open set and (U, m)-closed set will be introduced and some char- acterizations of them are achieved. Finally, some brand of fuzzy minimal continuous functions and their relations with fuzzy Um -set, (U, m)-open set and (U, m)-closed set are given. 1 Introduction set where 1X is the characteristic function on X. A family τ of fuzzy sets in X is called a fuzzy topology After the discovery of the fuzzy sets, many at- for X if tempts have been made to extend various branches (a) α1X ∈ τ for each α ∈ I, of mathematics to the fuzzy setting. Fuzzy topo- (b) A ∧ B ∈ τ , where A, B ∈ τ and logical spaces as a very natural generalization of W (c) α∈A Aα ∈ τ whenever, Aα ∈ τ for all α topological spaces were first put forward in the lit- in A. The pair (X, τ ) is called a fuzzy topological erature by Chang [11] in 1968. He studied a number space [17]. Every member of τ is called fuzzy open of the basic concepts including interior and closure set and its complement is called fuzzy closed sets of a fuzzy set, fuzzy continuous mapping and fuzzy [17]. In a fuzzy topological space X the interior and compactness. Several authors used Chang’s defini- the closure of a fuzzy set A (denoted by Int(A) and tion in many direction to obtain some results which Cl(A) respectively) are defined by are compatible with results in general topology. In 1976 Lowen [17] suggested an alternative and _ Int(A) = {U : U ≤ A, U is fuzzy open set} and more natural definition for achieving more results ^ which are compatible to the general case in topol- Cl(A) = {F : A ≤ F, F is fuzzy closed set}. ogy. For example with Chang’s definition, constant functions between fuzzy topological spaces are not Let f be a function from X to Y . It is a fuzzy necessarily fuzzy continuous but in Lowen’s sense function defined by all of the constant functions are fuzzy continuous. 8 W In 1985 Sostak [25] introduced the smooth fuzzy < A(x) f −1 ({y}) = ∅ topology as an extension of Chang’s fuzzy topol- f (A)(y) = x∈f −1 ({y}) : 0 f −1 ({y}) = ∅, ogy. It has been developed in many directions [12], [14] and [15]. for all y in Y , where A is an arbitrary fuzzy set in In [20] authors introduced minimal structures X [27]. and minimal spaces. Some result about minimal spaces can be found in [2], [7], [13], [18], [19], [22] Definition 2.1. Let (X, τ ) be a fuzzy topological and [24]. The concept of fuzzy minimal structure space. A fuzzy set A in X is said to be was introduced and studied in [1], [3], [4], [5], [6] (a) fuzzy semi open if A ≤ Cl(Int(A)) [9], and [8] which it extended fuzzy topology defined by Lowen [17]. In this paper we redefine fuzzy (b) fuzzy preopen if A ≤ Int(Cl(A)) [10], minimal structure as a function which is a general- (c) fuzzy α-open if A ≤ Int(Cl(Int(A))) [10], ization of fuzzy topology introduced by Sostak [25]. (d) fuzzy β-open if A ≤ Cl(Int(Cl(A))) [21]. The family of all fuzzy semi open, fuzzy pre- open, fuzzy α-open and fuzzy β-open sets is 2 Preliminaries denoted by F SO(X), F P O(X), F αO(X) and F βO(X) respectively. The complement of a fuzzy For easy understanding of the material incorpo- semi open, fuzzy preopen, fuzzy α-open and fuzzy rated in this paper we recall some basic definitions β-open set is called fuzzy semi closed, fuzzy pre- and results. For details on the following notions closed, fuzzy α-closed and fuzzy β-closed respec- we refer to [23], [25] and [26]. A fuzzy set in(on) tively. The union of all fuzzy semi open, fuzzy pre- a universe set X is a function with domain X and open, fuzzy α-open and fuzzy β-open sets of X con- values in I = [0, 1]. The class of all fuzzy sets on tained in A is called fuzzy semi interior, fuzzy prein- X will be denoted by I X and symbols A,B,... is terior, fuzzy α-interior and fuzzy β-interior of A used for fuzzy sets on X. 01X is called empty fuzzy and is denoted by sInt(A), pInt(A), αInt(A) and 1 71 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Velocity Control of an Electro Hydraulic Servosystem by Sliding Mamdani M. Aliyari Shoorehdeli1, M. Teshnehlab2 1. Computer department of Science and Research Branch, Islamic Azad University of Tehran, Iran. 1, 2. K. N. Toosi University of Tech Tehran, Iran. Aliyari@gmail.com, {m_aliyari, teshnehlab}@eetd.kntu.ac.ir Abstract- This paper addresses new hybrid approaches for velocity control of an electro hydraulic servosystem (EHSS) in presence of flow nonlinearities and internal friction. In our new approaches, we combined classical method based-on sliding mode control and Mamdani networks. The control by using adaptive networks need plant’s Jacobean, but here this problem solved by sliding surface. It is demonstrated that this new technique have good ability control performance. It is shown that this technique can be successfully used to stabilize any chosen operating point of the system. All derived results are validated by computer simulation of a nonlinear mathematical model of the system. The controllers which introduced have big range for control the system. Keywords: Electro Hydraulic, Mamdani networks, Strict Feedback, Sliding mode, Sliding Surface. 1 Introduction in some detail. In section 4, system properties and The EHSS is used in many industrial applications, the relation of new method and simulation results because of its ability to handle large inertia and describe and section 5 is the conclusion part. torque loads and, at the same time, achieve fast responses and a high degree of both accuracy and 2 System Description performance [1, 2]. Depending on the desired control objective, an A scheme of an electrohydraulic velocity EHSS can be classified as either a position, servosystem is shown in Figure 1. velocity or force/torque EHSS. Therefore, control The basic parts of this system are: 1. hydraulic techniques for electro-hydraulic servo system have power supply, 2. accumulator, 3. charge valve, 4. been widely studied over the past decade; the pressure gauge device, 5. filter, 6. two-stage details of these systems are given in the reference electrohydraulic servovalve, 7. hydraulic motor, 8. [3]. In [8] an intelligent CMAC neural network measurement device, 9. personal computer, and 10. controller using feedback error learning approach Voltage- to- current converter. introduced which is very complex, and [3] presents methods based on feedback linearization and backstepping approaches, that have good performances but the controller designing is not very simple procedure, in [9] authors proposed a simpler method than other methods based on Lyapunov stability approach but the results in this new hybrid approaches are very better and faster than other mentioned methods. The paper is organized like this: In section 2, the Figure 1: Electrohydraulic velocity servosystem. EHSS and its nonlinear mathematical model are described. In section 3, issues related to the sliding A mathematical representation of the system is mode design and Mamdani network are discussed derived using Newton’s Second Law for the 103 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran An On-line Fuzzy Backstepping Controller for Rotary Inverted Pendulum System Mahsa Rahmanian1, Mahdi Aliyari Shoorehdeli2, Mohammad Teshnehlab3 1, 2 Computer Department, Science & Research Branch, Islamic Azad University 3 Electrical Department, K. N. Toosi University of Tech 1 Mahsa_r_360@yahoo.com, 2Aliyari@gmail.com, 3Teshnehlab@eetd.kntu.ac.ir Abstract: In this study a new combination of This paper introduces a new combination of nonlinear backstepping scheme with on-line fuzzy backstepping scheme with an on-line fuzzy system system is presented for the rotary inverted pendulum to obtain a nonlinear controller to stabilize the system to achieve better performance in nonlinear pendulum at the upright equilibrium point. controller. The inverted pendulum, a popular mechatronic application, exists in many different 2 System Model and Dynamics forms. The common thread among these systems is Here, in this part the description of model and their goal: to balance a link on end using feedback dynamics are given. Fig (1-a) depicts the rotary control. The purpose of this study is to design a inverted pendulum in motion. Fig (1-b) depicts the stabilizing controller that balances the inverted pendulum as a lump mass at half the length of the pendulum in the upright position. pendulum. By applying the Euler-Lagrange equations, we can obtain the equations of motion as Keywords: Nonlinear backstepping, Fuzzy follows: approximator, Rotary inverted pendulum. (mr 2 ) + J eq θ& + mrLSin (α ) α 2 − mrLCos (α ) α = T − Beqθ & & && & 1 Introduction mL α − mrLCos (α )θ& − mgLSin(α ) = 0 4 2 & && (1) Inverted pendulum has been widely used in both 3 linear and nonlinear control education with applications to other under actuated mechanical where L is the length to pendulum's center of mass, systems, involving nonlinear dynamics, robotics and m is the mass of pendulum arm, r is the rotating arm aerospace vehicles testing [1]. length, θ is the servo load gear angle, α is the Recently, the pioneering work on fuzzy control via pendulum arm deflection, J eq is the equivalent backstepping has been done in [2-4]. In which, a fuzzy system is used to approximate the unknown moment of inertia at the load, Beq is the equivalent nonlinear function in each design step, and an viscous damping coefficient, g is the gravitational adaptive fuzzy controller was developed by meaning acceleration and T is the control torque. of backstepping technique for a class of SISO The Eq.(1) can be rewritten as the following state uncertain nonlinear systems [5]. equations: The rotary motion inverted pendulum, which is shown in Fig (1-a), is driven by a rotary servo motor x1 = x 3 & system [6]. The zero position for α and θ are x2 = x4 & defined as the pendulum being vertical ‘up’. 107 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Optimal Design of Type_1 TSK Fuzzy Controller Using GRLA F. Naderi, A. A. Gharaveisi and M. Rashidinejad Electrical Engineering Dept. of Shahid Bahonar University of Kerman Kerman, Iran a_gharaveisi@yahoo.com ABSTRACT A new methodology for designing optimal systematic GA-based fuzzy controller is presented in this paper. Our design is based on Genetic Reinforcement Learning Algorithm (GRLA), unlike conventional GA that is based on the competition between chromosomes only to survive, this method is based on competition and cooperation between chromosomes, GA tries to find good chromosomes and good combination for them to form an optimal fuzzy controller. The proposed GRLA design method has been applied to the cart-pole balancing system. The controller was capable of balancing ° the pole for initial conditions up to 80 . As a comparison we applied a Mamdani controller which is designed through normal GA and uses five membership functions for inputs and output variables to the same problem. the results show the efficiency of the proposed method. Keywords : Genetic Reinforcement Learning Algorithm (GRLA), TSK Fuzzy Controller I. INTRODUCTION if-then rules. So this fact has forced researchers to find a method that Fuzzy theory has been developed by automatically determines the parameters. L.A.Zadeh in 1965 [1]. Since conventional Some papers propose automatic methods control schemes are limited in their range of using neural networks (NN) [7,8] ,Fuzzy practical applications, fuzzy logic clustering [6] ,genetic algorithms(GA) controllers are receiving increased attention [3,9,10,11,12] , gradient methods[13,14], or for intelligent control applications [2]. Evolutionary Algorithm (EA) [4,22,23]Karr Fuzzy control systems employ a mode of used a GA to generate membership function approximate reasoning that resembles the for a fuzzy controller [15] in Karr’s work , decision-making process of humans. The the user has to define a method to set the behavior of a fuzzy controller is easily rules at first or hand-design this exhaustive understood by a human expert as knowledge task, then use the GA to design the mf only. is expressed by means of intuitive, linguistic Since the mf and rule set are highly rules. In the design of a fuzzy controller the dependent, hand-design a one, and GA- definition of membership functions and the design of the other, does not use the GA to establishment of control rules (if-then rules) its full advantage. So in most automatic are very important. designs For an FCS the optimization In [5], Procyk and Mamdani show that a of both the Membership function (mf) change in the membership function (mf) and the control rules of the FCS are may alter the fuzzy control system (FCS) required. performance significantly. Berenji [16, 17] introduced a method that Unfortunately the human experts are not learns to adjust the fuzzy mf of the linguistic sometimes able to express their knowledge labels used in different control rules through in the form of fuzzy 113 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran System of linear fuzzy differential equations M. Otadi a , S. Abbasbandy b and M. Mosleh a a Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh, Iran b Department of Mathematics, Faculty of Science, Imam Khomeini International University, Ghazvin, 34149-16818, Iran Mahmood_Otadi@yahoo.com , Abbasbandy@yahoo.com, Maryam_mosleh79@yahoo.com Abstract: In this paper, we discuss the solution of a system of linear fuzzy differential equations, where A and B are real n × n matrix and the initial condition x 0 is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient condition for the existence . derivative x ( t ) of a fuzzy process x(t). Keywords: Fuzzy number, Linear fuzzy differential equations, Fuzzy system 1. Introduction The concept of fuzzy numbers and fuzzy rithmetic exactly. One method of treating this uncertainty is operations were first introduced by Zadeh [19], to use a fuzzy set theory formulation of problem Dubois and Prade[8]. We refer the reader to [9] for [18]. The topic of Fuzzy Differential Equations more information on fuzzy numbers and fuzzy (FDEs) has been rapidly growing in recent years. arithmetic. Fuzzy systems are used to study a The concept of fuzzy derivative was first variety of problems ranging from fuzzy topological introduced by Chang and Zadeh [5] , it was spaces [6] to control chaotic systems [11], fuzzy followed up by Dobois and Prade [7] who used the metric spaces [17], fuzzy differential equations [3], extension principle in their approach. Other ethods fuzzy linear systems [1,2]. have been discussed by Puri and Ralescu [10]. One of the major applications of fuzzy number fuzzy differential equations were first formulated arithmetic is treating system of linear fuzzy by Kaleva [9] and Seikkala [18] in time dependent differential equations [20]. In modelling real form. Kaleval had formulated fuzzy differential systems one can be frequently confronted with a equations, in term of derivative [9]. Buckley and Feuring cite{bf} have give a very general differential equation formulation of a fuzzy first-order initial value problem. They first find the crisp solution, fuzzify where the structure of the equation is known, it and then check to see if it satisfies the FDE. represented by the vector field f, but the model Pearson cite{pear} has a property of linear fuzzy parameters and the initial value x0 are not known differential equations, 123 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A method for fully fuzzy linear system of equations H. Rouhparvar ∗, T. Allahviranloo † ∗ Department of Mathematics, Saveh Branch, Islamic Azad University, Saveh, Iran † Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Abstract:Fuzzy linear systems of equations play a aspects and the works on them are too limited. Some major role in various applications such as financial, of the most interesting works on these matrices can be economics, engineering and physics. We employ new seen in [5, 9]. In [8] a computational method repre- product-type operation which are introduced and studied sented for solving a FFLSEs based on Zadehs exten- in [4], as e.g. the cross product of fuzzy numbers that sion principle and in [18] provided a method to solve from the theoretical and practical point of view in fuzzy this problem based on their cuts. Now we provide a arithmetic, is efficiently of the multiplication based on method based on r-cuts and new definition of product Zadeh’s extension principle for finding a fuzzy vector x fuzzy numbers, i.e., the cross product to solve FFLSEs which satisfies Ax = b, where An×n and b are a fuzzy is computational and practical. In this paper we use matrix and a fuzzy vector, respectively. We transform triangular fuzzy numbers. fully fuzzy linear system of equations (FFLSEs) to The structure of this paper is organized as follows: extended crisp linear system in [12]. This systems can In Section 2, we recall some concepts from fuzzy arith- be solve as numerically, see [1, 2, 3, 6]. metic. We illustrate summary of the cross product in Section 3. In Section 4, we solve A ⊗ x = b by pro- Keywords: Fully fuzzy linear system of equations, posed method. The proposed method are illustrated Cross product, Fuzzy number, Fuzzy matrix. by solving some examples in section 5 and conclusion are drawn in Section 6. 1 Introduction Fuzzy linear system, Ax = b, where the coefficient ma- 2 Preliminaries trix A is crisp, while b is a fuzzy number vector, is In this section we represent definitions needful for next solved in [12, 13, 14]. Friedman et al. [12] use the em- sections. We denote by E 1 the set of all fuzzy numbers. bedding method given in [19]. Allahviranloo [1, 2, 3] uses the iterative Jacobi and Gauss Siedel method, the Adomian method and SOR method, respectively. Of 2.1 Fuzzy numbers course, the a lot of papers with different methods ex- ist in this content but in continuation to these works, Definition 2.1. A fuzzy subset u of the real line R people worked the case in which all parameters in a with membership function u(t) : R → [0, 1] is called a fuzzy linear system are fuzzy numbers, which we call fuzzy number if: it a Fully Fuzzy Linear System of Equations(FFLSEs), for example see [8, 16, 18]. (a) u is normal, i.e., there exist an element t0 such Here we will solve A ⊗ x = b, where A is a fuzzy ma- that u(t0 ) = 1, trix and x and b are fuzzy vectors. We will use fuzzy (b) u is fuzzy convex, i.e., u(λt1 + (1 − λ)t2 ) ≥ matrix defined in [10]. This class of fuzzy matrices con- min{u(t1 ), u(t2 )} ∀t1 , t2 ∈ R, ∀λ ∈ [0, 1], sist of applicable matrices, which can model uncertain ∗ Email address: rouhparvar59@gmail.com. (c) u(t) is upper semi continuous, 1 129 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Full fuzzy linear systems of the form Ax+b=Cx+d M. Mosleh a , S. Abbasbandy b and M. Otadi a a Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh, Iran b Department of Mathematics, Faculty of Science, Imam Khomeini International University, Ghazvin, 34149-16818, Iran Maryam_mosleh79@yahoo.com, Abbasbandy@yahoo.com, Mahmood_Otadi@yahoo.com Abstract: This paper mainly intends to discuss the solution of the full fuzzy linear systems (FFLS) Ax+b=Cx+d, where A and C are fuzzy matrices, b and d are fuzzy vectors. Ming Ma et al. introduced a new fuzzy arithmetic based on parametric form of fuzzy numbers, which we apply it for our purpose. Keywords: Fuzzy number, Full fuzzy linear systems, Fuzzy arithmetic, Parametric epresentation 1. Introduction column is an arbitrary fuzzy number vector. They The concept of fuzzy numbers and fuzzy used the parametric form of fuzzy numbers and arithmetic operations were first introduced by replaced the original fuzzy n × n linear system by Zadeh [16], Dubois and Prade [7]. Fuzzy systems a crisp 2n × 2n linear system and studied duality are used to study a variety of problems ranging in fuzzy linear systems Ax=Bx+y where A , B from fuzzy topological spaces [5] to control haotic are real n × n matrices, the unknown vector x is systems [8,11], fuzzy metric spaces [14], fuzzy vector consisting of n fuzzy numbers and the differential equations [3], fuzzy linear systems constant y is vector consisting of n fuzzy numbers, [1,2]. in [10]. In [1,2] the authors presented conjugate One of the major applications of fuzzy number gradient, LU decomposition method for solving arithmetic is treating fuzzy linear systems and fully general fuzzy linear systems or symmetric fuzzy fuzzy linear systems, several problems in various linear systems. Also, Wang et al. [15] presented an areas such as economics, engineering and physics iterative algorithm for solving dual linear system boil down to the solution of a linear system of of the form x=Ax+u, where A is real n × n matrix, equations. In many applications, at least some of the unknown vector x and the constant u are all the parameters of the system should be represented vectors consisting of fuzzy numbers and by fuzzy rather than crisp numbers. Thus, it is abbasbandy [4] investigated the existence of a immensely important to develop numerical minimal solution of general dual fuzzy linear procedures that would appropriately treat fuzzy equation system of the form Ax+f=Bx+c, where A, linear systems and solve them. B are real m × n matrices, the unknown vector x is vector consisting of n fuzzy numbers and the Friedman et al. [9] introduced a general model onstant f, c are vectors consisting of $m$ fuzzy for solving a fuzzy n × n linear system whose numbers. Recently, Muzziloi et al. [13] considered coefficient matrix is crisp and the right-hand side fully fuzzy linear systems of the form 135 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Solving fuzzy polynomial equation by ranking method H. Rouhparvar Department of Mathematics, Saveh Branch, Islamic Azad University, Saveh, Iran rouhparvar59@gmail.com Abstract: In this paper, we find real roots for fuzzy polynomial equations (if exists) by ranking fuzzy numbers. We transform fuzzy polynomial equation to system of crisp polynomial equations, this transformation perform with ranking method based on three parameters Value, Ambiguity and Fuzziness. Provided system of crisp polynomial equations can be solved numerically. Finally, we illustrate our approach by numerical examples. Keywords: Fuzzy number, Fuzzy polynomial, Value, Ambiguity, Fuzziness. 1 Introduction In Section 2, we review basic definition and the Polynomial equations play a major role in various notions of fuzzy numbers, Value, Ambiguity and areas such as mathematics, engineering and social Fuzziness. In Section 3, we represent fuzzy sciences. We interested in finding real roots of polynomial equation and proposed method for polynomial equation like solving it and provide two total examples. Some numerical examples are considered in Section 4 , and Conclusion comes in Section 5. that x ∈ ℜ (if exists) and C 0 , C1 , K , C n are fuzzy numbers, by a ranking method of fuzzy numbers. 2 Preliminaries This ranking method is provided for canonical representation of the solution of fuzzy linear In this section, we review some preliminaries system in [10]. The applications of fuzzy which are needed in the next section. For more polynomial equations are considered by [2]. Also, details, see [7,8,9]. numerical solution of fuzzy polynomial equations by fuzzy neural network is solved in [3] and linear Definition 2.1. A fuzzy subset C of the real line and nonlinear fuzzy equations are shown by ℜ with membership function C ( x) : ℜ → [0,1] is [1,4,5,6]. called a fuzzy number if In this paper, we propose a new method for solving 1. C is normal, i.e., there exist an element x0 an fuzzy polynomial equation based on ranking such that C ( x 0 ) = 1 , method which is introduced by Delgado et. al. 2. C is fuzzy convex, i.e., C (λx1 + (1 − λ ) x 2 ) [7,8]. They introduced three real indices called Value, Ambiguity and Fuzziness to obtain ≥ min{C ( x1 ), C ( x 2 )} ∀x1 , x 2 ∈ ℜ, ∀λ ∈ [0,1] , "simple", fuzzy numbers, that could be used to 3. C (x) is upper semi continuous, represent more arbitrary fuzzy numbers. Therefore, 4. support C is bounded, where support C = cl{x ∈ ℜ : C ( x) > 0},and cl is we use this parameters and transform fuzzy polynomial equation to system of crisp polynomial equations then with solving this system we can the closure operator. find real roots of fuzzy polynomial equation. 141 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Stabilization of Autonomous Bicycle by an Intelligent Controller N. Noroozi and F. Shabani Nia Department of Electrical Engineering, Shiraz University, Shiraz, Iran Abstract: Nowadays, urban traffic jams cause waste of time and air pollution. Bicycle is a convenient alternative as a mean of transportation for being confronted with these problems. However, bicycle is unstable in itself and it will fall down without human assistance like steering handle or moving upper body. It needs practice to ride a bicycle [1]. In this paper, an intelligent controller is proposed, which can stabilize a bicycle with suitable performance for the whole of considered range of disturbance. The original part of controller is consists mainly of a fuzzy controller. Also it is used genetic algorithms and neural networks for optimization and adaptation of scaling factors respectively. Keywords: Bicycle, Fuzzy Controller, Stability, Genetic Algorithms, Neural Networks genetic algorithms for optimization of response. I. Introduction Neural networks are proposed the controller to Nowadays, urban traffic jams cause waste of conform. time and air pollution. Bicycle will help to solve This paper is composed of five sections. In these problems. In addition, the energy conversion section II, dynamic modeling is shown. Section III efficiency of bicycle is critically higher than other shows the proposed control strategy. In section IV vehicles [2]. simulation results are implemented to verify the Soft computing approaches in decision proposed control strategy. The conclusions are making have become increasingly popular in summarized in section V. many disciplines. This evident from the vast number of technical papers appearing in journals II. The Model and conference proceeding in all areas of Assuming that the rider doesn't move upper engineering, manufacturing, sciences, medicine, body, the dynamic model of bicycle is represented and business. Soft computing is a rapidly evolving as follows [1] field that combines knowledge, techniques from neural networks, fuzzy set theory, and Iθ& = TGR + FCF . h & (1) approximate reasoning, and using optimization methods such as genetic algorithms. The where I, TGR, FCF, h, and θ mean moment of integration of these and other methodologies inertia, gravitational force, centrifugal force, forms the core of soft computing [6]. height of COG, and camber angle of bicycle This paper presents an intelligent controller respectively as shown Fig.1. for stabilization of bicycle by controlling its steering. The original part of controller is consists mainly of a fuzzy controller. Also it is used 153 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Solving fuzzy linear programming problems with piecewise linear membership functions by the determination of a crisp maximizing decision S. Effati and H. Abbasiyan e-mail:effati911@yahoo.com e-mail:abbasiyan58@yahoo.com Abstract: In this paper, we concentrate on linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers.We consider here only the case of fuzzy numbers with linear membership function. The determination of a crisp maximizing decision [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and non-convex in general. We propose here the ”augmented lagrangian penalty function method” and use it for solving these problems. We also compare the new proposed method with well known ”fuzzy decisive set method”. Finally, we give illustrative example and this solve by the new proposed method and compare the numerical solution with the solution obtained from fuzzy decisive set method. Keywords: Fuzzy linear programming, fuzzy number, augmented lagrangian penalty function method, fuzzy decisive set method. 1 Introduction A model in which the objective function is crisp– constraints. For solving these problems we use and that is, has to be maximized or minimized– and in compare two methods. One of them called the which the constraints are or partially fuzzy is no fuzzy decisive set method, as introduced by longer symmetrical. Fuzzy linear programming Sakawa and Yana [7]. In this methoda combination problem with fuzzy coefficients was formulated by with the bisection method and phase one of the Negoita [3] and called robust programming. simplex method of linear programming is used to Dubois and Prade [4] investigated linear fuzzy obtained a feasible solution. The second method constraints. Tanaka and Asai [5] also proposed a we use, is the ”augmented lagrangian penalty formulation of fuzzy linear programming with method”. In this method a combines the fuzzy constraints and gave a method for its algorithmic aspects of both Lagrangian duality solution which bases on inequality relation methods and penalty function methods. For this between fuzzy numbers. kind of problems we consider, this method is We consider linear programming problems in applied to solve concrete examples. which both technological coefficients and right- The paper is outlined as follows. In section 2, we hand-side numbers are fuzzy numbers. Each study the linear programming problem in which problem is first converted into an equivalent crisp both technological coefficients and right-hand-side problem. This is a problem of finding a point are fuzzy numbers. The general principles of the which satisfies the constraints and the goal with the augmented lagrangian penalty method is presented maximum degree. The crisp problems, obtained by in section 3. In section 4, we examine the such a manner, can be non-linear (even non- application of this method and fuzzy decisive set convex), where the non-linearity arises in method to concrete example. 205 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Convex Subalgebras of Residuated Lattice Shokoofeh Ghorbani and Abbas Hasankhani Department of Mathematics Shahid Bahonar University of Kerman Kerman, Iran sh.ghorbani@graduate.uk.ac.ir abhasan@mail.uk.ac.ir Abstract: In this paper we define the concept of fuzzy congruence relations, fuzzy subalgebras, fuzzy convex subalgebras on a residuated lattice and we obtain some related results. In particular, we show that there is a one to one corresponding between the set of all fuzzy convex subalgebras and the set of all fuzzy congruence relations in the residuated lattice. Keywords: Residuated lattice, Congruence relation, Convex subalgebra, Fuzzy set, Fuzzy relation. 2 Preliminaries 1 Introduction Definition 2.1[2, 9] A residuated lattice is an The concept of residuated lattice was introduced algebra ( L,∧,∨,∗, →,0,1) where and studied by Krull [7], Dilworth [4], Ward and LR1) ( L,∧,∨,0,1) is a bounded lattice, Dilworth [11], Ward [10], Bables and Dwinger [1] LR2) ( L,∗,1) is a commutative monoid, and Pavelka [8]. The origins of residuated theory lie in the study of ideal lattices of rings. Zadeh in LR3) c ≤ a → b if and only if c ∗ a ≤ b for all [12] introduced the notion of fuzzy set μ in a a, b, c ∈ L . nonempty set X , as a function from X into [0,1]. Theorem 2.2 [6, 8, 9] Let ( L,∧,∨,∗, →,0,1) be a In the next section we review the basic residuated lattice. Then we have the following: definitions and some theorems from [2], [3], [5], 1 1 → x = x , x → x = 1, x → 1 = 1 , [9] and [12]. In section 3 we introduce the concept 2 x∗ y ≤ x ∧ y, of fuzzy congruence relations on a residuated 3 x ≤ y if and only if x → y = 1 , lattice and we see that the set of all fuzzy 4 x ∗ ( x → y ) ≤ x, y , congruence relations on a residuated lattice is a complete lattice. In section 4, we define the 5 x → y ≤ x∗z → y∗z , concept of fuzzy subalgebras; fuzzy convex 6 x ≤ y if and only if x ∗ z ≤ y ∗ z , subalgebras and we obtain some related results. 7 x → y ≤ ( z → x) → ( z → y ) , Finally, we show that there is a bijection between 8 x → y ≤ ( y → z) → ( x → z) , the set of all fuzzy convex subalgebras and the set of all fuzzy congruence relations on a residuated 9 x → ( y → z) = x ∗ y → z , lattice. Hence the set of all fuzzy convex 10 x ∗ ( y ∨ z ) = x ∗ y ∨ x ∗ z , subalgebras of residuated lattice is a complete for all x, y, z ∈ L . lattice. 211 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Algebraic Fuzzy Subsets of Non-commutative Join Spaces H. Hedayatia , R. Amerib a Department of Basic Sciences, Babol University of Technology, Babol, Iran b Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran Email: {h.hedayati, ameri}@umz.ac.ir Abstract liminaries of hypergroups and fuzzy sets which will be used in the next sections. In section 3 we study fuzzy The aim of this note is the study of important alge- closed and fuzzy normal subhypergroups. In section 4 braic fuzzy subsets of transposition hypergroups (non- we introduce the notions of fuzzy invertible and fuzzy commutative join spaces). In this regards, we first intro- reflexive subset of a hypergroup, and then we investi- duce the notions of fuzzy closed, fuzzy normal, fuzzy gate the relationships between fuzzy closed, fuzzy nor- reflexive and fuzzy invertible subsets of transposition mal, fuzzy invertible and fuzzy reflexive subsets. hypergroups and, then we investigate their basic prop- erties. Keywords: Fuzzy Hypergroup, Fuzzy Closed set, 2 Preliminaries Fuzzy Normal, Fuzzy Invertible, Fuzzy Reflexive. In this section we gather all definitions and simple prop- erties we require of hypergroups and fuzzy subsets and 1 Introduction set the notions. The notion of hypergroup introduced by F. Marty [24]. Let H be a nonempty set and P∗ (H) the family of all Since then many researchers have studied this field and nonempty subsets of H. developed it, for example see [2, 4, 8, 9, 10, 11, 12, 19, A map . : H × H −→ P∗ (H) is called hyperoperation 26]. Transposition hypergroups are large class of multi or join operation. valued systems. Many well-known hypergroups such as The join operation is extended to subsets of H in nat- hypergroups, weak cogroups, join spaces, polygroups, ural way , so that A.B or AB is given by canonical hypergroups, as well as ordinary groups are all transposition hypergroups [19]. AB = {ab|a ∈ A and b ∈ B }. The notion of a fuzzy subset introduced by L. Zadeh in 1965 [27] as a function from a nonempty set X to unit The relational notation A ≈ B (read A meets B) is used real interval I = [0, 1]. Rosenfeld defined the concept of to asserts that A and B have an element in common, that a fuzzy subgroup of a given group G [25] and then many / is, A ∩ B = 0. The notations aA and Aa are used for researchers has developed it in all subject of algebra. {a}A and A{a} respectively. Generally, the singleton Also fuzzy sets has been a good developed in hyper- {a} is identified by its element a. alebraic structures theory(for example see [1],[3],[4], In H right extension / and left extension are defined [5], [6], [7], [13], [14], [15], [16], [17], [21], [22], by [23],[29]). a/b = { x ∈ H | a ∈ xb}, The second author in [1] introduced some basic re- sults of fuzzy transposition hypergroups. Now in this ba = { x ∈ H | a ∈ bx }. note we follow [1] and introduce some another impor- tant fuzzy subsets of transposition hypergroups, such A hypergroup is a structure (H, .) that satisfies two as fuzzy normal, fuzzy reflexive and fuzzy invertible axioms, subsets and then we obtain some related basic results (Reproductivity) aH = H = Ha for all a ∈ H; of these notions. In section 2 we gather all the pre- (Associativity) a(bc) = (ab)c for all a, b, c ∈ H. 1 217 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran An Ant Based Algorithm Approach to Vehicle Navigation Hojjat Salehi-nezhad and Fereydoun Farrahi-Moghaddam Department of Electrical Engineering, S.B University of Kerman, Kerman, Iran h.salehi@mail.uk.ac.ir ffarrahi @mail.uk.ac.ir Abstract This paper presents an algorithm to search for the best direction between two desired origin and destination intersections in cities using ant algorithms, which is known as Ant-based Vehicle Navigation (AVN) algorithm. As travelers have their own parameters to select a direction, adjustable parameters were considered in this algorithm in order to satisfy the most important passengers’ needs. A practical model of this algorithm has applied on a part of Kerman city and its validity was examined. By using this AVN algorithm the traffic problem could be decreased efficiently without employing geographical positioning system (GPS). Keywords: Ant algorithms; Vehicle navigation; Vehicle traffic; Travel time 1. Introduction ACO algorithm has plenty of applications in release on the route transiting in. By means of this, network problems such as water distribution they do their complex daily activities such as networks [18], computer networks [7] and finding and sorting foods. transportation networks [17]. For example, in The idea of employing the foraging behavior of ants computer network problems, routing of packets as a method of stochastic combinatorial and finding paths from source to destination nodes optimization was initially introduced by Dorigo in has a closed relation with the cost and type of his PhD thesis [1]. This is very important for utilization of that network. ACO with its specific travelers to get the best direction relevant to their type of agents is a perfect tool for optimization of preferences, even though they be familiar or such networks, which results in reducing cost in unfamiliar with a city. We want to use ants for path finding and packet routing [7]. Transportation finding the best path between two specific locations networks are similar to computer networks by according to different local and statistical considering vehicles as network packets and routes parameters important for city travelers supporting as network connections, therefore same solution them. could be used for both types of networks. This paper is organized as follows. The next section In this paper an algorithm is proposed to find the and section 3 reviews the basic principles of the best direction satisfying city travelers using ant ACS algorithm and AVN algorithm respectively. algorithms. Although real ants are blind, they are Sections 4 renders the details of the proposed capable of finding the shortest path from food method and experimental results are presented in source to their nest by exploiting information of a section 5. Finally, the paper in concluded in section liquid substance called pheromone, which they 6. 237 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Novel ranking method of fuzzy numbers M. Barkhordary a T. Allahviranloo b T. Hajjari c a Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran b Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14515, Iran c Department of Mathematics, Firuz Kuh Branch, Islamic Azad University, Firuz Kuh, 132, Iran Mahnaz_barkhordari@yahoo.com, tofigh@allahviranloo.com, tayebehajjari@yahoo.com Abstract: In this paper, a novel method for ranking of fuzzy numbers is proposed. This method is based on the center of mass at some α-cuts of a fuzzy number. Our method can rank more than two fuzzy numbers simultaneously. Also some properties of method are described. At last, we present some numerical examples to illustrate our proposed method, and compare them with other ranking methods. Keywords: Ranking fuzzy numbers; Center of mass. human intuition, indiscrimination, and difficulty of 1 Introduction interpretation. What seems to be clear is that there exists no uniquely best method for comparing For ranking of fuzzy numbers, a fuzzy number fuzzy numbers, and different methods may satisfy needs to be evaluated and compared with the different desirable criteria. In the existing fuzzy others, but this may not be easy. Since fuzzy number ranking methods, many of them are based numbers are represented by possibility on the area measurement with the integral value distributions, they can overlap with each other and about the membership function of fuzzy numbers it is difficult to determine clearly whether one [5, 20, 17, 21, 7, 11, 13, 9, 14, 18, 16, 15]. Yager fuzzy number is larger or smaller than another. [8] proposed centroid index ranking method with Fuzzy set ranking has been studied by many weighting function. Cheng [4] proposed a centroid researchers. Some of these ranking methods have index ranking method that calculates the distance been compared and reviewed by Bortolan and of the centroid point of each fuzzy number and Degain [2]. More recently by Chen and Hwang [3], original point to improve the ranking method [23]. and it still receives much attention in recent years They also proposed a coefficient of variation (CV [5, 10, 17, 18]. Many methods for ranking Fuzzy index) to improve Lee and Lis method [16]. numbers have been proposed, such as representing Recently, Tsu and Tsao [6] pointed out the them with real numbers or using fuzzy relations. inconsistent and counter intuition of these two Wang and Kerre [18, 12] proposed some axioms as indices and proposed ranking fuzzy numbers with reasonable properties to determine the rationality the area between the centriod point and original of a fuzzy ranking method and systematically point. The rest of our work is organized as follows. compared a wide array of existing fuzzy ranking Section 2, contains the basic definitions and methods. Almost each method, however, has notations used in the remaining parts of the paper. pitfalls in some aspect, such as inconsistency with In Section 3, introduces the ranking method and 287 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Trapezoidal Membership Function Block for Fuzzy Applications S. Momeni, A. Khoei*, Kh. Hadidi and Gh. Yosefi+ Department of Microelectronic laboratory of Urmia University, Urmia 57159, Iran * A.khoei@mail.urmia.ac.ir + gyosefi@yahoo.com Abstract: A new Switched Capacitor Membership Function circuit, which is based on an offset insensitive SC amplifier and presenting trapezoidal-shape transcharacteristics is proposed. The circuit is realized in a 0.35-um standard CMOS technology and simulation by Hspice is carried out. Keywords: Fuzzy rule, Membership degree, Memebership Function Block, Trapezoidal MFB. capacitive arrays, etc.), thus simplifying the layout 1 Introduction process. A fundamental cell in fuzzy systems is the Over recent years, due to inherent ability of fuzzy Membership Function Block (MFB) which returns signal processing in expressing complex control the membership degree of a variable with respect laws by using simple systems of rules, application to a given fuzzy set. In this paper, modifying a of fuzzy systems has become very popular [2-3]. triangular-shape Membership Function Block, a Moreover, in some applications, fuzzy control has trapezoidal-shape Membership Function Block in been proved to achieve better performances with SC technique is presented. The proposed MFB is respect to conventional methods. realized in a 0.35um standard CMOS technology A large number of basic building blocks [5-8] or and simulation results are given. fuzzy systems, suitable for a VLSI digital or analog implementation, are contained in literature. 2 The Transcharacteristic equation In particular, digital implementations have the advantage of both simple design procedure and A trapezoidal MFB, shown in fig.1 can be good accuracy but they require a larger silicon area mathematically represented by the following with respect to equivalent analog ones. This area equations: occupation increases if the circuit has to communicate with the real world because A/D and D/A converters are mandatory for both inputs and ⎧ Vmax ⎪0 Vin 〈Vt1 − outputs. On the other hand, analog implementation α (1) ⎪ ⎪α (V − V ) + V Vmax has better performances in terms of silicon area Vt1 − 〈Vin 〈Vt1 ⎪ in t1 max α and speed requirements, but they need a large ⎪ Vout = ⎨Vmax Vt1 〈Vin 〈Vt 2 effort during the design. ⎪ Vmax ⎪−α (Vin − Vt 2 ) + Vmax Vt 2 〈Vin 〈Vt 2 + The Switched Capacitor (SC) technique appears to ⎪ α constitute a good compromise between speed, ⎪ Vmax ⎪0 Vin 〉Vt 2 + accuracy, area and effort of design. In fact, ⎩ α although its speed limitation compared to a continuous-time implementation, it provides the benefits of both small area occupation and good Referring fig. 1 parameters a and Vmax represent accuracy. Moreover, the efforts during the circuit the slope of the transcharacteristic and its realization can be minimized by using macro cells maximum value respectively, while Vt1 and Vt2 of fundamental blocks (opamps, switches, show the interval during which the trapezoid reaches its maximum value. 293 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Ranking Fuzzy Numbers by Sign Length T. Hajjari, M. Barkhordary Department of Mathematics, Firuz Kuh Branch, Islamic Azad University, Firuz Kuh, 132, Iran Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran tayebehajjari@yahoo.com, mahnaz barkhordari@yahoo.com Abstract : Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper,we introduce an approximate method for ranking of fuzzy numbers based on the centroid point of the surface bounded above by the graph of the membership function of fuzzy number below by X-axis. The calculation of proposed method is far simple than the other approaches. Keywords: Ranking, Fuzzy Numbers, Centroid Point. 1 Introduction Ma, Kandel and Friedman [21]. Nowadays many researchers have developed methods to compare In many applications, ranking of fuzzy numbers and to rank fuzzy numbers. Some of those is an important component of the decision methods are counter-intuitive and non process. Many authors have investigated the use discriminating [1, 2, 7, 13, 22, 24]. Thus it of fuzzy sets in ranking alternatives and they causes a natural need of defuzzification of a have studied different methods of raking fuzzy fuzzy numbers which is easy to handle and have sets. Particularly, the ranking of fuzzy numbers. a natural interpretation. In 1976 and 1977, Jain [17, 18] proposed a In [1] is defined a metric between fuzzy method using the concept of maximizing set to numbers. Then it used to rank the fuzzy numbers order the fuzzy numbers. Jain’s method is that and it is called ranking by sign distance. the decider considers only the right side Furthermore, it is compared with some previous membership function. A canonical way to extend methods. Asady and Zendehdel also give a new the natural ordering of real numbers to fuzzy method in [4] which is called ”distance numbers was suggested by Bass and minimization”. Now we turn to introduce our Kwakernaak [8] as early as 1977. Dubios and proposed approach. In this paper the idea of the Prade 1978 [15], who used maximizing sets to ordering of fuzzy quantities are to convert a order fuzzy numbers. In 1979, Baldwin and fuzzy quantity into a real number and base the Guild [5] indicated that these two methods have comparison of fuzzy quantities on that of real some disturbing disadvantages. Also in 1980, numbers. In the other words, our method is Adamo [3] used the concept of -level set in order placed in the first class of Kerre’s categories to introduce _-preference rule. In 1981 Chang [6] [23]. introduced the concept of the preference function The rest of paper is organized as follows. Section P(A) of an alternative A. Yager in 1981 [25, 26] 2 contains the basic definitions and notations use proposed four indices which may be employed in the remaining parts of the paper. In Section 3, for the purpose of ordering fuzzy quantities in [0, we will introduce our idea and investigate some 1]. Bortolan and Degani [7], Chen [9], properties of our method. Some numerical Choobineh [11], Cheng [10] have presented examples are illustrated and are compared with some methods , and also more recently some some previous methods in Section 4. The final numerous ranking techniques have been section is conclusion. purposed and investigated by Chu, Tsao [12] and 297 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Ranking of fuzzy numbers by left and right ranking Functions B. Agheli , M. Adabitabar Firozja Department of mathematics, Islamic Azad University, Qaemshahr, Iran agheli_142@yahoo.com Abstract: In this paper we proposed a new approach for ranking of fuzzy numbers with membershipfunction. Initially the membership function of comparison between crisp and fuzzy numbers is proposed. We extend it to ranking of fuzzy numbers. Finally we compare the proposed definitionwith some of the known ones. Keywords: Fuzzy Numbers; Ranking. 1 Introduction Recently, fuzzy systems are used to study a variety ⎧ a2 − x of problems ranging from fuzzy topological spaces ⎪ L ( a − a ), a1 ≤ x ≤ a 2 to control chaotic systems, fuzzy metric spaces,fuzzy ⎪ 2 1 ⎪1, a2 ≤ x ≤ a3 linear systems and particle physics. The concept of μ A (x) = ⎨ ~ (1) fuzzy numbers and arithmetic operations with this ⎪ R ( x − a 3 ), a3 ≤ x ≤ a 4 ⎪ a4 − a3 numbers were first introduced and inve- stigated by ⎪ Zadeh and others. Fuzzy ranking is a topic which has ⎩0, otherwise been studied by many researchers, too[1,7,4,6,8]. Each method has a shortcoming. Where L and R are strictly decreasing functions But, in this study the membership function of defined on [0, 1] and satisfying ranking between crisp and fuzzy numbers is the conditions: proposed and then it is used for ranking fuzzy L (t ) = R (t ) = 1 if t ≤ 0 (2) numbers. The paper is organized as follows: Background on L (t ) = R (t ) = 0 if t ≥1 fuzzy concepts is presented in section 2. A com- ~ ~ parison between crisp and fuzzy numbers with its A GLRFN A is denoted as A = ( a1 , a 2 , a 3 , a 4 ) LR ~ properties is introduced in section 3. Subsequently, and an α-level interval of fuzzy number A as: in section 4 a ranking between two fuzzy numbers [ A ]α = [ Al (α ), Ar (α )] with its properties for fuzzy numbers is considered. Then in section 5, for comparing of new approach = [ a 2 − ( a 2 − a1 ) L−1 (α ), a 3 + ( a 4 − a 3 ) R −1 (α )] (3) with some of other approaches some numerical examples are brought. Finally, conclusion 3 Comparison between crisp and fuzzy is drawn in Section 6. number ~ Let A = ( a1 , a 2 , a 3 , a 4 ) ∈ GLRFN and x be a crisp 2 Background number then we define the degree of omparison ~ A fuzzy set A = (a1, a2 , a3 , a4 ) is a generalized left right fuzzy number A˜ and crisp number x as follows: fuzzy numbers (GLRFN) of Dubois and Prade [5, 7], if its membership function satisfy the following: 303 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran An Application of Possibility Goal Programming to the Time-Cost Trade off Problem M.Ghazanfari1, K.Shahanaghi2, A.Yousefli3 Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran 1:mehdi@iust.ac.ir 2:shahanaghi@iust.ac.ir 3:ayousefli@ind.iust.ac.ir Abstract: Activity duration is uncertain due to the variations in the real world such as weather, resource availability, etc. Utilization of uncertain planning leads to project scheduling with more stability against environmental variations. This paper presents a new optimal model for time-cost trade-off problem in fuzzy environment. In order to solve this problem, we develop a new possibility goal programming approach. Significant feature of this model is determination of optimal activity duration in form of triangular fuzzy numbers. To validate the algorithm developed here, a case study will be presented. Keywords: time-cost trade off, possibility goal programming, fuzzy sets, fuzzy decision variable. 1 Introduction analytical. Among them are Siemens's model [2] Since the late 1950s, Critical-Path-Method (CPM) and Moselhi's model [3]. Some researchers used techniques have become widely recognized as of operation research's methods to model and valuable tools for the planning and scheduling of solve time-cost trade off problems [4, 5, 6]. Also projects. But in many cases, project should some methods were developed based on implement before the date that was calculated by metaheuristic models such as simulated annealing CPM method. Achieving this goal, can be used and genetic algorithm [7, 8]. The above- more productive equipment or hiring more mentioned time-cost trade off models mainly workers. But it is clear that the project cost focuses on deterministic situations. Recently, increase. Therefore we should find the most cost project managers have paid special attention to effective way to complete a project within a uncertain scheduling. These models are specific completion time. Several mathematical categorized into two parts: probabilistic models and heuristic models have been generated to solve and fuzzy models. Among of probabilistic models time-cost trade off problems [1]. These models is Ang's model [9]. In many projects, required mainly focused on deterministic situations. information for estimation of project parameters is However, during project implementation, many not available or is incomplete. Also in many cases uncertain variables dynamically affect activity the project is under performance for the first time, duration, and the costs could also change this compels us to use expert opinion in accordingly. In this paper, we propose an optimal forecasting the project parameters. Some authors mathematical model to handle the time-cost trade have claimed that fuzzy set theory is more off problems in uncertain environment and a new appropriate to model these problems, for example approach to solve proposed algorithm. leu et al [1], Hapk and Slowinski [10], Leu et al 1.1 Literature review of time-cost trade off [11], Wan [12]. problem 1.2 Literature review of mathematical Based upon whether activity duration is certain or programming with fuzzy variable not, time-cost trade off models can be categorized into two parts: deterministic scheduling and Generally speaking, in fuzzy linear programming nondeterministic scheduling. Traditional time-cost problems, the coefficients of decision variables are trade off models mostly focuses on deterministic fuzzy numbers whereas decision variables are situations. Most of these models are heuristic and crisp ones. This means that in an uncertain 307 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Multi Hybrid Genetic Algorithm for the Quadratic Assignment Problem Farhad Djannaty ; Hossein Almasi Department of Mathematics, University of Kurdistan, Sanandaj, Iran FDjanaty@uok.ac.ir, halmasi@uok.ac.ir Abstract: Quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems which can model many real life problems. Because of its theoretical and practical importance, QAP has attracted attention of many researchers. In this paper, a multi hybrid genetic algorithm for solving QAP is proposed. The key feature of our approach is the hybridization of three metaheuristics, tabu search, simulated annealing and ant system with genetic algorithm. These metaheuristics are used to create a good initial population and later to improve individuals in future generations. Our proposed approach is applied to a number of standard test problems and our computational results are compared with those of three metaheuristics when applied on the same problems alone. It is understood that our approach is one of best algorithms which deals with QAP. Keywords: Quadratic Assignment Problem, Genetic Algorithm, Tabu Search, Simulated Annealing, Ant System. amount of time. Therefore, the only possible way 1 Introduction to deal with large instances of QAP is by taking advantage of heuristics. These heuristic algorithms The quadratic assignment problem is a famous can obtain a good solution quickly. The most combinatorial optimization. Koopmans and important heuristic approaches used for solving Beckmann initially stated this problem in 1957 QAP are: simulated annealing [3], genetic [20]. The QAP is formulated as follows. Let two algorithm [31], ant colony optimization [13, 29], matrices F [ fij ]n n , D [ d kl ]n n and the set of the tabu search [30], greedy randomized adaptive search (GRASP) [22] and scatter search [4]. integers from 1 to n be given. Find a permutation 1 , 2 ,..., n that minimizes n n 2 Metaheuristics z f ij d i j . i 1 j 1 In this section, we briefly describe metaheuristics Some of the applications of QAP are described that have been used in our proposed approach. below: campus and hospital planning [5, 10], First, we describe the main ideas of the simulated backboard wiring [28], scheduling [14], design of annealing of Connolly [3] and then the “robust control panels and typewriter keyboards [26], tabu search” of Taillard [30] is considered. Next, ranking of archeological data [21], statistical we explain Fast Ant System (FANT) of Taillard analysis [18], analysis of reaction chemistry [12], [29]. The source codes for these methods are numerical analysis [1], placement of electronic available on the Internet at components [23] and memory layout optimization http://ina.eivd.ch/collaborateurs/etd/default.html. in signal processors [32 ]. Finally, a summary of the hybrid genetic algorithm Sahni and Gonzalez showed that the QAP is is discussed. NP-hard and that there is no f-approximation polynomial algorithm for the QAP unless P = NP 2.1 Simulated annealing [27]. In general, exact algorithms cannot solve problem instances of size n 30 in a reasonable 313 1386 7-9
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Implementation of Evolutionary Algorithm and Fuzzy Sets for Reliability Optimization of Engineering Systems M. MOHAMMADI 1,.H. FARAHMAND 2, M. RASHIDINEJAD 2 ,E.ESLAMI3 1 Mathematical Department, Islamic Azad University of Najaf abad 2 Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman 3 Mathematical Department, Shahid Bahonar University of Kerman, Kerman mmohammadi@mail.yu.ac.ir Abstract: This article uses an evolutionary algorithm to solve the series parallel redundancy optimization problem which is in a fuzzy framework. Reliability optimization provides a means to help the reliability engineer achieve such a goal. Most methods of reliability optimization assume that systems have redundancy components in series and / or parallel systems and that alternative designs are available. Optimization concentrates on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirements. A fuzzy simulation- based evolutionary algorithm is then employed to solve these kinds of fuzzy programming with fuzzy Goal and fuzzy constraints. Finally, numerical examples are also given. Keywords: evolutionary algorithm, reliability analysis, reliability optimization, genetic algorithm, Fuzzy simulation 1 Introduction As systems have grown more complex , the Reliability optimization provides a means to help consequences of their unreliable behaviour have the reliability engineer achieve such a goal. Most become severe in terms of cost , effort , lives , and methods of reliability optimization assume that so on , and the interest in assessing system systems have redundancy components in series reliability and the need for improving the and/ or parallel systems and that alternative reliability of products and systems have become designs are available. Optimization concentrates on very important . The reliability of a system can be optimal allocation of redundancy components and defined as the probability that the system has optimal selection of alternative designs to meet operated successfully over a specified interval of system requirements. In the past two decades, time under stated conditions. In the past few numerous reliability optimization techniques have decades, the field of reliability has grown been proposed. Generally, these techniques can be sufficiently large to include separate specialized classified as linear programming, dynamic subtopics, such as reliability analysis, failure programming, integer programming, and geometric modelling, reliability optimization, reliability programming, Heuristic method, Lagrange growth and its modelling, reliability testing, multiplier, and so on. [2]. reliability data analysis, accelerated testing , and life cycle cost [1]. 321 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran One-sided Process Capability Indices and Fuzzy lower Confidence Bounds for them M.T. Moeti Member of Young Researchers Club, Islamic Azad University, Arak branch, Iran mt_moeti@yahoo.com M. Mashinchi Faculty of Mathmatics and Computer Sciences, Shahid Bahonar University, Kerman, Iran mashinchi@mail.uk.ac.ir A. Parchami Faculty of Mathmatics and Computer Sciences, Shahid Bahonar University, Kerman, Iran parchami@graduate.uk.ac.ir Abstract: Process capability indices are used to measure the capability of a process to reproduce items within the specified tolerance preset by the product designers or customers. After introducing fuzzy one- ~ ~ sided process capability indices C PU and C PL , we obtain fuzzy lower confidence bounds for the introduced indices, where instead of precise quality we have one triangular membership function for one- sided specification limit. Key words: Lower confidence bound; Fuzzy process capability indices; Ranking function. 1 Introduction numbers and they are expressed in fuzzy terms, the classical capability indices could Process Capability Indices (PCIs) C p , C pk not be applied. For such cases Yongting [32] and C pm are appropriate for processes with introduced a process capability index C ~ as p two-sided specification limits (SLs). Some a real number and it was used by procedures have been developed based on Sadeghpour-Gildeh [27]. Lee investigated a these indices [3, 8, 21 and 22] for the process capability index, C pk , as a fuzzy set practitioners to use in making decision on [11]. Parchami et al. introduced fuzzy PCIs whether their processes meet the preset as fuzzy numbers and discussed relations capability requirements. Also, the indices C PU that governing between them when SLs are and C PL are designed specifically for fuzzy rather than crisp [15, 18]. Also they processes with one-sided SLs. obtained fuzzy confidence intervals for these After the inception of the notion of fuzzy new PCIs and they presented an approach to sets by Zadeh [33], there are efforts by many testing fuzzy PCI [19, 20]. Similarly fuzzy authors to apply this notion in statistics. For capability indices extended by Moeti et al. these trends one can see [28, 29, 30]. In quality where the SLs are L-R fuzzy intervals [16]. control topic, where SLs are non-precise 327 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Confidence regions for the Taguchi Index in Fuzzy Process Z. Ramezani, A. Parchami, M. Mashinchi Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran ramezani_zeinab@yahoo.com, parchami@graduate.uk.ac.ir, mashinchi@mail.uk.ac.ir ~ Abstract: In this paper we present several fuzzy confidence intervals for fuzzy process capability index C pm in a fuzzy process based on Roubens ranking function, where we have two membership functions for specification limits. Keyword: Triangular fuzzy numbers, Confidence Interval, Process capability indices, fuzzy statistics, Ranking function. ~ estimators for C pm and then we obtain various 1. Introduction ~ approximate confidence intervals for C pm . In the past few years, three major univariate capability indices have been developed and discussed in the literature. They are C p , C pk and 2. Preliminary The above introduced traditional PCIs can be C pm In most cases, the normal distribution and a classified into two kinds. The first kind deals large sample size are assumed for population of solely with the process variation in relation to a data. Discussion of these process capability specified tolerance region. The second kind indices can be found in [2, 3, 7, 9, 10, 11, 16, 22, considers not only the process variation relative to 26]. the tolerance region but also the deviation of A common method is to use the process capability process mean from target value. The index C p is indices (PCIs) to compare the actual performance an example of the first kind and C pk and C pm of a process to its prior engineering-specified performance. Many papers on PCIs (see, e.g., are of the second kind. references listed in [9]) and some books [11] have In [3] it is pointed out that the exact sampling been published. properties of the estimates of C pk were more After the inception of the notion of fuzzy sets by complex than the ones for C pm . Zadeh [31], there are efforts by many authors to A process capability index C pm is defined as, apply this notion in statistics[27]. When, some information of a process are not Usl − Lsl Usl − Lsl Usl − Lsl C pm = = = precise and they are expressed in fuzzy terms, the 2 6σ T 6 E( X − T ) 6 σ 2 + (μ − T ) 2 traditional capability indices could not be applied. ~ That was introduced in [3] and [14], where Lsl For one case a process capability index C p as a and Usl are lower and upper specification limits, real number was introduced in [30] and it was respectively, and the target value is ~ used in [24]. A process capability index, C pk , as a T = Usl + Lsl 2 . Through this paper we suppose fuzzy set was introduced in [12]. When that the process of the characteristics follows the specification limits (SLs), are triangular numbers, normal distribution with mean μ and variance σ 2 . Parchami et al. proposed fuzzy process capability Let ℜ be the set of real number. Let indices as fuzzy numbers and discussed relations FT (ℜ) = {Ta,b,c | a, b, c ∈ ℜ, a ≤ b ≤ c}, where that governing between them when specification limits are fuzzy rather than crisp [18-20]. ⎧( x − a) /(b − a) if a ≤ x < b, ~ ⎪ In this paper we discuss on C pm when SLs are T a ,b , c = ⎨ (c − x) /(c − b) if b ≤ x < c, (1) ⎪ 0 o.w. triangular fuzzy number. At first we introduce two ⎩ 335 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Method of Generating a Random Sample From a Fuzzy Distribution Function A. Khorsand 1 , R. Amirzadeh, A. Bozorgnia 2 1 A Member of Young Researchers Club, Islamic Azad University Mashhad Branch, Mashhad, Iran, attieh_khorsand@yahoo.com 2 Islamic Azad University Mashhad Branch, Mashhad, Iran, amirzadeh_r@yahoo.com, bozorg@math.um.ac.ir Abstract: In practical applications, it is very important to generate a random sample or equivalently a sequence of random fuzzy numbers from a fuzzy distribution function. In this paper, we propose fuzzy probability integral trans- formation theorem for fuzzy random variables. As a result of this theorem, we provide a method to generate a sequence of random fuzzy numbers from a fuzzy distribution function. To do this, we use the random fuzzy numbers on [0, 1]. Our attention is on the case where the left and right sides of the membership functions of random fuzzy numbers are quadratic functions. For illustrating the method we give a numerical example. Keywords: Extension Principle, Fuzzy random variable, probability integral transformation theorem, Random fuzzy number, Triangular shaped fuzzy number. Ralescu [14]. Wu [16] considered the 1 Introduction construction of the fuzzy distribution function of fuzzy random variables using a family of closed The topic for statistical inference under fuzzy intervals. In this paper, we propose fuzzy environment was studied by many researchers. probability integral transformation theorem for Gebhardt et al. [4], and Taheri [15] gave a good fuzzy random variables. Then we provide a review in this topic. Some authors paid attention method of generating a random sample from an to generate a random fuzzy number. A method arbitrary fuzzy distribution function. Our random for generating a random LR fuzzy number was fuzzy numbers will have random base. We proposed in ([1], [6], [7], [9], [12], [13]). Next, believe this method gives a better picture of Ferson and Ginzburg [3] provided another way to random fuzzy numbers. construct a random triangular fuzzy number. Liu The organization of this paper is as follows. In and Chen [11] generated a random triangular section 2, we give a brief review of fuzzy random fuzzy number and a random trapezoidal fuzzy variables. In section 3, we propose fuzzy number. Buckley in [2], proposed another probability integral transformation theorem and method to produce a random triangular shaped its inverse for fuzzy random variables. We fuzzy number, where the left and right sides of provide a method of generating a random sample the membership functions of fuzzy numbers are from an arbitrary fuzzy distribution function, in quadratic functions. All of these methods are section 4. The final section is the conclusion part. based on crisp random variables. Our motivation An illustrative example is given to clarify the is based on fuzzy random variables. method. The concept of fuzzy random variables was introduced by Kwakernaak [10] and Puri and 363 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy linear regression analysis with trapezoidal coefficients 1,∗ 2 3 3 T. Razzaghnia , E. Pasha , E. Khorram , A. Razzaghnia 1 Department of Statistics, Islamic Azad University, Roudehen Branch, Tehran, Iran. 2 Department of Mathematics, Teacher Training University, Tehran, Iran. 3 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran. ∗ E-mail: t_razaghnia@yahoo.com. Abstract : In this paper, we aim to extended the constraints of Tanaka’s model. Applied coefficients of the fuzzy regression by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidal one. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models is presented and a numerical example is given in order to compare the proposed models with previous one. Error values shows advantage of the presented models with respect to constraints of Tanaka’s model. Keywords: Fuzzy numbers, Fuzzy linear regression, Possibility distribution, Mathematical programming. 1. Introduction Fuzzy linear regression was proposed by Tanaka et supposed to be due to fuzziness of system structure. al. [17] in 1982. Many different fuzzy regression This structure was represented as a fuzzy linear approaches have been proposed by different function whose parameters were given by fuzzy sets. researchers since then, and also this subject has They resorted to linear programming to develop their drawn much attention from more and more people regression model. concerned. In general, there are two approaches in In [17], the coefficients of the fuzzy regression are fuzzy regression analysis: linear programming- symmetric triangular fuzzy numbers. In this paper, we based method [6,11,16,17] and fuzzy least squares explain limitations of these methods and we extended method [1,2,3,4,7,10,12,13,14].The first method is the symmetric triangular fuzzy coefficients to based on minimizing fuzziness as an optimal asymmetric trapezoidal fuzzy numbers. Also we use criterion. The second method used least-square of possibility distribution for asymmetric trapezoidal errors as a fitting criterion. The advantage of first fuzzy numbers and we prove a theorem about approach is its simplicity in programming and possibility of two asymmetric trapezoidal fuzzy computation, while that the degree of fuzziness numbers. between the observed and predicted values is The paper is organized as follows. In section 2, some minimized by using fuzzy least squares method. elementary properties of fuzzy numbers and fuzzy Tanaka et al.[17] regarded fuzzy data as a linear regression are described. The propose method possibility distribution, the deviations between the is presented in section 3. A numerical example is observed values and the estimated values were illustrated to compare the proposed method with previous ones, in section 4. 371 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Probability on balanced lattices M. Saeb and M. Mashinchi Faculty of Mathematics and Computer Sciences Shahid Bahonar University of Kerman , Kerman , Iran mahdie.saeb@gmail.com , mashinchi@mail.uk.ac.ir Abstract: The aim of this paper is to define the One can observe an asymmetry of the set of probability on some newly defined balanced lattices. values of characteristic function and Then we will find the formula of the defined membership functions: if the state of (certain) probability on these balanced lattice. inclusion of an element is denoted by 1, the state of (certain) exclusion might be denoted by -1, rather than 0. This observation would be Keywords: fuzzy set, balanced set, balanced worthless since most of studies of fuzzy set lattice, probability on a lattice. operators and all operators defined on crisp sets have been valued in the unit interval [0,1]. 1 Introduction Moreover, both scales: unipolar, with the unit interval [0,1], and biopolar, with the symmetric The paper presents two newly defined balanced interval [-1,1] , are indistinguishable in the lattices L b and L b . It investigates the meaning of the linear mapping i ( x ) = 2x − 1 . See * probability on these lattices. The definitions of [1]. balance lattices L , L * and the probability on 2.2 The lattices L * and L them are reminded in section 2. At last section, L b and L b will be introduced and the * Definition 2.2.1 [4] The lattice L is the set probability on them is discussed. The exact formula of the probabilities on these lattices are L = {( x , y ) ( x , y ) ∈ [0,1]2 , } found. with the order ( x 1 , y 1 ) ≤L ( x 2 , y 2 ) ⇔ x1 ≤ x 2 & y1 ≥ y 2. 2 Preliminaries We denote its units by 0L = ( 0,1) and 1L = (1, 0 ) . See Figure 1. In this section we review some notions that we need through this paper. 2.1 Balanced sets A classical fuzzy set A in a universe X can be defined in terms of its membership function µA : X → [ 0,1] . Membership functions, by analogy to characteristic functions, define fuzzy connectives: union, intersection and complement. The definitions are expressed, Theorem 2.2.2 [4] (L , ≤L ) is a complete as in the case of the crisp sets, by max, min lattice. and complement to 1. 377 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Dp;q DISTANCE AND THE STRONG LAW OF LARGE NUMBER FOR NEGATIVELY DEPENDENT FUZZY RANDOM VARIABLES B. Sadeghpour Gildeh and R. Zaman Department of Statistics, University of Mazandaran, Babolsar, Iran sadeghpour@umz.ac.ir Abstract:In this paper, we extend strong laws variables, have been studied by several people. of large numbers (SLLN) of real random vari- Y. Feng [3] provided a good review about SLLN ables to negatively dependent fuzzy random of fuzzy random variables. variables. The main purpose of this paper is extending SLLN theorems of negatively dependent real- Key words: Fuzzy numbers; Fuzzy set- valued random variables to negatively depend- valued random variables; Negatively depend- ent fuzzy random variables. In section 2, we ent; Pairwise negatively dependence; The recall some basic concepts of fuzzy numbers. In strong law of large numbers. section 3, the de…nition negatively dependent fuzzy random variables have been presented, 1 Introduction and …nally, in section 4 we prove some theor- ems on the convergence of a sequence on negat- The concept of dependence permeates our ively dependent fuzzy random variables based Earth and its inhabitants in a most profound on Dp;q -distance. manner. The last thirty years of the 20th century have witnessed a rapid resurgence in investigations of dependence properties from 2 Preliminary statistical and probabilistic points of view Joe [5]. Limit theorems on real-valued dependent In this section we …rst recall some notions of random variables have been extended in the lit- fuzzy sets, fuzzy numbers and some operations erature Lehman and E.L. [7]. With the devel- on fuzzy numbers. And then we present Dp;q - opment of the theory and application of fuzzy distance de…ned on the space of fuzzy numbers set, the study of fuzzy set-valued random vari- [10]. ables was initiated by several authors, in par- De…nition 2.1 ([10]) Let E be a universal ticular Puri and Ralescu [9] introduced the no- e set, then a fuzzy set A of E is de…ned by its tion of fuzzy random variables. The limit the- e membership function A : E ! [0; 1]. For all orems on independent fuzzy random variables, e x 2 E , A(x) is the membership grade of x to for example the strong law of large numbers e A. (SLLN) for sums of independent fuzzy random De…nition 2.2 ([10]) A is called the 1 383 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Reducible Fuzzy Markov Chain and Fuzzy Absorption Probability B. Sadeghpour Gildeh and A.Dadgar Department of Statistics, University of Mazandaran, Babolsar, Iran sadeghpour@umz.ac.ir Abstract: In this paper Markov chains with both the state and action are fuzzy, the transi- fuzzy states are considered.The main objective tion of states is de…ned using a fuzzy relation. is to study reducibility of a Markov chain with In [2] a Markovian decision process with fuzzy fuzzy states.It is shown that if the Markov chain state is considerd. associated with the process of non-fuzzy states In this paper we consider absorbing and is reducible the corresponding Markov chain as- transient fuzzy class in fuzzy Markov chains. sociated with the process of fuzzy states is not Fuzzy states occur essentially in two kinds of necesserily reducible. After presenting defe- situations. First where the states of the sys- nition of absorbing fuzzy state and transient tem cannot be percisely measured and thus the fuzzy state we show how absorbing fuzzy states states used to model the system are intrinsi- are constructed.Then we prove a relation about cally fuzzy. While in the second kind of situ- probability of absorpaition from transient state ations, the actual states can be exactly mea- to an absorbing class, and illustrait it with ex- sured and are observable, but the number of amples. states is so large that the decisions are not as- Keywords: Markov chain, fuzzy state , sociated with the exact states of the system. reducible, absorption probability, absorbing In these situations, the decisions are associated state, transient state. with fuzzy states which can be de…ned as fuzzy sets on the original non-fuzzy state space of the 1. Introduction system. In a seminal paper Bellman and Zadeh [1] 2. Preliminary …rst studied a fuzzy decision process.The au- In this section we recall some de¢ nitions thors consider stochastic systems in afuzzy en- of fuzzy Markov chain and the probability of vironment.The fuzzy Markov chains have a po- fuzzy event. tential application in fuzzy Markov algorithms De…niton 2.1. [2] A …nite Markov chain fXn g proposed by Zadeh in [8]. There have been a few other papers published on fuzzy Markov is a Markov stochastic process whose state chains . In [5] the elements in trasition matrix space is a …nite set S = fs1;:::; sM g. The are fuzzy proabilities. The paper [7] is about a proability of Xn+1 = sj when Xn = si is Markov fuzzy process with a transition possi- denoted by pij = Pr(Xn+1 = sj jXn = si ). bility measure in an abstract state space. In [3] P = (pij )M M is called the transition matrix 1 389 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Traffic Rate Controller (FTRC) for Mobile Ad hoc Network Routers Masood Niazi Torshiz Islamic Azad University-Mashhad branch Khavaran Higher Education of Institute, Mashhad, Iran E-mail:niazitrshz@mshdiau.ac.ir Abstract: Characteristics of mobile ad hoc networks such as lack of central coordination, mobility of hosts, dynami- cally varying network topology, and limited availability of resources make QoS provisioning very challenging in such networks. The FTRC consists of two sections. The first section, which is Fuzzy AIMD, uses additive increase multiplica- tive decrease (AIMD) rate control algorithm as base. In AIMD, the node increments its transmission rate with increment rate of c Kbps and decreases its transmission rate by r percent. Fuzzy AIMD accepts the packet delay and the "delay- threshold d" as inputs and calculates the c and r by using a set of fuzzy rules. The second section is Fuzzy Regulation, which selects a set of flows that have a major part in causing congestion, and notifies the corresponding sources to re- duce their sending rates. The selection of flows is done according to the parameters "flow priority" and "the difference between actual rate and agreed rate". Keywords: QoS, Mobile Ad hoc Network, Fuzzy Control, Traffic Management 1. Introduction sion rate with increment rate of c Kbps and de- Mobile ad hoc networks are autonomous dis- creases its transmission rate by r percent. FTRC tributed systems that comprise a number of mo- accepts the packet delay and the differentiated bile nodes connected by wireless links forming delay as inputs and calculates the parameters c arbitrary time-varying wireless network topolo- and r by using a set of fuzzy rules. gies [1-3]. Mobile nodes function as hosts and Fuzzy Regulation module selects a set of flows routers. As hosts, they represent source and des- that have a major part in causing congestion, and tination nodes in the network, while as routers, notifies the corresponding sources to reduce they represent intermediate nodes between a their sending rates. The selection of flows is source and destination, providing store-and- done according to the parameters "flow priority" forward services to neighboring nodes. Nodes and "the difference between actual rate and that constitute the wireless network infrastruc- agreed rate". Fuzzy regulation module computes ture are free to move randomly and organize the probability of selecting a flow to be a mem- themselves in arbitrary fashions. Therefore the ber of this set. wireless topology that interconnects mobile The rest of this paper is organized as follows. In hosts/routers can change rapidly in unpredict- section 2 we describe the proposed fuzzy AIMD able ways or remain relatively static over long in detail. The proposed Fuzzy regulation algo- periods of time [4-6]. In addition to being rithm is explained in Section 3. In Section 4, we bandwidth constrained, mobile ad hoc networks evaluate the performance of the Fuzzy AIMD are power constrained because network nodes and Fuzzy Regulation mechanisms via computer rely on battery power for energy. Providing suit- simulation. Section 5 concludes the paper. able quality of service (QoS) support for the de- 2. Fuzzy AIMD livery of real-time audio, video and data in mo- The AIMD rate control algorithm determines the bile ad hoc networks presents a number of sig- departure rate of the traffic shaper according to nificant technical challenges [7-11]. the packet delay feedback. The typical AIMD The FTRC uses AIMD rate control algorithm as rate control algorithm works as follows. Every T base, in which, each node increases its transmis- seconds, each node increases its transmission 397 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Fuzzy Routing Algorithm for Low Earth Satellite Networks Boshra Rajaee, Mohammad Hossein Yaghmaee Ferdowsi Univercity of Mashhad Mashhad, Iran boshra.rajaee@gmail.com ,hyaghmae@ferdowsi.um.ac.ir Abstract : Low Earth Orbit (LEO) satellite networks have dynamic, yet deterministic topologies. Because of dynamic characteristics would result in the re-routing all connections that are passing through a turned off link. But on the other hand, because of deterministic characteristics, we have some useful information about future of network. In this paper we attempt to develop an algorithm to reduce the number of re-routings by assigning routes that are more permanent. This is done by using a fuzzy system that before routing assigns weights to all links based on their handover time and residual bandwidth. Performance of algorithm is investigated using simulation experiments. Keywords: Satellite networks, LEO, routing, fuzzy, handover. Another unique feature of LEO satellites is due to the fact that they are not in geo-synchronous orbit, 1. Introduction and hence will not appear stationary to a stationary observer on earth. In addition to Up Down Links Low earth orbit (LEO) satellite systems can (UDL), the Inter-Satellite Link (ISL) also changed provide users with low-cost and truly global wireless based on the distance and viewing angel between services, regardless of user locations [1]. Hence, them. there has been a lot of recent interest in developing Changes of UDL and ISL connectivity’s result in efficient schemes for channel allocation and handoff a dynamic network topology with challenging in such systems. LEO satellite systems have certain routing problems. Any connection that is through a unique features not found in other satellite and connection that will be turned off may be re-routing. ground-based wireless communication systems. We If the number of connections that need to be re- list some of them here. routed due to link handover is large, this will cause While geo-synchronous satellites orbit earth at an signaling overhead in network. Moreover, handover altitude of about 36,000 km, LEO satellites orbit calls may be blocking during the re-routing process, earth in the 500–2000 km altitude range. Besides that is not desirable. reducing the propagation delay suffered by signals, A protocol for routing in LEO satellite networks the lower orbital altitude also means a lower power has been developed in [2], that is called Probabilistic requirement at the hand-held terminals, thus Routing Protocol (PRP). During the routing phase of improving the portability of the terminal. a newly arriving call, the PRP eliminates the links A large number of satellites will be required to that will be turned off before the call releases the ensure that there is always at least one satellite in link due to call termination or connection handover. view for every location on earth. For example, the Since the algorithm has no knowledge of the call IRIDIUM system (the target system in our research) duration or exact terminal location, route usage time uses a 66-satellite network to provide global is only known probabilistically. The probability coverage. A typical LEO satellite system will consist distribution function of the route usage time of the of a number of low-earth orbits with a fixed number call is determined to realize algorithm. Our purpose of satellites traversing each orbit. in this research is to delete the need for call statistics 403 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A metaheuristic Algorithm for New Models of Fuzzy Bus Terminal Location Problem with a Certain Ranking Function S. Babaie-Kafaki, R. Ghanbari and N. Mahdavi-Amiri Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran kafaki@math.sharif.edu, rghanbari@math.sharif.edu, nezamm@sina.sharif.edu Abstract: Bus network design is an important problem in public transportation. In real word, some parameters of this problem are uncertain. We introduce two new models for bus terminal location with fuzzy parameters. In the first formulation, the number of possible passengers corresponding to each node is a fuzzy number. In the second formulation, an additional assumption of fuzzy neighbourhood is considered. These problems being NP-hard, we use the genetic algorithm with a newly designed crossover operator for solving them. Results of computational experiments demonstrating the efficiency of the proposed algorithm are reported. Keywords: Fuzzy bus network, location problem, ranking function, genetic algorithm. 6, 7, 16, 18, 19]). This paper is organised as 1 Introduction follows. In Section 2, we give two new formulations for the fuzzy bus terminal location Bus network design is an important problem in problem (FBTLP) as fuzzy integer programming public transportation. The main step of the design problems [12]. Then, after stating some properties is determining the number of required terminals of fuzzy numbers in Section 3, we explain and their locations. This is a special type of facility adoption of the genetic algorithm (GA) for both location problem, an NP-hard combinatorial formulations in Section 4. Finally, in Section 5, we optimization problem [14]. test an implementation of our proposed algorithm Consider a set F of potential facilities, each with on some test problems, and demonstrate the a setup cost c ( F ) , and let U be a set of users (or efficiency of the algorithm by the numerical results obtained. In Section 6, we conclude and give costumers) who must be served by these facilities. suggestions for further research. The cost of serving user u with facility f is given by the distance d (u , f ) between them (often 2 Two Formulations of the FBTLP referred to as service cost or connection cost as well). The facility location problem consists of For stating the crisp formulation of the FBTLP [1], determining a set S ⊆ F of facilities to be located we consider a set of nodes (by their coordinates) in a city. We suppose that the number of enter and so as to minimize the total cost (including setup exit of passengers in every node (that is called the and service) of covering all the customers: potential of the node) is available. Also, we ∑ f ∈S ∑ cos t ( S ) = c ( f ) + min d (u , f ) . (1.1) u ∈U f ∈S suppose that if a node is accepted as a bus terminal, it can service the other nodes that are Note that we assume each user is allocated to the located in its neighbourhood. So, we want to select closest open facility. an optimal subset with k members from the set of For location problems, it is usually assumed that candidate nodes for dedicating bus terminals. exact data are known. However, in real Below, we list the parameters of FBTLP. applications, location problems can be J : The set of nodes to receive service. appropriately modelled using fuzzy parameters (some fuzzy location problems can be seen in [4, 5, I : The set of candidate nodes for bus terminals. 471 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Finding the Inversion of a Square Matrix and Pseudo-inverse of a Non-square Matrix by Hebbian Learning Rule Zeinab Ghassabi, Ali Khaki-Sedigh Tehran Azad University, Science and Research Branch, KNTU rose_z60gh@yahoo.com, sedigh@kntu.ac.ir Abstract: In this paper, we discuss a neural network based on hebbian learning rule for finding the inverse of a matrix. First we described finding the inverse of a matrix by mentioned neural network. Finally, experimental results for square and non-square matrices are presented to show the effectiveness of the approach. Proposed method is also scalable for finding the inversion of large-scale matrices. Keywords: Hebbian Learning rule, neural networks, solving simultaneous linear equations Neural Network (RNN) and neural networks with 1 Introduction perceptron learning rule were studied to find matrix inversion. RNN (i.e. continuous approach) Finding the inversion of a matrix is considered to recovers its inputs to find matrix inversion while in be one of the basic problems widely encountered in the neural networks with perceptron learning rule science and engineering since it is frequently used (i.e. discontinuous approach), the matrix weight is in many applications (e.g. robotics, signal updated until all the outputs of neurons are same as processing, Wiener and Kalman filtering). In many desire ones. applications an on-line (e.g. real time) inversion of In this paper, a one-layer neural network that a matrix is desired. updates its weights by hebbian learning rule was In monitoring and control of dynamic systems, applied for inverting of square and nonsquare there is often a need for finding a real-time matrices. matrix inversion of a large-scale matrix. If Hebbian learning rule is one of the first unsupervising learning rules of neural networks such a large-scale problem needs to be solved and it is the base of all rules used for associative in real time, existing numerical methods and neural networks. This rule first proposed by sequential techniques may not scale well. Donald Heb in 1949 [5]. There are a variety of methods for matrix The rest of the paper is organized as follows: inversion, usually classified as direct and iterative. Section 2 presents problem formulation, while the Direct methods are distinguished by the Fact that neural network model and hebbian learning rule they find the correct solution in a finite number of for inverting of matrices is presented in section 3 operations. Iterative methods are characterized by with experimental results discussed in section 4. an initial estimate of the solution, and subsequent update of the estimate based on the previous estimate and some error measure. Iterative 2 Problem Formulation to Find matrix algorithms are sometimes preferred, especially in Inversion problems of medium/large size [7]. Finding the inversion of a matrix with constant and 2.1 A is a square Matrix time varying coefficients has been studied in the field of neural networks [1, 2, 3] with varying results in a highly parallel fashion. Recurrent 491 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Solving Fuzzy Integral equations by Differential Transformation Method Y. Nejatbakhsh T. Allahviranloo N. A. Kiani Islamic Azad University Islamic Azad University Islamic Azad University Firouzkooh Branch Science and Research Branch Science and Research Branch Department of Applied Mathematics Department of Applied Mathematics Department of Applied Mathematics Tehran; Iran Tehran; Iran Tehran; Iran y_nej@yahoo.com tofigh@allahviranloo.com narsiskiani@yahoo.com Abstract: In this paper, we are going to solve Fuzzy integral equations (FI)s by differential transformation method(DTM). Intrinsically, DTM evaluates the approximating solution by the finite Taylor series. The differential transformation method does not evaluate the derivative symbolically; instead, it calculates the relative derivatives by an iteration procedure described by the transformed equations obtained from the original equations using differential transformation. The proposed method provides the Taylors series expansion solution for the domain between any adjacent grid points. Some numerical examples are given to illustrated the proposed extension of DTM to solve fuzzy Fredholm integral equations. Key–Words: Differential transformation, one dimensional Volterra integral equations, Numerical treatments Fuzzy integral Equations, Fuzzy number. 1 Introduction their associated numerical algorithms, it is Fuzzy set theory is a powerful tool for modeling necessary to present an appropriate brief uncertainty and for processing vague or introduction to preliminary topics such as fuzzy subjective information in mathematical models. numbers and fuzzy calculus. The concept of Their main direction of development have been fuzzy sets which was originally introduced by diverse and its application to the very varied real Zadeh [11] led to the definition of the fuzzy problems, for instance in the golden mean [5], number and its implementation in fuzzy control Practical systems [8], quantum optics and [4] and approximate reasoning problems [12, gravity [9], synchronize hyperchaotic system 13]. The basic arithmetic structure for fuzzy [10], medicine [1], engineering problems. The numbers was later developed by Mizumoto and topics of fuzzy differential equations (FDE) and Tanaka [14, 15], Nahmias [16], Dubois and fuzzy integral equations (FIE) which attracted Prade [17, 18], and Ralescu [19], all of which growing interest for some time, in particular in observed the fuzzy number as a collection of relation to fuzzy control, have been rapidly alevels, 0 ≤ ct ≤ 1 [20]. Additional related developed in recent years. The first step which material can be found in [21, 22, 23, 24, 25, 27, included applicable definitions of the fuzzy 28, 29, 30, 31, 32]. derivative and the fuzzy integral was followed The fuzzy mapping function was introduced by by introducing FDE and FIE and establishing Chang and Zadeh [5]. Later, Dubois and sufficient conditions for the existence of unique Prade[6] presented an elementary fuzzy calculus solutions to these equations. Finally, numerical based on the extension principle [11]. Puri and algorithms for calculating approximates to these Ralescu [33] suggested two definitions for fuzzy solutions were designed. Prior to discussing derivative of fuzzy functions. The first method fuzzy differential and integral equations and was based on the H-difference notation and was 497 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran FUZZY TOPOLOGICAL SPACES ALIREZA KAMEL MIRMOSTAFAEE1 Abstract. In this paper, we discuss about various definitions of fuzzy topological spaces. Some obstacles which appear in theory of fuzzy topological spaces will be dis- cussed. 1. introduction The concept of a fuzzy set, which was introduced by Zadeh in [4] motivated some authors to generalizing many concepts of general topology to fuzzy topological space. In this paper, we investigate some of these results to find more appropriate definition of a fuzzy topology on a space, which gives generalization of basic concepts of topology such as open sets, neighborhoods, continuity and compactness. 2. Fuzzy topology We begin with several preliminary definitions. Let X be a set, by a fuzzy set in X we mean a function µ : X → [0, 1]. In fact, µ(x) represents the degree of membership of x in the fuzzy set X. For example, every characteristic function of a set, is a fuzzy set. The characteristic functions of subsets of a set X are referred to as the crisp fuzzy sets in X. Let A and B be fuzzy sets in a space X, with the grades of membership of x in A and B denoted by µA (x) and µB (x), respectively. Then we say that (1) A = B if and only if µA ≡ µB . (2) A ⊂ B if and only if µA ≤ µB . (3) C = A ∪ B if and only if µC ≡ max{µA , µB }. (4) D = A ∩ B if and only if µD ≡ min{µA , µB }. (5) E = A if and only if µE ≡ 1 − µA . Key words and phrases. Fuzzy topology. 1 503 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran COMMON FIXED POINT THEOREM IN COMPLETE FUZZY METRIC SPACES SHABAN SEDGHI ——————————————————————————————————– Abstract. In this paper, we establish a common fixed point theorem in com- plete fuzzy metric spaces which generalizes some results in [15]. ——————————————————————————————————– 1. Introduction and Preliminaries The concept of fuzzy sets was introduced initially by Zadeh [17] in 1965. Since then, to use this concept in topology and analysis many authors have expansively developed the theory of fuzzy sets and application. George and Veeramani [5] and Kramosil and Michalek [8] have introduced the concept of fuzzy topological spaces induced by fuzzy metric which have very important applications in quantum particle physics particularly in connections with both string and (∞) theory which were given and studied by El Naschie [1, 2, 3, 4, 16]. Many authors [6, 10, 11, 12, 13] have proved fixed point theorem in fuzzy (probabilistic) metric spaces. Definition 1.1. A binary operation ∗ : [0, 1] × [0, 1] −→ [0, 1] is a continuous t-norm if it satisfies the following conditions (1) ∗ is associative and commutative, (2) ∗ is continuous, (3) a ∗ 1 = a for all a ∈ [0, 1], (4) a ∗ b ≤ c ∗ d whenever a ≤ c and b ≤ d, for each a, b, c, d ∈ [0, 1]. Two typical examples of continuous t-norm are a ∗ b = ab and a ∗ b = min(a, b). Definition 1.2. A 3-tuple (X, M, ∗) is called a fuzzy metric space if X is an arbitrary (non-empty) set, ∗ is a continuous t-norm, and M is a fuzzy set on X 2 × (0, ∞), satisfying the following conditions for each x, y, z ∈ X and t, s > 0, (1) M (x, y, t) > 0, (2) M (x, y, t) = 1 if and only if x = y, (3) M (x, y, t) = M (y, x, t), (4) M (x, y, t) ∗ M (y, z, s) ≤ M (x, z, t + s), (5) M (x, y, .) : (0, ∞) −→ [0, 1] is continuous. Let (X, M, ∗) be a fuzzy metric space . For t > 0, the open ball B(x, r, t) with center x ∈ X and radius 0 < r < 1 is defined by B(x, r, t) = {y ∈ X : M (x, y, t) > 1 − r}. 2000 Mathematics Subject Classification. 54E40; 54E35; 54H25. Key words and phrases. Fuzzy contractive mapping; Complete fuzzy metric space. The corresponding author: sedghi gh@yahoo.com (Shaban Sedghi Ghadikolaee). 1 507 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬ 515
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Signed Decomposition of Fully Fuzzy Linear Systems (a)∗ (b) Nasser Mikaeilvand Tofigh Allahviranloo (a) Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran. (b) Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Abstract In this paper, we discuss fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system and finally, Numerical examples are used to illustrate this approach and compare its results with another methods. keywords: Fuzzy numbers, Fully fuzzy linear systems, Systems of fuzzy linear equations, Non-zero solutions. 1 Introduction Systems of linear equations are used to solving many problems in various area such as structural mechanics applications in civil and mechanical struc- tures, heat transport, fluid flow, electromagnetism,.... In many applications, at least one of the system’s parameters and measurements are vague or im- precise and we can present them with fuzzy numbers rather than crisp num- bers. Hence, it is important to develop mathematical models and numerical procedure that would appropriately treat general fuzzy system and solve them. The system of linear equations AX = b where the elements, aij , of the matrix A and the elements, bi , of the vector b are fuzzy numbers, is called Fully Fuzzy Linear System (F F LS). The n×n(F F LS) has been studied by many authors [2, 3, 4, 7, 8, 15, 16, 17, 18, 19, 20, 21]. Buckly and Qu in their continuous work [2, 3, 4] suggested ∗ Corresponding author Email: NaserMikaealvand@yahoo.com 1 521 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Iteration approach of solving interval and fuzzy linear system of equations ∗ M. Adabitabar Firozja Department of mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran. Abstract In this paper, first norm of interval vectors is defined and then it is extended to norm of fuzzy number vectors. Finally is applied for solving the system of linear equations as X = AX + b that A is a real n × n matrix and b is a interval or fuzzy vector. Keywords: Metric Distance; Fuzzy Numbers; Norm; Linear equation. 1 Introduction Xizhao et al. [3] introduced the iteration algorithms for solving this prob- lems by metric distance subject to A ∞ < 1 but we solve them subject to A 1 < 1. The paper is organized as follows: Fuzzy background is presented in section 2. The proposed norm of interval vector and interval matrix are discussed in section 3. The proposed norm of fuzzy vector and fuzzy matrix are discussed in section 4. Iteration approach for solving the system of linear equations as X = AX + b is introduced in section 5. Finally, conclusion is drawn in Section 6. 2 Fuzzy Background ˜ A fuzzy set A = (a1 , a2 , a3 , a4 ) is a generalized left right fuzzy numbers (GLRFN) of Dubois and Prade [2], if its membership function satisfy in the following:  a −x  L( a22−a1 ), a1 ≤ x ≤ a2 ,  1, a2 ≤ x ≤ a3 ,  µA (x) = ˜ x−a (1)   R( a4 −a33 ), a3 ≤ x ≤ a4 ,  0, otherwise Where L and R are strictly decreasing functions defined on [0, 1] and satis- fying the conditions: L(t) = R(t) = 1 if t≤0 (2) L(t) = R(t) = 0 if t≥1 ∗ Corresponding author: M. Adabitabar Firozja E-Mail: mohamadsadega@yahoo.com 1 533 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran 1 FUZZY BANACH ALGEBRA I. SADEQI AND A. AMIRIPOUR Abstract. In this paper first we show that there is a logical gap on the fuzzy norm which is used in the theorem (1.2) in [2] so that this theorem in [1] and all related theorems assumed in [1] and [2]do not hold true . Then we revise and correct the definition of fuzzy function N (x, t) to get a fuzzy norm in the theorem (1.2) in [2]. By using the revised fuzzy norm in the theorem (2.6) instead, the theorem and all related results will remain true. We also give the definition of fuzzy Banach algebra and get some results. 1. Introduction Our notations and definitions follow [1]. Let X be a vector space, a fuzzy subset N of X × R is called a fuzzy norm on X if the following conditions are satisfied for all x, y ∈ X and c ∈ R: (N1) N (x, t) = 0 for all non-positive real number, (N2) N (x, t) = 1 for all t ∈ R+ if and only if x = 0 t (N3) N (cx, t) = N (x, |c| ), for all t ∈ R+ and c = 0 (N4) N (x + y, t + s) ≥ min{N (x, s), N (y, t)}, for all s, t ∈ R (N5) N (x, .) is a non -decreasing function on R, and supt∈R N (x, t) = 1. The pair (X, N ) is said to be a fuzzy normed space. As an example of fuzzy normed space let (X, ) be a normed space. Define, 0 t≤ x N (x, t) = 1 t> x Then one can easily check that (X, N ) is a fuzzy normed space. For more examples of the fuzzy normed space see the papers [1] and [2]. In [1], the author has constructed α-norms by using the concept of fuzzy norms and vice versa. Also by applying the α-norms on the normed space, they proved that F (X, Y ), the space of all fuzzy bounded operators from the fuzzy normed space (X, N1 ) to the fuzzy normed space (Y, N2 ), is a fuzzy normed space. Since bounded operators have crucial 1 Corresponding author Date: March 11, 2007. Key words and phrases. fuzzy normed space, fuzzy bounded operator. 1 539 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Some Properties of Zariski Topology on the Spectrum of Prime Fuzzy Submodules R. Mahjoob, R. Ameri Mathematics Department, Faculty of Basic Sciences University of Mazandaran Babolsar-Iran e-mail: r.mahjoob@umz.ac.ir, ameri@umz.ac.ir Abstract Let R be a commutative ring with identity and let M be an R-module. We topologize F Spec(M ), the collection of all prime Fuzzy submodules of M , analogous to that for F Spec(R), the spectrum of fuzzy prime ideals of R, and investigate the properties of this topological space. Keywords: prime Fuzzy submodules, fuzzy prime spectrum, L-top modules , Zariski topology. 1 Introduction Let R be a commutative ring with identity and M be a unitary R-module. The prime spectrum Spec(R) and the topological space obtained by introducing Zariski topology on the set of prime ideals of a commutative ring with identity play an important role in the fields of commutative algebra, algebraic geometry and lattice theory. Also, recently the notion of prime submodules and Zariski topology on Spec(M ), the set of all prime submodules of a module M over a commutative ring with identity R, are studied by many authors ( for example see [11-14] ). As it is well known Zadeh introduced the notion of a fuzzy subset µ of a nonempty set X as a function from X to unit real interval I = [0, 1]. J. E. Goguen in [5] replaced I by a complete lattice L in the definition of fuzzy sets and introduced the notion of L-fuzzy sets. Fuzzy submodules of M over R were first introduced by Negoita and Ralescu [17]. Pan [21] studied fuzzy finitely generated modules and fuzzy quotient modules. In the last few years a considerable amount of work has been done on fuzzy ideals in general and prime fuzzy ideals in particular, and some interesting topological properties of the spectrum of fuzzy prime ideals of a ring are obtained (see [4, 6- 10]). 1 547 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A NEURAL NETWORK MODEL FOR SOLVING STOCHASTIC FUZZY MULTIOBJECTIVE LINEAR FRACTIONAL PROGRAMS S. EFFATI 1 , H. SADOGHI2 , Z. SABERI 1 Abstract. The paper deals with stochastic fuzzy multiobjectives linear frac- tional programs. It is transformed to its equivalent deterministic crisp multiob- jective linear program by using a modified possibility programming approach. Then is converted to a neural network model. Our linear neural network is able to generated optimal solutions. We solve neural network model with one of numerical method.Finally, simple numerical examples are provided for the sake of illustration. 1. Introduction. The chance-constrained approach and the possibility programming technique, that has been stated by Negi and Lee [1] and modified by Iskander [2], are utilized to transform the suggested program to its equivalent deterministic-crisp multiobjective linear program in the case of exceedance possibility or the case of strict exceedance possibility[3]. In this paper we use neural network for solving the stochastic fuzzy multiobjective linear fractional program . Recently, several new dynamic solvers using artificial neural network models have been developed .See e.g.Tank and Hop- field (1985), Kennedy and Chua (1987), Rodriguez-Vazquez et al(1990), Wu et al (1996), Xia et al(2002), Effati(2006). In the present paper, one neural network model for a stochastic fuzzy multiobjective linear fractional program is converged to real solutions. 2. Problem Formulation In general, consider a stochastic fuzzy multiobjective linear fractional program- ming problem of the following form: cr1 x1 + . . . + crn xn + cr0 (2.1) Maximize , r = 1, . . . , p, dr1 x1 . . . + drn xn + dr0 Key words and phrases. Possibility programming,Chance-constrained,Stochastic fuzzy multi- objective linear fractional programs, Neural networks. 1 555 ‫ﻫﻔﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻓﺎزي ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Application of a hybrid GA-BP optimized neural network for springback estimation in sheet metal forming process M. E. Golmakani, K. Kamali, M.-R. Akbarzade-T., M. Kadkhodayan, M. Davarynejad kaveh.kamali@gmail.com Abstract: There is a small but important deviation in sheet metal bending between the component angle and tool angle after unloading because of springback, i.e. elastic deformation. Since springback is unavoidable, the precision and reliability of products and subsequent assembly operations are severely affected. As a result of this lack of robustness intelligent technologies have received much attention in a wide range of metal-forming applications. Developments in faster computation techniques have made artificial neural networks (ANNs) and genetic algorithms (GA), very popular choices in modelling of sophisticated phenomenon. The present work, in order to construct the estimation model of springback, intends to integrate ANN with a hybrid genetic algorithm-back propagation (GA-BP) training method to determine appropriately the weights of neural network, making up for the defects of back propagation (BP) algorithm. In this paper, based on the available Experiments, three automotive body alloys using a range of die radius, friction coefficients and controlled tensile forces in a draw-bend process are considered. By using the developed estimation model further study on the relation of springback and various process parameters are carried out. Keywords: Springback, Prediction, Metal forming, Neural network, Genetic algorithm 1 Introduction has been the key to precision forming and ultra- The fabrication of sheet metal bending is widely precision design of tools. The springback used in automobile and aircraft industrial processes phenomenon is influenced by a combination of Needless to say; it is because a final sheet product various process parameters, such as the tool shape of desired shape and appearance can be quickly and dimension, the sheet thickness, frictional and easily produced with relatively simple tool set. contact condition, the material properties, and so The production of high quality formed products in on. The reliability and the stability of metal a short time and at a low cost is an ultimate goal in forming processes are usually low because of their manufacturing. However, sheet metal forming may dependence on many material and process frequently produce the unacceptable products with parameters. As a result of this lack of robustness wrinkle, tear, poor dimension precision, and so on, intelligent technologies have received much unless tool and process parameters are attention in a wide range of metal-forming appropriately chosen. In particular, the dimension applications in order to make a forming system precision becomes a major concern in sheet metal with a large flexibility without the need of skilful bending process owing to the considerable elastic experts, to achieve higher product accuracy and recovery during unloading which leads to spring- product quality. Developments in faster back. In fact there was some deviation in sheet computation techniques have made intelligent metal bending between the component angle and techniques such as artificial neural networks tool angle after unloading because of springback, (ANNs) a very popular choice in modelling of i.e. elastic deformation. Because of the existence of sophisticated phenomenon. ANN originated from springback, the precision of products and the research on the biological brain. ANN models subsequent assembly operations were severely attempt to achieve good performance via dense affected. So how to effectively control springback interconnection of simple computational elements. 29 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Vehicle Type Recognition Using Probabilistic Constraint Support Vector Machine Hadi Sadoghi Yazdi1, Sohrab Effati2 1-Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran 2-Department of Mathematics, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran Abstract: The support vector machine (SVM) is one of the most powerful methods in the field of statistical learning theory for constructing a mathematical model in pattern classification. This paper presents a new support vector machine classifier for recognition of vehiche type which has been captured from traffic scene images. A new support vector machine classifier is presented with probabilistic constrains which presence probability of samples in each class is determined based on a distribution function. Noise is caused to found incorrect support vectors thereupon margin can not be maximized. In the proposed method, constraints boundaries and constraints occurrence have probability density functions which it helps for achieving maximum margin. Experimental results in the machine identification shows superiority of the probabilistic constraints support vector machine (PC-SVM) relative to standard SVM. Keywords: Pattern recognition, Vehicle type recognition, Machine identification, Support vector machine, Probabilistic constraints. 1. Introduction offending drivers is examples of vision-based Pattern recognition are widely used in surveillance systems which for this purpose various applications. In the pattern recognition type of machine is necessary. Vehicle type usually there are two steps of processing recognition or machine identification includes associated. In the first step, pattern features are two main stages: image segmentation and extracted in order to remove redundant recognition. Segmentation is the first step in information and emphasize only on the more this procedure which objects are extracted important data. Second step include applying using spatial and temporal methods [35, 36, extracted suitable features to a classifier. In and 37]. Edge, region, texture and color this stage, extracted features is categorized features are used in spatial segmentation and which tells the class that the target pattern frame differencing and background subtraction belongs to. As there usually exist noises in the are used in temporal segmentation. The optical practical applications, it is important that the flow method is a typical spatio-temporal classification should have the capability of segmentation. After detection of vehicles in the noise immune. The support vector machine scene, a matching algorithm is used in the (SVM) is a new classification technique in the search area for finding similar vehicles in two field of statistical learning theory which has consecutive frames. Finally, suitable features been applied with success in pattern are extracted from segmented target (vehicle) recognition applications like signature for applying to classifier which this work verification [1], face detection [2], speech proceed to it. recognition [3], ECG beat recognition [4], star Such learning only aims at minimizing the pattern recognition [5], hypertension diagnosis classification error in the training phase, and it [6]. cannot guarantee the lowest error rate in the A lot of research has been done on intelligent testing phase. In statistical learning theory, the transportation systems that from its results is support vector machine (SVM) has been the surveillance of road traffic based on developed for solving this bottleneck. Support machine vision techniques. Identifying the vector machines (SVMs) as originally 113 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran On-line Identification and Prediction of Lorenz's Chaotic System Using Chebyshev Neural Networks A. Ashraf-Modarres V. Johari-Majd Tarbiat Modarres University Tarbiat Modarres University a_modarres@modares.ac.ir majd@modares.ac.ir Abstract: In this paper, a single layer functional link ANN based on Chebyshev polynomials is used for identification and prediction of chaotic systems. This model is linear in their parameters and nonlinear in the inputs. Therefore, on- line system identification is achievable by the use of recursive least squares method with forgetting factor. The remarkable prediction performance was gained using proposed Chebyshev neural network (CNN) model and recursive nonlinear predictor method on noise free chaotic Lorenz series. Keywords: Identification, Prediction, Chaotic Systems, Chebyshev Neural Networks. FLANN based on Chebyshev polynomials to show 1 Introduction that functional network architectures provide simpler and more efficient techniques to predict A large set of methods has been developed recently nonlinear time series. Because of single layer which apply artificial neural networks (ANN) to structure of CNN, its computational complexity is the tasks of identification and prediction of intensively less than MLP and can be used easily nonlinear dynamic systems. Different neural for on-line identification purposes [9, 12]. network structures for nonlinear dynamic system modeling and identification is presented in [1]. The This paper is structured as follows. In Section 2 we identification and prediction of nonlinear chaotic give a brief introduction to Chebyshev neural systems, which show "sensitive dependence on networks. In this section, also we describe how initial conditions" behavior, occupy an important CNN can be used for identification and prediction place among of researcher interests. applications. Section 3 introduces Lorenz's system, while section 4 presents the simulation results of At present, most of the works on identification and the multi-step ahead prediction on mentioned prediction of nonlinear chaotic system using neural chaotic system using CNN. Section 5 gives some networks are based on multilayer perceptron conclusions. (MLP) with backpropogation learning [2-4]. 2 Chebyshev neural network (CNN) Identification and prediction of chaotic system using radial basis functions neural networks 2.1 Structure of CNN (RBFNN) are dealt in [5-7]. A comparative study on the effects of different basis functions used in The CNN architecture used in this paper has a the RBF neural networks for time series prediction single layer structure, which introduced in [9]. purpose has been reported in [8]. CNN is a functional link network (FLN) based on Chebyshev polynomials. Among orthogonal Recently, there has been a considerable interest in polynomials, the Chebyshev polynomials occupy the functional link artificial neural network an important place, since, in the case of a broad (FLANN) [9-12]. In this paper we use a type of class of functions, expansions in Chebyshev 123 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Novel Hybrid Structure and Criteria in Modeling and Identification A. Jajarmi, H. F. Marj, R. Shahnazi and N. Pariz* Electrical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran Abstract: In this paper, a hybrid structure based on combination of linear and fuzzy models is proposed. The proposed structure is a trade-off between goodness of fit and modeling simplicity. For evaluation of the hybrid model two criteria are also suggested which are compatible with both Akaike Information Criterion (AIC) and Schwarz-Rissanen Information Criterion (SRIC), respectively. The proposed criteria can also be used for evaluation of both linear and fuzzy models. The proposed hybrid structure is used to model a transformer’s current time series and results are compared with linear and fuzzy models by using suggested criteria. Comparison results indicate the effectiveness of the proposed hybrid structure. 1 Introduction suitable or not. A good model is the one which minimizes the error between the model and the In past decades, the modeling and system training data. On the other hand, a good model is identification are challenging and yet open the one which is as simple as possible. Therefore, problems. This is due to the fact that in modeling, a general criterion to check optimality trade-off it is necessary to find a good trade-off between between two conflicting modeling objectives keeping the model simple and minimizing the (simplicity and goodness of fit) is necessary [1]. error between the model and the training data. So, an identification criterion has two parts: one However, keeping model simple conflicts with the part is related to the error and the other is related other modeling objective, that is goodness of fit to model complexity. One of the most important [8]. One of the main advantages of linear model is criteria for linear models is Akaike Information its simplicity and therefore fast convergence. Criteria (AIC) which is suggested by Akaike in Nonetheless due to the fact that most of real 1974 [1]. In 1978, Schwarz [2] and Rissanen [3], systems are nonlinear, utilizing linear models to independently, derive a common criterion which is identify these systems is not suitable, since the called SRIC. Other criteria that are similar to AIC nonlinearity cannot be properly modeled and so have also been discussed in [4]-[7] where their the model loses accuracy. On the other hand, difference is only in penalty coefficient for nonlinear models such as fuzzy models used for complexity selected as a function of sample size. nonlinear systems have goodness of fit, but more In [8] AIC and SRIC are modified for evaluating complexity. Therefore, constructing simple and fuzzy models construction. Certainly, the efficient model structure is a very important issue importance of simplicity and fitting the training in nonlinear system identification. After a new data can be changed with respect to model model is constructed, it should be checked if it is application. * Emails: A. Jajarmi: am_ja80@stu-mail.um.ac.ir. H. F. Marj: ha_fa16@stu-mail.um.ac.ir. R. Shahnazi: shahnazi@ieee.org. N. Pariz: n-pariz@um.ac.ir. 141 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Design of a VLSI Hamming Neural Network For arrhythmia classification Behzad Ghanavati Behbod Mashoufi St_b.ghanavati@urmia.ac.ir B.mashoufi@urmia.ac.ir Microelectronics Research Center of Urmia University, Urmia, Iran Abstract: The implantable cardioverter defibrillators (ICDs) detect and treat dangerous cardiac arrhythmia. This paper describes a VLSI neural network chip to be implemented using 0.35 μ CMOS technology which acts as an intercardia tachycardia classification system. The Hamming net used to classify non binary input pattern and also reduce impact of noise, drift and offset inherent in analog application. Keywords: Implantable tachycardia arrhythmia classifier, Neural Network, Hamming Net. 1 Introduction In recently year, Artificial Neural Networks have been studied extensively and applied in medical field, and have been demonstrated to have much better pattern recognition ability. In this paper we present a neural network circuit used in a biomedical application, which is the implantable cardioverter defibrillator (ICDs). Figure 1: A typical waveform of ECG Implantable cardioverter defibrillator is a device which monitors the heart and delivers electrical Most morphology changes appear in the QRS- shock therapy in the event of a life-threatening complex. The QRS-complex for both the ST and arrhythmia. VT arrhythmia’s are shown in figure 2. [2] At present most ICDs use only timing information Our studies indicate that; only two works are from leads to classify rhythms [1].This means that reported using Neural Network to detect such they can not distinguish some dangerous rhythms morphology changes [2][4].their Networks need to from safe one, as in the case of ventricular- have training system and the weights of their tachycardia arrhythmia. [2] Networks are off-chip learning. Our chip is used to distinguish between two types of arrhythmia. The sinus tachycardia (ST) arrhythmia and the ventricular tachycardia (VT) arrhythmia, The ST is a safe arrhythmia occurs during vigorous exercises and is characterized with rate of 120beat/minute. The VT is a fatal arrhythmia with the same rate. They can be separated only by detecting the morphology changes in each one [2]. A typical waveform from an electrocardiogram (ECG) is shown in figure 1. It consists of several Figure 2: Morphology change of QRS complex for both complexes, the P-complex, the QRS-complex, the ST & VT T-complex and the U-complex [3]. 177 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Designing an optimal PID controller using Imperialist Competitive Algorithm Esmaeil Atashpaz-Gargari & Caro Lucas e.atashpaz@ece.ut.ac.ir & lucas@ipm.ir Abstract— in this paper we use a new search heuristic called “Imperialist Competitive Algorithm” to design a optimal PID controller for a sample system. The PID controller is designed in such a way that it minimizes the sum of settling time, rise time, maximum overshoot and integral absolute error. A comparison among Imperialist Competitive Algorithm and Genetic Algorithm is made through designing the controller. I. output has the desired properties. At first In Section I. INTRODUCTION II, we briefly describe the Imperialist Competitive P roportional-integral-derivative controller (PID Algorithm. Then in Section III, we formulate the controller) is a generic control loop feedback problem by introducing the PID controller and mechanism widely used in industrial control defining some of the most important characteristics systems. A PID controller attempts to correct the of the system output. In section IV we apply a GA error between a measured process variable and a and ICA to the problem of designing a PID desired set point by calculating and then outputting controller. Finally in Section V, we present our a corrective action that can adjust the process conclusions. accordingly, based upon three parameters: proportional gain ( K p ), integral time constant II. A BRIEF DESCRIPTION OF IMPERIALIST COMPETITIVE ALGORITHM ( K i ), and derivative time constant ( K d ). Imperialism is the policy of extending the power Traditionally, the problem has been handled by a and rule of a government beyond its own trial and error approach. In the past decade more boundaries. A country may attempt to dominate systematic methods have been introduced [1]. others by direct rule or by less obvious means such Ziegler-Nichols tuning formula is one of the best as a control of markets for goods or raw materials. known tuning methods [2]. PID controllers are the The latter is often called neocolonialism [9]. subject to many researches in the area of control Imperialist Competitive Algorithm (ICA) [8] is a engineering and some other methods are proposed novel global search heuristic that uses imperialism for tuning a PID controller [3] - [5]. and imperialistic competition process as a source of Some papers use evolutionary methods to design inspiration. Figure 1 shows the pseudo code for this a PID controller. [6] uses a multi objective genetic algorithm. Like other evolutionary ones, this algorithm to tune a PID controller. In [7] a fuzzy- algorithm starts with an initial population. In this genetic approach is used for autotuning a PID algorithm any individual of the population is called controller. a country. Some of the best countries in the This paper illustrates an application of Imperialist population are selected to be the imperialist states Competitive Algorithm (ICA) [8], by designing a and all the other countries form the colonies of these PID controller for a given system such that the imperialists. All the colonies of initial population 203 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fractional PID Controller Design based on Evolutionary Algorithms for Robust two-inertia Speed Control Arman Kiani -B Naser Pariz Kiani@kiaeee.org n.pariz@um.ac.ir Department of Electrical Engineering Ferdowsi, University of Mashhad, Mashhad, Iran Abstract: This paper deals with the speed control of two-inertia system by fractional order PI l D m controller design with evolutionary algorithms. Fractional controller means the order of I, D controllers will not only be integer but also can be any real number. The significance of frictional order control is that it is a generalization and "interpolation" of the classical integer order control theory, which can achieve more adequate modeling and clear-cut design of robust control system. However, most of fractional order control researches were originated and concentrated on the control of chemical processes, while in motion control the research is still in a primitive stage. In this paper, we tune the controller parameters with EA to control of the two-inertia system, which is a basic control problem in motion control. The novelty of the proposed paper is using EA to tune the Fractional PI l D m parameters and implementing this controller as a robust controller in comparison with classical PID. Keywords: Genetic Algorithm, Fitness function, Fractional Calculators, PI l Dd controller, PID controller. 1. Introduction However, because of the absence of appropriate mathematical methods, fractional-order dynamic Recently, several authors have considered systems were studied only marginally in the theory mechanical systems described by fractional-order and practice of control systems. Works in [10], state equations [1], [2], [3], which mean equations [11], [12], [13], and [14] must be mentioned, but involving so-called fractional derivatives and the study in the time domain has been almost integrals (for the introduction to this theory see avoided. [4]). Fractional Order Control (FOC) means controlled New fractional derivative-based models are more systems and/or controllers described by fractional adequate than the previously used integer-order order differential equations. Expanding calculus to models. This has been demonstrated, for instance, fractional orders is by no means new and actually by Caputo [7], [8], Friedrich [6] and [5]. Important had a firm and long standing theoretical foundation. The idea of using fractional-order controllers for fundamental physical considerations in favor of the the control of dynamic systems belongs to use of fractional-derivative-based models were Oustaloup, who developed the so-called given in [8] and [1]. Fractional order derivatives Commande Robuste d’Ordre Non Entier (CRONE) and integrals provide a powerful instrument for the controller, which is described in his book [4] along description of memory and hereditary effects in with examples of applications in various fields (see various substances, as well as for modeling also other references in [16]). In this paper some dynamical processes in fractal (as defined by in effective methods for the time domain design of [9]) media. This is the most significant advantage fractional-order systems are presented. A concept of the fractional-order models in comparison with of a PI_D_-controller, involving fractional-order integer-order models, in which, in fact, such effects integrator and fractional-order differentiator, is or geometry are neglected. introduced. An example is provided to demonstrate the necessity of such controllers for the more 217 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Neural Networks for Fault Detection and Isolation of a Nonlinear Dynamic System a b Roozbeh Razavi Far a , Hadi Davilu , Caro Lucas a Department of Nuclear Engineering, Amirkabir University of Technology, Tehran, Iran. b Center of Excellence on Control and Intelligent Processing, Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. E-mail Address: razavi_roozbeh@aut.ac.ir Abstract: The proper and timely fault detection and isolation of industrial plant is of premier importance to guarantee the safe and reliable operation of industrial plants. The paper presents application of a neural networks-based scheme for fault detection and isolation, for the pressurizer of a PWR nuclear power plant. The scheme is constituted by two components: residual generation and fault isolation. The first component generates residuals via the discrepancy between measurements coming from the plant and a nominal model. The neural network estimator is trained with healthy data collected from a full-scale simulator. For the second component detection thresholds are used to encode the residuals as bipolar vectors which represent fault patterns. These patterns are stored in an associative memory based on a recurrent neural network. The proposed fault diagnosis tool is evaluated on-line via a full-scale simulator to detect and isolate the main faults appearing in the pressurizer of a PWR. Keywords: Neural Networks, Fault Detection and Isolation, Nonlinear Dynamic System, Pressurizer. 1. Introduction practice. Different applications of fault diagnosis to industrial processes, which include conventional Fault diagnosis is usually performed by a three steps and artificial intelligence techniques are reported in algorithm [1]. One or several signals are generated [4]. However, for the second type of techniques, which reflect faults in the process behavior. These most of the power plant applications use a signals are called residuals. On the second step, the combination of analytical and/or computational residuals are evaluated. A decision, regarding time intelligence tools [5]. Using adequate data base and and location of possible faults, is obtained from the methods for on-line and/or on-line training, neural residuals. Finally, the nature and the cause of the networks are able to reproduce the dynamics of fault is analyzed by the relations between the complex nonlinear systems; after training, they can symptoms and their possible causes. In order to estimate quite precisely the output of nonlinear describe the fault free behavior of the process under systems [6, 7]. Employing measurements of the supervision, a mathematical model is employed; due process under normal operation, if possible, or with to this fact, the term model-based fault diagnosis is the help of a realistic simulator, a suitable neural used. Model-based approaches have dominated the network can be trained to learn the process input- fault diagnosis research for many years [2, 3]. output behavior. The residuals generated using a The main disadvantage of this method is that, being neural network estimator can be evaluated via based on a mathematical model; it can be very thresholds to obtain fault patterns. The fault pattern sensitive to modelling errors, parameter variations, recognition can be done by means other neural noise and disturbances. The success of the model- network, which allows isolating different faults. based method is heavily dependent on the quality of This paper presents a neural network scheme for the models; accurate modelling for a complex fault diagnosis. It uses for residual generation an nonlinear system is very difficult to achieve in estimator, which consists of a bank of recurrent 275 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Semi-active Control of Structures Using Neuro-Inverse Model of MR Dampers A. Khajekaramodin H. Haji-kazemi A. Rowhanimanesh M-R. Akbarzadeh Dept. of Civil Eng. Dept. of Civil Eng. Dept. of Electrical Eng Dept. of Electrical Eng Ferdowsi University Ferdowsi University Ferdowsi University Ferdowsi University a -karam@gmail.com hkazemi@ferdowsi.um.ac.ir rowhanimanesh@gmail.com akbarzadeh@ieee.org Abstract: A semi-active controller-based neural network for nonlinear benchmark structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (NIMR) is constructed to replicate the inverse dynamics of the MR damper. Linear quadratic Gaussian (LQG) controller is also designed to produce the optimal control force. The LQG controller and the NIMR models are linked to control the structure. The effectiveness of the NIMR is illustrated and verified using simulated response of a full-scale, nonlinear, seismically excited, 3-story benchmark building excited by several historical earthquake records. The semi-active system using the NIMR model is compared to the performance of an active and a clipped optimal control (COC) system, which are based on the same nominal controller as is used in the NIMR damper control algorithm. The results demonstrate that by using the NIMR model, the MR damper force can be commanded to follow closely the desirable optimal control force. The results also show that the control system is effective, and achieves better performance than active and COC system. Keywords: Structural Control, Semi-active, Neural Network, Nonlinear, MR Damper and relatively cost-effective; they require small 1 Introduction activation power. The magnetorheological (MR) damper is One challenge in the use of semi-active generating a great interest among researchers in technology is in developing nonlinear control semi-active control of civil structures [1-6]. The algorithms that are appropriate for implementation MR damper is smart semi-active control device in full-scale structures. Numerous control that generates force to a given velocity and applied algorithms have been adopted for semi-active voltage. The MR damper filled with a special fluid systems. These algorithms are either conventional that includes very small polarizable particles that methods based on mathematical formulation [1-6] can change its viscosity rapidly from liquid to or intelligent methods based on neural networks or semi-solid and vice versa by adjusting the fuzzy logic [7–12]. magnitude of the magnetic field produced by a coil Interest in a new class of computational wrapped around the piston head of the damper. intelligence systems known as artificial neural The magnetic field can be tuned by varying the networks (ANNs) has grown in the last few several electrical current sent into the coil. When no years. This type of network has been found to be a current is supplied, the MR damper behaves powerful computational tool for organizing and similar to ordinary viscous damper, whereas its correlating information in ways that have been fluid starts to change to semi-solid as the current is proven to be useful for solving certain types of gradually sent through the coil. Consequently, problems that are complex and poorly understood. semi-active control using MR dampers are The applications of ANNs to the area of structural powerful devices that enjoy the advantages of control have grown rapidly through system passive devices with the benefits of active control. identification, system inverse identification or Additionally, they are inherently stable, reliable, controller replication [7-9]. 289 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Evolutionary Constrained Design of Seismically Excited Buildings, Part I: Actuators Placement Alireza Rowhanimanesh Abbas Khajekaramodin Mohammad-R. Akbarzadeh-T. Department of Electrical Engineering Department of Civil Engineering Department of Electrical Engineering Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad rowhanimanesh@gmail.com karamodin@gmail.com akbarzadeh@ieee.org Abstract: Optimal placement of actuators and sensors is an important problem in control of structures that is often selected without any systematic method. Appropriate placement strongly influences on the performance of control system. This study is presented in two parts In this paper as the first part, Actuators Placement is presented. In this way, a general method is suggested based on a proposed constrained genetic algorithm to determine the optimal placement of actuators in structures. The optimal placement scheme is general for passive, active and semi-active controls. It can handle linear and nonlinear constraints and it does not depend on strategy of control and dynamics of control system such as nonlinearities. The efficiency of proposed method is evaluated on the 20-story benchmark building. The optimal scheme is applied on the sample active LQG control system to place 25 and 5 actuators. The results show that the proposed method could find the optimal placement of actuators and improve the performance of control system. Generally, the proposed method is an approach to achieve the best utilization of available resources. Keywords: Earthquake, Structural Control, Structural Design, Actuators Placement, Constrained GA. 1. Introduction their installation is hard and only few numbers of them can be installed in each story. Thus, to Civil structures might be excited by natural achieve the best utilization, the optimal placement hazards such as earthquakes and strong winds. must be found before installation. In the following, Since damages in some structures such as some of the previous works are reviewed. Martin buildings and bridges might be dangerous for and Soong (1980) [2] considered the placement of people and reconstruction of the damaged active devices in structures for modal control. structures is very costly, designing a system that Lindberg and Longman (1984) [3] discussed the can protect and control structures against these appropriate number and placement of devices dynamic loads is valuable. The first proactive based on modal control. Vander Velde and researches on structural control were started by Carnignan (1984) [4] focused on structural failure Yao in 1972 [1]. The initial methods are based on modes to place the devices, and some other works passive actuators such as dampers. Next, to reach performed by Ibidapo (1985) [5] and Cheng and higher levels of control, active control methods Pantiledes (1988) [6]. Most of these methods are were proposed. In these methods, complex control often problem specific. Takewaki (1997) [7] used algorithms can be programmed on a digital a gradient-based approach to search for an optimal computer and suitable commands are sent to placement. Teng and Liu (1992) [8] and Xu and active actuators. The recent method is semi-active Teng (2002) [9] developed an incremental control that uses some actuators such as algorithm and Wu et al. (1997) [10] used both controllable dampers. This approach includes the iterative and sequential approaches. Zhang and advantages of both previous methods. A challenge Soong (1992) [11] and Lopez and Soong (2002) that is common in all of these three methods is [12] proposed sequential search methods for optimal placement of actuators and sensors that is optimal damper placement. The main problem of often neglected and selected according to guess these methods is converging to local optima. and experience without any systematic method. Simulated annealing as a guided random search Appropriate placement strongly influences on the was employed to place devices by Chen (1991) performance of control system. This problem is [13] and Liu (1997) [14]. Although these method more necessary for actuators than sensors, because could solve the problem of local optima, but they they’re more expensive, have limited capacities, couldn’t always provide general and efficient 297 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Semantic Fuzzy Image Segmentation Using Human Interaction Hadi Sadoghi Yazdi, Seyed Ebrahim Hosseini Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran E-mail: sadoghi@sttu.ac.ir Abstract The aim of this paper is presentation of a new fuzzy image segmentation algorithm. In the proposed algorithm, human knowledge is used in clustering features for fuzzy image segmentation. In fuzzy clustering, the membership values of extracted features for each pixel at each cluster change proportional to zonal mean of membership values and gradient mean of adjacent pixels. The direction of membership variations are specified using human interaction. The proposed segmentation approach is applied for segmentation of texture and documentation images. Results show that the human interaction eventuates to clarification of texture and reduction of noise in segmented images. a) Using suitable interaction equipments for interactive 1. Introduction image segmentation in which segmentation is Image segmentation is not done as well without performed by high-performance hardware for better consideration of semantic respects [1]-[2]. The human usage of human mind, like three dimensional mice [6]. brain uses methods which has semantic respects in image b) Manual segmentation using professional operator in segmentation to receive specific aims. Albeit researchers medical image segmentation [7]-[9] and map have presented numerous segmentation approaches [3] recognition [10]. but image segmentation by a human being is completed c) Manual initialization in image segmentation intelligently so that different mathematical approaches algorithms, for example applying initial value in 3D and or learning based methods can not present suitable image segmentation to deformable surfaces [11]. effective method [2], [4]. In this paper a novel human interaction image Image segmentation based on recognition [4], [5] tries segmentation algorithm is presented which have manifest to use recognition of objects in the scene. As a result, features as follows, segmentation is performed perfectly, but applied • Increasing the performance of image recognition systems in these methods utilize low level segmentation algorithms by increasing suitable features such as color, texture and edges therefore, can controllable parameters. not be accept as semantic segmentation approachs. • Prediction of parameters using human Although, one aim in image segmentation in various interaction. applications is automation, but because of need of wide Figure (2) shows configuration of the proposed initial knowledge or an expert system like human, interactive fuzzy image segmentation. segmentation can not be completed unless with human interaction. Fig 1 shows this interaction. Fig. 1: Interactive image segmentation system A few researches have been accomplished to image segmentation by Human Computer Interaction (HCI) which can be categorized in three groups, Fig.2: structure of the proposed interactive fuzzy image segmentation system 375 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Improving Power System Stability by Designing Supplementary Controller of HVDC Using Real Genetic Algorithm Saeid Haidari, Malihe M. Farsangi and Hossein Nezamabadi-pour Electrical Engineering Department of Shahid Bahonar University, Kerman mmaghfoori@mail.uk.ac.ir, nezam@mail.uk.ac.ir Abstract: This paper investigates the ability of Real Genetic Algorithm (RGA) in designing supplementary controller of High Voltage Direct Current (HVDC) link to damp the power system oscillation. A conventional lead-lag structure is considered for the supplementary controller. The aim of the proposed control strategy is to choose the best controller parameters in such a way that the dominant eigenvalues of the closed-loop system are shifted to the left-hand side of s- plane as far as possible. Also, the binary version of genetic algorithm (BGA) is used to design a supplementary controller for HVDC. The characteristic convergence and time simulation results show that both versions of GA have good capability in solving the problem but RGA gives better results. Keywords: Real genetic algorithm, binary genetic algorithm, power system stability, dynamic stability, HVDC. adjusting control angles to absorb more or less 1 Introduction reactive power. Therefore, HVDC links can be effectively used for HVDC links has been widely applied in power damping electromechanical oscillations, stabilizing transmission for a number of years and have power swings, reducing the life-fatigue effects of provided utilities around the world with important Sub-Synchronous Resonance (SSR), etc. The technical solutions to a wide range of transmission development of Voltage Source Converter (VSC) needs due to their excellent and flexible control technology (used for instance in HVDC Light ability. interconnections) can improve also the network Direct Current transmission can be between voltage compensation and the transmission grid independent systems or between points within a load-ability, reducing the risks of voltage instability system. By DC link power flow can be controlled and collapse [1-7]. precisely and very rapidly. By controlling its power Since, their contributions to the damping of system transfer, the DC link can help the system operator to oscillations are of great importance for achieving dictate the power flows in the adjacent ac lines. satisfactory system performance, in this paper a Also, by rapidly changing its power transfer, it can supplementary controller is designed for a HVDC improve ac system stability. It can damp out post- link. Despite the potential of modern control disturbance swings. It can act as a voltage regulator techniques, intelligent control is used to design a by switching its reactive power banks or by conventional lead-lag structure. BGA is used to design supplementary controller of HVDC in [8-10]. 381 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Soft Computing Approach in MAS Modeling Ehsan Rafiee1, Morteza Analoui1,Bardia Aghabeigi1, Seyyed Mohammad Saeed Tabatabaee1,Mohammad Jafar Abdi1 Computer Engineering Department, Iran University of Science and Technology { E.Rafiee, Analoui, B.Aghabeigi, S.Tabatabaee, M.Jafarabdi }@gmail.com Abstract. Nowadays multi-agent modeling is one The online coach within the simulation league of the important problems in problem-domains in has become more powerful over the last few years. which several agents are involved. One of the Therefore, new options with regard to the main reasons for modeling agents is to become recognition of the opponent’s strategy are possible. capable of predicting their behaviors in special For example, the online coach is the only player situations. In this paper a modeling algorithm for who gets the information of all the objects on the multi-agent systems is presented which is field. This leads to the idea for determining the applicable in domains like RoboCup coach opponents play system by the online coach and competitions. (a very chaotic and uncertain then choose an effective counter-strategy. domain with large number of agents).This In recent years the coach competition structure algorithm is a combination of a classic data has been changed in a way which tries to more mining algorithm named association rule mining concentrate on opponent modeling and counters and fuzzy set theory which leads to a soft strategy design. This task specially is divided into computing approach. Also some evaluation three subtasks: extracting game patterns from methods for recognition of models are presented some log file which can be processed offline, and finally, some experiments for measuring designing some counter strategies which can be accuracy of models and evaluation methods are used to make the patterns occur, and developing a outlined. recognition engine which observes the game and announces the recognized patterns. Keywords: MAS; Fuzzy Logic; Association Rule In this paper a data mining approach is Mining; Opponent Modeling, RoboCup presented for discovering opponent behaviors. Multi agent systems have found many Discovered behaviors are represented in the form applications in so many different areas and bring of a rule-based model. out many interesting challenges. Multi agent Several unsupervised mining algorithms such as modeling is one of major challenges that its main association rule mining have been presented for goal is prediction of opponents’ behaviors. This mining rule-based models so far. In this paper a leads to a new branch of modeling problems, thus classic algorithm of association rule mining called a lot of research on opponent-modeling over plan Apriori-Tid has been chosen as a base algorithm recognition and domain-dependent operator for mining every possible rule in opponent hierarchies is done. Yet, most approaches cannot behaviors. In domains such as coach simulation be applied in dynamic, non-discrete and uncertain there are some attributes that impose some extra multi-agent-systems. complexity to rule mining problems. For example In soccer coach simulation league, coach is one continuous variables that constitute opponent autonomous agent providing advice to other behaviors stand as a problem named quantitative autonomous agents about how to act. This advice variables. Standard algorithms for extracting is in format of standard coach language called association rules use several discretization Clang. The problem of creating agents, is the methods in preprocessing phase to overcome this problem of designing intelligent systems to control problem but these discretization leads to problems and observe multiple robots and provide the robots such as sharp boundaries and data loss. In this with the suitable advice to enhance their paper a combined approach of Apriori-Tid and performance. fuzzy logic has been presented for overcoming 407 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran An Evolutionary Control Model for a Generic Multiagent System Using Artificial Immune Systems B. H. Helmi, A. T. Rahmani, N. Helmi* Department of Computer Science and Engineering, Iran University of Science and Technology, Narmak, Tehran, 1684613114, Iran, *Department of Computer Engineering, Islamic Azad University of mashhad, bh_helmi@comp.iust.ac.ir, rahmani@iust.ac.ir, nonahelmi@gmail.com Abstract: In this paper we propose a method for controlling the behaviour of agents in a multiagent environment. We demonstrate here that functionalities of the biological immune systems are apt to apply in multiagent systems. The AIS- based multiagent system consists of a set of exploring agents in the workspace to find a task. When agents see a task they bid to do it, wining of bidders is based on the ability of them to do the task. The one with a higher ability will gain on the task. After achieving a task, the agent matures itself as a result of competence, avoiding the other agents to grab the task. Agent also requests help when even after maturation is not able to do the task entirely by its own. Through this mechanism, a self-organized, distributed system with complete interactions between components is achieved. Experimental results are presented, proving the efficiency of the overall system. Keywords: Multi agent system, Artificial Immune System. adapts to, is multiagent sys-tem. We can apply 1 Introduction control mechanism and communication strategy of immune system to multiagent systems. Natural Immune System is a complex system The multiagent system we proposed in this paper, consisting of collection of autonomous agents. No address how agents with differ-ent capabilities central control exists in immune system, but the achieve continuously emerging tasks in a dynamic components work successfully as a whole. The environment through communication and strategic agents communicate with each others and complete control. For delineation the behavioral strate-gies each other’s operations. So immune system is a and rules that govern our system we define a self-organized fully distributed system, capable of formal model. Besides, a coopera-tion model is memory management, self-organization, and presented in this paper. adaptive control. It also has properties such as In natural immune system one of the most specificity and diversity [1]. These properties of important properties is to be adaptive. When an natural immune system are of great interest in unfamiliar antigen enters the body, even if there is adapting immune system paradigm to various no specific antibody for that antigen, the immune engineering systems. This adopted engineering system tries to create one which is able to analogue is called Artificial Immune System annihilate it, so one of the significant parts of our (AIS). AIS has been studied widely in the fields of system is maturation of agents to successfully Artificial Intelligence (AI) due to its deep handling the tasks. Through capability maturation, inspiration to the engineering sciences. The Artificial Immune System (AIS) agents are able to essences of human im-mune system properties are accomplish the tasks more skilled. The other imitated to perform complicated tasks, for property of our pro-posed system is that it imitates example, learning strategies, adaptive control, the immune memory, not exactly, but to help the memory managements and self-organization. One system to make more powerful responses to of these engineering systems that immune system already seen tasks. 417 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Match Making Method in a Multi-Agent Bilateral Market Hamed Kebriaei Vahid Johari Majd Ashkan Rahimi-Kian M.Sc. Student Associate Professor Assistant Professor Tarbiat Modares University Tarbiat Modares University University of Tehran hamed.kebriaei@gmail.com majd@modares.ac.ir arkian@ut.ac.ir Abstract: In this paper, an agent matching architecture for bilateral contracts of a multi agent market is proposed. The bilateral market contains a number of sellers and buyers who face opponents for negotiation and signing bilateral contracts. Each agent has a hierarchical representation of trading commodity attributes, where based on that it will create a tree structure of attributes. Using this structure, we apply a modified version of fuzzy similarity algorithm to compute similarity between each pair of buyer and seller agents' trees. Then, we use game theory and the concept of Stackelberg equilibrium to assess the matchmaking among the seller and buyer agents. Agents who lose contract or want to sign a new contract have a chance to restart the procedure. Keywords: Multi agent, market, fuzzy similarity, game theory. The Agent's objective and market supply and 1. Introduction demand are essential factors for decision making in multi-agent markets, and simultaneous decision In today's world with rapid developments of making leads to competition among agents. Thus, an internet, electronic commerce is growing fast. Now, Agent decision directly affects the objectives of we can have multi-agent systems with software other agents and their decisions. Therefore the issue agents as brokers, sellers and buyers that can of coordination in such an environment seems to be a negotiate and sign bilateral contracts for us. Usually necessary task. Game theory can be used to manage the interactions among agents in a multi-agent this conflict [10,14]. market are complex. In this paper, we present a model for Agents are typically interested in multi-attribute matchmaking among sellers and buyers in a bilateral commodities with interdependency among the market. This approach helps agents, in presence of attributes. The interdependency of these attributes is decisions confliction; they make most possible considered in several research works in different beneficial decision and facilitate bilateral contracts. ways. Some assumed nonlinear utility functions for This paper is organized as follows: In section 2, the agent [9, 12], and several papers used the some preliminary backgrounds on weighted tree hierarchical model for multi attribute goods such as similarity algorithm and fuzzy similarity measures is the tree representation model [1, 11]. discussed. In section 3, the proposed agent matching An agent normally specifies a desirable range of architecture is presented. This section includes the services (or products) it needs instead of specifying new fuzzy similarity measure and game theoretical them with crisp values. This is because specifying approach for matchmaking among agents. the amounts of services in crisp values may cause profit loss for the agent. Therefore, a fuzzy 2. Preliminary Background representation of supply or demand for products/services seems to be a reasonable approach 2-1. Tree Similarity Algorithm [7, 8]. 423 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Optimized Elastic Bunch Graph Matching using Genetic Algorithm for Face Recognition Mohamd Hoseyn Sigari, Adel Torkaman Rahmani Computer Engineering Department of Iran University of Science and Technology mo_sigari@comp.iust.ac.ir Abstract: In this paper a new method for optimization of Elastic Bunch Graph Matching (EBGM) algorithm in frontal face recognition is presented. In EBGM algorithm, some pre-determined wavelength of Gabor wavelet is used to extract features from face image. For optimization of EBGM algorithm, Genetic Algorithm (GA) is used to select the best wavelengths of Gabor wavelet. For evaluation, algorithm has been tested on 300 classes of FERET face database. In training phase, only one image per class is trained. The recognition rate of optimized EBGM is about 91%. Also the optimized EBGM can run 1.5 times faster than original EBGM. Keywords: Elastic Bunch Graph Matching (EBGM), Face Recognition, Gabor Wavelet, Genetic Algorithm. 1 Introduction facial images. One can argue that this method Facial image is the most common biometric could potentially offer the better of the two types characteristic used by humans to make a personal of methods [1,2]. recognition, hence the idea to use this biometric in technology. Face identification involves extracting 2 Related Works a feature set from a two-dimensional image of the face image and matching it with the templates Face recognition is an old challenging problem in stored in a database. This is a non intrusive method pattern recognition research. Many of researchers [1]. focus his/her researches on this branch. Face The applications of face recognition range from recognition had been investigated from early 1970s static (mug shots) to dynamic, uncontrolled face to now. In this section, only some last researches identification in a cluttered background (subway about Elastic Bunch Graph Matching algorithm and airport). More applications of face recognition have been investigated. and its commercial products are discussed in [2]. First time, Wiskott et al [3] introduced Elastic Face recognition methods are divided to three Bunch Graph Matching (EBGM) algorithm for categories: template based, feature based and face recognition in 1997. In EBGM algorithm, hybrid method. Template based approaches such as faces are represented by graphs, which used Gabor Principal Component Analysis (PCA) and wavelet transform for extracting features in each Independent Component Analysis (ICA), use node of graph. The node of graphs has been named template matching methods and use the whole face landmark and the Gabor coefficients of landmarks region as the raw input of recognition system to have been named as jet. In recognition phase, the find the best matching. In other hand, feature based algorithm recognizes novel faces by first localizing approaches such as EBGM, extract some local a set of landmark features using bunch graph features from face image and compare features of model and then measuring similarity between these facial images for recognition. Hybrid method such features. as human perception system, uses both template Wiskott et al [4] compared EBGM algorithm with based and feature based approaches to recognize other high recognition rate algorithms on FERET 441 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A NEW AND ROBUST APPLE EVALUATION METHOD USING IMAGE PROCESSING H. Mirzaei, M. Saraee Electrical and computer engineering department, Isfahan University of technology mirzaei.hamid@yahoo.com, saraee@cc.iut.ac.uk Abstract: Fruit evaluation is a necessary component of vegetable and fruit sorting system. Recently, machine vision applications for sorting and inspecting some fruit vegetables have been studied by many scientists. In this paper a new and robust computer vision based system for apple evaluation using image processing is presented to automatically grade apples. The process of segmentation of apples is performed by applying a threshold and a few morphological operations such as opening and closing. Next each apple gets a label using run-length algorithm. Now calculating the measure properties of the apple can be done easily. The next step is detecting the apple skin bruises and the defected areas of apple skin that can be done performing tophat operation on the image. By comparing the results of our approach with the standard apples we can clearly see that our approach will produce good results for sorting the apples. Keywords: Apples, color, image processing, machine vision. 1 Introduction Nowadays, because of the advances in electronic Computer vision is a young technology starting technology, machine vision technology can be from 1960s [1]. From 1970s it began to grow in applied to the development of an automatic fruit both theory and application rapidly. It is reported evaluator. Machine vision enables to handle a large that more than 1000 papers are published each year amount of raw data and perform remote judgment. in various fields of this technology like medical Computer vision based food evaluation is a hard diagnostic, automatic manufacturing, robot but necessary task for increasing the speed of guidance, remote sensing and etc [2]. The main sorting food products and reducing human errors in core of machine vision systems is image this process. This technology can provide a reliable processing and image analysis with numerous judgment system independently from human methods to achieve various properties. Recently subjective factors. the usage of computer vision is growing rapidly in In Japan fruit vegetables are generally sorted into many applications to substitute visual senses of grades based on size or weight before human [3], [4], [5], [6], [7]. marketing[11]. Traditionally evaluation of food products is But these properties are not the only factors which performed by humans. These manual operations can be used to describe the quality of fruits. are time consuming. Moreover the accuracy of this Among them the shape and color are extremely operation cannot be guaranteed [8]. For example a important but unfortunately these properties are human must grade at least 20 apples in a second mostly neglected and grade sorting based on shape, that can produce lots of errors and it relates to damage and color (for example in the case of subjective factors. During the last decade scientists orange, apple, and cucumber) is still in the initial have studied on several methods for automatic stage and in most cases performed manually. evaluating the quality of food products and fruits This paper presents a new and robust grade [9] and numerous works in this category have been judgment system with a high performance rate reported [10]. using image processing technology. The simplicity 465 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran AUTOMATIC QUALITY CONTROL OF FRIED POTATO USING MACHINE VISION Ehsan Lotfi, Hosein Mirzaee esilotf@gmail.com Islamic Azad University of Mashhad , Iran. Khorasan Research Center for Technology Development, Mashhad, Iran. Abstract: Frying of potatoes causes some changes in their microstructures. By studying these changes we have presented quite suitable features for automatic analysis of microscopic images taken from fried potatoes, and have also introduced a new mechanism based on machine vision for automatic quality control of fried potatoes. Experimental results show that the presented structure may well be used for controlling the quality of related products. Keywords: Neural networks, Machine Vision, Texture recognition, Quality control, Potato microstructures. 1 INTRODUCTION cell walls. In [3] the rate of penetration of oil in the potato during frying has been estimated by the changes in the One of the methods for preparing food is frying. This tissue surface and X-ray photography. There are many more method is widely used throughout the world and nearly papers that have worked on fat uptake, e.g. [8], [5], and [6]. everywhere such fried food is controlled in terms of quality And some works on quality control of fried potatoes used and health. One food material that has attracted numerous classification methods and neural network such as [10], studies to its frying in the past is potato. Our goal here is to [11]. In [10] there is an approach to classify the potato chips let the analysis and qualitative control of fried potato be using pattern recognition from digital color macroscopic done algorithmically; or in other words, automatically and images. In [9], analysis of digital color macroscopic images by a machine. To that purpose we shall first review the of fried potato chips were combined with parallel LC-MS works of the past in order to extract suitable features for based analysis of acrylamide in order to develop a rapid tool machine vision. In [1] there is an analysis of the for the estimation of acrylamide during processing. [11] that microstructures of potatoes while being fried. In this paper uses image analysis and artificial neural network for quality it has been shown that by increasing temperature from 20°C control of potatoes in chips industry and [12] that includes to 150°C the potato cells change their shapes and their texture analysis of fried potato. circularity decreases. Also, the starch granules inside the According to what was said above, we rewrite the process cells swell and gelatinize, and expand to whole volume. In of microscopic changes in potatoes during frying: (1) raw this paper it has been shown that after gelatinization, the potato cell, (2) swelling of starch granules inside the cell, starch of the cells get dehydrated and then shrink. In [2] and (3) gelatinization of swollen starch granules, and (4) [1] it has been expressed that studying the frying of potato shrinkage of potato cells. The algorithm we have presented cells clearly shows that the starch granules constantly swell enables the machine to automatically determine and figure and expand throughout the cell in a certain temperature (e.g. out in which state the potato microstructures are, and 60°C to 70°C) by the intercellular water. In [3] it has been whether or not the fried potato is in its best form in terms of said that after this phase, steam bubbles crack and pass quality. The overall structure of the paper is such that we through the pores in the cell walls and find their way into first describe the proposed structure for separating the the oil interface. In [4] it has been shown that before being tissues and inferring the results, then we point out to the dehydrated in higher temperatures, the swollen starch equipment being used and finally explain the results of granules remain like a compact mass pressed on the outer implementation and assessment of the algorithms. 471 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Wavelet-Based Neuro-Fuzzy System for DGPS Corrections Approximation M. R. Mosavi Department of Electrical and Computer Engineering, Behshahr University of Science and Technology, Behshahr, 48518-78413, Iran E-mail: M_Mosavi@iust.ac.ir Abstract: When Global Positioning System (GPS) measurements are made by two users within the same GPS satellite transmission sight, the associated errors are mainly similar. Consequently, knowing the exact location of the receiver with respect to GPS satellites within view allows the measurements errors to be estimated. Thus, these error estimates may be extracted by other nearby GPS users if relayed properly. This correction scheme is the idea behind Differential GPS (DGPS). Inspired by the theory of Multiresolution Analysis (MRA) of wavelet transforms and fuzzy concepts, a Fuzzy Wavelet Network (FWN) is proposed for approximating DGPS corrections. The FWN combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the Wavelet Neural Network (WNN). Each fuzzy rule corresponding to a WNN consists of single-scaling wavelets. The non-orthogonal and compactly supported functions as WNN bases are adopted. The online structure/parameter learning algorithm is performed concurrently in the FWN. The tests results on the collected real data are given to illustrate the performance and effectiveness of the proposed model. The results emphasize that RMS error reduces to less than 0.7m. Also, it is shown that performance FWN is better than single WNN. Keywords: Fuzzy Wavelet Network, Wavelet Neural Network, DGPS, Corrections, Approximation 1 Introduction GPS is an operational constellation consisting of satellite pseudorange are computed. These 24 satellites orbiting the earth every 12 hours, and estimated errors are used to correct the rover acting as reference points from which receivers on position, hence, improving its accuracy [2]. earth triangulate their positions. The GPS has Recently, wavelets have become a very active made navigation systems practical for a number of subject in research area. Especially, WNNs land-vehicle navigation applications. Today, GPS- inspired by both the feedforward networks and based navigation systems can be found in motor wavelet decompositions have become a popular vehicles, farming and mining equipment, and a tool for function approximation. For the WNN variety of other land-based vehicles (e.g., golf with fixed wavelets, the main problem is the carts and mobile robots) [1]. selection of wavelet bases/frames. The wavelet Inaccuracies in the GPS signal can come from a bases have to be selected appropriately since the variety of sources: satellite clocks, imperfect choice of the wavelet basis can be critical to satellite orbits, the receiver errors, and the signal's approximation performance. For WNN with trip through the earth's atmosphere. One efficient variable wavelet basis, a new approach has first way to reduce sources of error is by been presented by initializing the WNN as differentiation. Differential corrections are truncated wavelet frames, then follows by training obtained by comparing the base station "true" with a Back Propagation (BP) algorithm. Also, the location with the estimated location. traditional AutoRegressive (AR) external input Consequently, the errors associated with each model is incorporated with WNN introduced by 487 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Creating New Color Space Using Convex Constraint Programming Applied to Skin Color Detection Hadi Sadoghi Yazdi Seyyed Meysam Hosseini Seyyed ebrahim hosseini Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran Abstract: Each three-component collection such as {Red, Green, Blue} (RGB), and {Luminance Y, Chrominance Cr, Chrominance Cb} (YCbCr) is termed as a color space. Many color spaces are related to each other by linear transformations that are captured by 3×3 matrices. Hence a given color, and thereby any color image, can be represented in terms of another color space by transforming its 3-d vector representation using the 3 × 3 matrix. The Main target of this paper is introduce new color transform from viewpoint of convex constraint programming. Skin detection is used as benchmark problem for the proposed algorithm. In the New color space, the skin and non-skin classes are separated as well. This problem is converted to a convex constraint programming which Lagrange multipliers method is used for solving this problem. Founded converting matrix is tested in skin detection in simple to complex scene. Obtained results over many databases are compared with existing methods which show superiority of the proposed method. Skin and non-skin clusters in the new space color have clustering criteria better than RGB and YCbCr color space. Keywords: Color space; Convex constraint programming; Skin detection; Clustering criteria; Lagrange multipliers. 1. Introduction CIE standardized color order systems by specifying Color is a 3-dimensional psychophysical the light source, the observer and the methodology phenomenon and is represented in color space used to derive the values for describing a color. The models whereby individual colors are specified by XYZ color system is also accepted then and it has points in these spaces. R, G, B primaries can been used ever since. In this system, Y represents produce a gamut of (28)3 different colors [1]. RGB is the brightness (or luminance) of the color, while X the color space usually used in digital images. Each and Z are virtual (or not physically realizable) pixels use 8 bits for each one of its color components of the primary spectra [3]. components (R, G and B), in a total of 24 bits for Many color spaces are presented but other pixel. The color space converter transforms the color viewpoint is theories of color vision which are information form the RGB space to the other spaces derived from the sums and differences of the three as YCbCr space and it should maintain the cone types. One mechanism (often referred to as the representation of each one of the new space ‘‘luminance’’ mechanism) signals a weighted sum components with the same amount of bits used to of long-wavelength-selective (L) and medium- represent each component of the input space (R, G wavelength-selective (M) cones, i.e., ‘‘L+M’’ (with and B). The calculations performed in the color some debate regarding the contribution of short space conversion from RGB to YCbCr are presented wavelength selective (S) cones: [4, 5, and 7]. Two below. Parcels of each R, G and B input components chromatic mechanisms signal weighted sums and are considered in the calculation of the output differences of the cones. The ‘‘L-M’’ mechanism components in the space YCbCr [2]. signals differences between L- and M-cones (and is often referred to as the ‘‘red/green’’ mechanism). ⎡ Y ⎤ ⎡ 0.299 0.578 0.114 ⎤ ⎡ R ⎤ ⎢Cb ⎥ = ⎢− 0.169 − 0.331 The ‘‘S-(L+M)’’ mechanism signals differences ⎢ ⎥ ⎢ 0.5 ⎥ ⎢G ⎥ ⎥⎢ ⎥ (1) between S-cones and the sum of L- and M-cones ⎢Cr ⎥ ⎢ 0.5 ⎣ ⎦ ⎣ − 0.419 − 0.081⎥ ⎢ B ⎥ ⎦⎣ ⎦ (and is often referred to as the ‘‘blue/yellow’’ mechanism). 515 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Path Planning in a Plane With Fixed Obstacles M. Zamirian a ,∗ , A.V. Kamyad b a Department of Mathematics Islamic Azad University of Bojnourd, Iran b Department of Mathematics Ferdowsi University of Mashhad,Mashhad 91775-1159, Iran Abstract: In this paper a new approach for finding optimal path planning in a plane with fixed obstacles is discussed. We consider a movable rigid body in a plane with fixed obstacles. The goal is to find the optimal path which brings rigid body from a given initial point to a given final point such that the length of path is minimum and the distance between rigid body and obstacles is maximum. By considering the length of path and the distance between rigid body and obstacles as objective functions, we obtain a multi-objective problem. Because of the imprecise nature of decision maker's judgment, these multiple objectives are viewed as fuzzy objectives. Then we determine intervals for the optimal value of objective functions such that these intervals for the distance between rigid body and obstacles are given and for the length of path is achieved by solving two optimal non-linear programming problems (ONPP). Now, we define a strictly monotonic decreasing or increasing membership function as degree of satisfaction for any objective functions on achieved intervals. Then the optimal policy is to find an optimal path which maximize all of membership functions, simultaneously. Thus, we obtain an ONPP which gives a (local) Pareto solution for original goal. Numerical example is also given. Keywords: Optimal path planning; Multi-objective; Membership function; Pareto optimal. approach based on measure theory for finding 1. introduction approximation optimal path planning problem in the present of obstacles. In all of above references The problem of finding an optimal path planning the distance between rigid body and obstacles are for a movable rigid body in a plane with fixed assumed crisp values. But, in practice we desire to obstacles is one of the most applicable problems, achieve the shortest path with the greatest distance especially in robot industrial and recently surgery between rigid body and obstacles, simultaneously. planning and etc. Latombe [1] has gathered novel All of these objectives are contradictory such that methods for path planning in the present of the optimization of one objective implies the obstacles and some extensions of them. In sacrifice of other target. Then we need a multi- reference [2] two novel approaches, constrained objective decision making technique to look for a optimization and semi-infinite constrained satisfying solution from these conflict objectives. optimization, for unmanned under water vehicle Optimization for a multi-objective problem is a are considered. In reference [3] is presented a new procedure looking for a compromise policy. The result, called a Pareto optimal that consists of an infinite number of alternatives. In references [4,5] * Corresponding author there are many methods according to different E-mail address: zamirianm@yahoo.com criteria. For example, Cohon [5] categorized two methods generating and preference-base. The 631 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Improvement of STATCOM Performance with Optimum LQR and Pole placement Controller Based on Genetic Algorithm S.Eshtehardiha - Gh.Shahgholian Department of Electrical Engineering, Islamic Azad University, Najafabad Branch, Esfahan, Iran Fax: +98331 2649936 Email: shahgholian@iaun.ac.ir Abstract: Static Synchronous Compensator (STATCOM) is a device capable of solving the power quality problems at the power system. These problems happen in milliseconds and because of the time limitation; it requires the STATCOM that has continuous reactive power control with fast response. In this paper, a LQR (Linear Quadratic Regulator) and Pole placement method for STATCOM control is introduced. The former controller designing needs to positive definite matrix selection and the later is relative to desired pole places in complex coordinate. In this article, matrixes coefficients and dominant poles of closed loop transfer function are selected based on Genetic algorithm method. These methods are tested in MATLAB, and their results are obtained. Keywords: STATCOM, Genetic algorithm, LQR controller, Pole placement. fixed capacitors [10]-[12]. The mechanically 1 Introduction switched capacitors and Static Var Compensator Stability enhancement is of great importance in (SVC) which include actual energy storage power system design. As we all known, generator elements such as capacitors or inductors, in that the excitation control plays an important role in ability for energy storage is not a strict requirement stability enhancement of power systems. Generator but is only necessary for system unbalance or excitation controllers are helpful in achieving rotor harmonic absorption. So it is an ideal three-phase angle stability or voltage regulation enhancement reactive power source supplies (or absorbs) exactly [1]. With only excitation control, the system zero real power on an instantaneous basis. Two stability may not be maintained if a large fault basic controls are implemented in a STATCOM. occurs close to the generator terminal, or The first is the a.c. voltage regulation of the power simultaneous transient stability and voltage system, which is realized by controlling the regulation enhancement may be difficult to reactive power interchange between the achieve. With the development of power STATCOM and the power system. The other is the electronics technologies, several Flexible AC control of the d.c. voltage across the capacitor, Transmission System (FACTS) devices [2] at through which the active power injection from the present or in the further can be used to increase the STATCOM to the power system is controlled [13]. power transfer capability of transmission networks PI controllers have been found to provide and enhance the stability of the power system. The stabilizing controls when the a.c. and d.c. STATCOM is normally designed to provide fast regulators were designed independently. However, voltage control and to enhance damping of inter- joint operations of the two have been reported to area oscillations. A typical method to meet these lead to system instability because of the interaction requirements is to superimpose a supplementary of the two controllers [13,14].The STATCOM AC damping controller upon the automatic voltage and DC voltage controllers can be the proportional control loop [3]. Several recent articles have plus integral (PI) controllers [13].The modelling reported that STATCOM can provide damping to a and control design are usually carried in the power system [4]-[8]. They have also been shown standard synchronous d–q frame[15]. Although, to improve torsional oscillations in a power system the cascade control structure yields good [9].The three-phase STATCOM differs from other performance, it is not very much effective for all reactive power supply devices as well, such as operating conditions because of the unsuitability of 637 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Multi-objective VAr Planning with STATCOM Using Immune Algorithm Malihe M. Farsangi, Hossien Nezamabadi-pour Electrical Engineering Department of Shahid Bahonar University, Kerman mmaghfoori@mail.uk.ac.ir, nezam@mail.uk.ac.ir Abstract: In this paper, the ability of Immune Algorithm (IA) is investigated for VAr planning with the STATic synchronous COMpensators (STATCOM) in a large-scale power system. To enhance voltage stability, the planning problem is formulated as a multi-objective optimization problem for maximizing fuzzy performance indices. The multi-objective VAr planning problem is solved by the fuzzy IA and the results are compared with those obtained by the fuzzy Genetic Algorithm (GA). Keywords: Immune algorithm, genetic algorithm, STATCOM, multi-objective optimization, fuzzy performance indices. 1 Introduction function, known as cost, is added to the objective function used in [10]. The VAr planning problem Voltage collapse and other instability problems can is formulated as a multi-objective optimization be related to the system’s inability to meet VAr problem for maximizing fuzzy performance demands [1]. Efforts have been made to find the indices, which represent minimizing voltage ways to assure the security of the system in terms deviation, RI 2 losses and the cost of installation of voltage stability. Flexible AC transmission resulting in the maximum system VAr margin. To system (FACTS) devices are good choice to validate the results obtained by the IA, the problem improve the voltage profile in a power system, is solved by GA. which operates near the steady-state stability limit and may result in voltage instability. Taking advantages of the FACTS devices depends greatly 2 Immune Algorithm and Genetic on how these devices are placed in the power Algorithm system, namely on their location and size. Over the last decades there has been a growing A brief explanation of IA and GA is given interest in algorithms inspired from the observation below: of natural phenomena [2-8]. The ability of different algorithms is investigated by the authors in VAr 2.1 Immune Algorithm planning by SVC based on single objective and multi-objective functions [9-10]. Also, the ability The immune algorithm (IA) has desirable of modal analysis is investigated where this characteristics as an optimization tool and offer method meets difficulties in placing SVC significant advantages over traditional methods. optimally [9]. The IA may be used to solve a combinatorial This paper investigates the applicability of the optimization problem. Immune algorithm (IA) in the VAr planning In the IA, antigen represents the problem to be problem with STATCOM. Also, other objective solved. An antibody set is generated where each member represents a candidate solution. Also, 643 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Allocation of Static Var Compensator Using Gravitational Search Algorithm Esmat Rashedi , Hossien Nezamabadi-pour, Saeid Saryazdi, Malihe M. Farsangi Electrical Engineering Department of Shahid Bahonar University, Kerman Rashedi_es@yahoo.com, nezam@mail.uk.ac.ir, saryazdi@mail.uk.ac.ir, mmaghfoori@mail.uk.ac.ir Abstract: Gravitational optimization (GO) is used to place the Static Var Compensator (SVC) in a large power system based on its primary function, where the optimization is made on two parameters: its location and size. The primary function of a SVC is to improve transmission system voltage, thereby enhancing the maximum power transfer limit. To validate the results, Particle Swarm Optimization (PSO) Algorithm is applied and the performances of GO and PSO are compared. The results show GO quickly finds the optimal solution in finding the location and size of SVC. Keywords: Gravitational optimization, particle swarm optimization, voltage stability, FACTs devices, SVC. 1 Introduction In the last decades, efforts have been made to find search, simulated annealing, ant colony and the ways to assure the security of the system in particle swarm optimization. These algorithms terms of voltage stability. It is found that flexible have been proven to be very effective for static and AC transmission system (FACTS) devices are dynamic optimization problems. good choices to improve the voltage profile in Study on the use of heuristic approaches to seek power systems that operate near their steady-state the optimal location of FACTS devices in a power stability limits and may result in voltage instability. system is carried out by the researches around the Many studies have been carried out on the use of world [1-10]. FACTS devices in voltage and angle stability. In this paper a new optimization algorithm is used Taking advantages of the FACTS devices depends known as Gravitational Optimization (GO). The greatly on how these devices are placed in the proposed optimization algorithm is based on power system, namely on their location and size. gravitational law and laws of motion based on Over the last decades there has been a growing following definition by English mathematician Sir interest in algorithms inspired from the observation Isaac Newton in 1687: every particle in the of natural phenomena. It has been shown by many universe attracts every other particle with a force researches that these algorithms are good that is directly proportional to the product of their replacement as tools to solve complex masses and inversely proportional to the square of computational problems such as optimization of the distance between them. objective functions, training neural networks, GO algorithm was introduced by Rashedi in 2007 tuning fuzzy membership functions, machine [11]. Now in this paper the ability of the proposed learning, system identification, control, etc. algorithm in power system for Var planning by Various heuristic approaches have been adopted by SVC is investigated. To validate the results researches including genetic algorithm, tabu obtained by GO, PSO is applied and the 649 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Using Genetic Algorithm for Supply Chain Network Optimization Farshad Varasteh Iran University of Science and Technology fvarasteh@softhome.net Abstract: Supply chain networks(SCN), consisting and societies. The reality of supply chain networks of manufacturers, distributors, retailers, and today includes not only competition but also consumers, provide the critical infrastructure for cooperation since decisionmakers in the supply the production of goods, their distribution, and chains must interact not only in terms of the their ultimate consumption in today’s globalized product flows but also in terms of pricing in order economies and societies. The network design to satisfy the consumers. At the same time, problem is one of the most comprehensive strategic decision-makers in supply chains are characterized decision problems that need to be optimized for by their individualized objectives, which may long-term efficient operation of whole supply include not only profit maximization, but also risk chain. Supply chain network design is to provide minimization, as well as the incorporation of an optimal platform for efficient and effective environmentally conscious objectives, to various supply chain management. It usually involves degrees. The concept of supply chain networks is multiple and conflicting objectives such as cost, as applicable to services as it is to goods. service level, resource utilization, etc. This paper In recent years, the supply chain network (SCN) proposes a solution procedure based on genetic design problem has been gaining importance due to algorithms to find the set of Paretooptimal increasing competitiveness introduced by the solutions for multi-objective SCN design problem. market globalization [14]. Firms are obliged to Finally, the algorithm is examined on an artificial maintain high customer service levels while at the company willing to develop its supply chain same time they are forced to reduce cost and network and results are of satisfactory. maintain profit margins. Traditionally, marketing, distribution, planning, manufacturing, and Keywords: Supply chain Management, Genetic purchasing organizations along the supply chain algorithm, Multi-objective optimization, Supply operated independently. These organizations have chain network. their own objectives and these are often conflicting. But, there is a need for a mechanism 1 Introduction through which these different functions can be integrated together. Supply chain management Supply chains are characterized by decentralized (SCM) is a strategy through which such integration decision-making associated with the different can be achieved. The network design problem is economic agents but are, in fact, complex one of the most comprehensive strategic decision network systems. Hence, any formalism that problems that need to be optimized for long-term seeks to model supply chains and to provide efficient operation of whole supply chain. It quantifiable insights and measures must be a determines the number, location, capacity and type system-wide one and network-based. Indeed, of plants, warehouses, and distribution centres to such crucial issues as the stability and resiliency be used. SCN design problems cover wide range of of supply chains, as well as their adaptability and formulations ranged from simple single product responsiveness to events in a global environment type to complex multiproduct one, and from linear of increasing risk and uncertainty can only be deterministic models to complex non-linear rigorously examined from the view of supply stochastic ones [4,7,8,12]. In traditional supply chains as network systems. Supply chain chain management, the focus of the integration of networks, consisting of manufacturers, SCN is usually on single objective such as distributors, retailers, and consumers, provide the minimum cost or maximum profit. However, there critical infrastructure for the production of are no design tasks that are single objective goods, their distribution, and their ultimate problems. [6] proposed a multiobjective genetic consumption in today’s globalized economies optimization procedure for the 701 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Implementing of A New CMOS Adaptive Neuro Fuzzy Logic Controller (FLC) Chip Gh. Yosefi A. Khoei Kh. Hadidi S. Aminifar Department of Departement of Departement of Scientific staff of Microelectronic Microelectronic Microelectronic Mahabad Islamic Azad Laboratory of Urmia Laboratory of Urmia Laboratory of Urmia University University, Urmia 57159, University, Urmia 57159, University, Urmia 57159, Iran Iran Iran gyosefi@yahoo.com A.Khoei@urmia.ac.ir Kh.Hadidi@urmia.ac.ir saminifar@yahoo.com Abstract: In this paper, we present away of using application of neuro fuzzy inference system (Anfis) architecture to implement a new fuzzy logic controller chip. Anfis which tunes the fuzzy inference system with a backpropagation algorithm based on collection of input-output data makes fuzzy system to learn. This training is given from a standard response of the system and membership functions are suitably modified. For adaptive Anfis based fuzzy controller and its circuit design, we propose new circuits for implementing each controller block, and illustrate the test results and control surface of Anfis controller along with CMOS fuzzy logic controller using Matlab and Hspice software respectively. For implementing controller according to Anfis training, we proposed new and improved integrated circuits which consist of Fuzzifier, Min operator and Multiplier/Divider. The control surfaces of controller are obtained by using Anfis training and simulation results of integrated circuits in less than 0.075mm2 area in 0.35μm CMOS standard technology. Keywords: Anfis, Fuzzy controller chip, CMOS, Neural Network, Backpropagation and Hybrid Algorithm 1 Introduction In the effort to realize intelligent brain-like the early sixties Widrow and Holf developed information processing functions, such as intelligent systems such as ADALINE and association, perception, and recognition, one very MADALINE. The publication of the Mynsky and important and challenging approach is to mimic Paper in 1969 publisehed the book with some brain functions and structures. In the brain, a discouraging results, that stopped the fascination of neuron receives many electric impulses via a few artificial neural networks for sometime, and even thousand synapses, and it outputs spike pulses. A achievements in the mathematical foundation of typical neuron has three parts: dendrites, a soma, the back propagation algorithm by Werbos in 1974 and an axon. Pulse signals called spikes are fed went unnoticed. The current rapid growth of the into the dendrites via synapses, the effects of the neural network area started in 1982 with Hopfield inputs are gathered up at the soma, and a spike recurrent network and Kohonen unsupervised pulse goes to the axon as the output [9]. To analyze training algorithms. The backpropagation and apply neuronal information processing, it is algorithm described by Rumelhard in 1986 caused essential to model real neurons. rapid development of neural networks. [3] Artificial neural networks started when McCulloch Artificial Neural Networks (ANNs) enjoy some and Pitts in 1943 developed their model of an distinguished characteristics and are composed of elementary computing neuron and when Hebb in simple elements operating in parallel and including 1949 introduced his learning rules. A decade latter the ability to learn from data, to generalize patterns Rosenblatt introduced the perceptron concept. In in data, and to model nonlinear relationships. 743 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A High-Resolution and Low-Power Maximum Circuit for Application in Fuzzy Systems Taghi Taghizade Abdollah Khoei Khairollah Hadidi Microelectronic research labratory of urmia university a.khoei@urmia.ac.ir Abstract: A CMOS modular high-resolution and low-power voltage-mode Maximum circuit is presented. The proposed technique also allows straightforward implementation of Minimum circuit. In this structure a latched comparator circuit is used to determine full-level logics to recognize the maximum voltage between two input voltages. This comparator uses a positive feedback mechanism to generate the analogue input signal in to a full- scale digital level. Then with some transmission- gates the maximum voltage is placed at the output of cell. The circuit has been implemented in 0.35µm standard CMOS technology with 2 volts power supply. Simulation results determine a maximum clock frequency of 167MHz for comparator with 1mv Maximum circuit resolution and 100µw power consumption per cell. Keywords: Maximum circuit, Based on Latched comparator, low power, high resolution, fuzzy systems. 1 Introduction Maximum circuits, vitality part of fuzzy systems differential CMOS latched comparator to select the and neural networks, identify the highest signal maximum voltage. Latched comparators consist of intensity between two inputs. They have been two stages. First stage is a preamplifier with widely used in several areas such as data infinite gain and second is a digital latch circuit. compression, image processing, self organizing Since the amplifiers used in comparators don’t networks and vector quantization [1], [2], [3]. need to be either linear or closed loop, they can Circuit performances can be measured in terms of incorporate positive feedback to attain virtually speed, resolution and power consumption. Many infinite gain [5]. Considering the limited gain in Maximum circuit architectures have been proposed the implementation of actual preamplifier design, in the literatures. There are two broad methods to the actual latched comparators employ an amplifier implementation of maximum circuits. First method circuit with infinite gain and a positive feedback is current mode method. The current mode latched circuit. In order to aforementioned features structures use the current signal as the carrier of of latched comparators we can obtain high information. They are easier to implement since resolution. Because by applying positive feedback, the current signal can be added simply by wiring circuit gain becomes higher and consequently two signal lines together [4]. Voltage mode is the higher systematic resolution will obtain. second method. Its structures have one potential Furthermore, this paper presents a low power advantage over current mode designs. In current architecture for Max circuit. mode structure, in order to sustain information, a current must flow dissipating the energy. In 2 Comparator Circuit Description voltage mode structures, the voltage can be maintained on capacitive storage elements Figure 1 shows the electrical schematic of latched practically without dissipating energy, provided the comparator topology. It comprises a differential leakage current is neglected. This paper presents a preamplifier, a voltage controlled flip-flop and a high-resolution and low-power voltage mode Max bias generation circuit [6], [7]. When clock is high circuit based on latched comparator, also a Min transistor M10 is switched-on and each outputs of circuit. The proposed Max circuit uses a latch circuit has been pulled to different or same 749 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A High Speed, Low Power Four-Quadrant CMOS Multiplier in Current-Mode to Realize the Simplified Center-of-Gravity Defuzzifier A. Naderi , A.Khoei and Kh. Hadidi Microelectronics Research Laboratory, Urmia University st_a.naderi@urmia.ac.ir , a.khoei@urmia.ac.ir , kh.hadidi@urmia.ac.ir Abstract: In this paper a new CMOS current-mode four-quadrant analog multiplier based on squarer circuit is proposed which is applicable for realization the Center-of-Gravity defuzzification strategy. The major advantages of this work are low power consumption, high speed and high precision. Current mode realization of the circuits leads to simple configurations. The circuit is designed and simulated using HSPICE simulator by level 49 parameters (BSIM3v3) in 0.35μm standard CMOS technology. The simulation results of defuzzifier demonstrate a linearity error of 1.1%, a THD of 0.97% in 1MHz, a -3dB bandwidth of 41.8MHz and a maximum power consumption of 0.34mW. Keywords: Simplified centroid strategy, CMOS multiplier, Defuzzifier circuit, Fuzzy logic, Squarer circuit. 1 Introduction A fuzzy processor consists of four fundamental high. Some other multipliers [3,9] are not very units: the so-called fuzzification unit, decision- optimal for low voltage, low-power fuzzy making logic unit, defuzzification unit and applications. Several techniques of reducing power knowledge base. In this paper, we propose an consumption in CMOS analog multiplier circuits analog current-mode defuzzifier circuit which is have recently been described. They are the usable based on a squarer circuit. One of the most popular floating gate MOS [4], subthreshold mode [5], or defuzzification methods is the Center-of-Gravity class-AB mode [6].They suffer from being highly (COG). To realize this method we need two precise, low power and high speed circuits. operations: multiplication and division. In the next This work is a low power, high speed analog section we will explain a method in which we will multiplier circuit using “dual translinear loops” to reduce these two operations into one operation, realize the COG defuzzifier. In addition, the dual which is multiplication. Then, here we describe translinear loops allow the design of analog multiplication operation or multiplier circuit and multiplier circuit that exhibit wide bandwidth, high review previous works. At present, the power dynamic range and high speed. consumption is a key parameter in the designing of high performance mixed-signal fuzzy integrated 2 Circuit Descriptions circuit. The linearity, speed, supply voltage and power dissipation are the main metrics of One of the most popular defuzzification methods is performance. We try to design specific structures the COG. The general expression of the COG or topologies for the analog multiplier that have defuzzification can be written as: high speed, low power dissipation and good n linearity for fuzzy application. In multiplier circuit presented in [1], two supply voltages VDD and VSS ∑ y i μ yi i =1 are required, and also nonlinearity error is COG = (1) n considerable. In the other circuit introduced by [3] ∑ μ yi linearity is good but the power consumption is i =1 753 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Micropower CMOS Analog Circuit for Gaussian Functions Azad Mahmoudi Aabdollah Khoei Kheirollah Hadidi Microelectronic Research Centre of Urmia University st_a.mahmoudi@urmia.ac.ir a.khoei@urmia.ac.ir kh.hadidi@urmia.ac.ir Abstract: In this paper, a low power CMOS analog circuit that generate the Gaussian function for pattern matching and classification applications is presented. The function is constructed by a novel current mode analog multiplier that is used as a signal squarer and exponential characteristics of MOS transistors in weak inversion. Due to low power consumption, compact structure and wide dynamic range can be easily integrated as a building block of a neural signal processing systems. Keywords: Neural networks, classification and pattern matching algorithms, Gaussian function, neural hardware, analog circuits, translinear loop in weak inversion approximation [5] have been reported. The 1 Introduction Gaussian function is defined in Equation (1), where x is the input and y the output of the Pattern matching and classification are applications − x2 y = Ae 2δ 2 where neural algorithms show promising (1) capabilities because neural classifier algorithms can easily handle multidimensional problems [1]. function and A, σ are adjustable constants which In many neural networks, the algorithm for training define, respectively, the amplitude and the width of is based on probability distributions and pattern Gaussian function. matches ranked as probabilities of a match [2]. In many cases these probability density functions can The function is constructed in three steps. First the be modeled by normal distributions (or input x is squared by means of a novel topology of combinations). a current mode multiplier/divider based on translinear loop with MOS transistors operating in Although these algorithms primarily implemented weak inversion region and then converted to in software, but their capabilities to perform many proportional voltage with a transistor working in different analog functions such as pattern linear region, secondly the voltage level shifted to recognition and image processing make them a proper voltage level and finally an exponential attractive in hardware implementation. Because of obtained with a MOS transistor operating in weak its excellent integration of processing capabilities, inversion mode completes the transfer function. the analog approach has been taken in many In Section 2 the novel current mode CMOS neural chips. In this paper a low power multiplier/divider circuit presented. In section 3 the analog circuit that produce the Gaussian function Gaussian circuit is reported. Sections 4 and 5 for neural or signal processing algorithms is present the mismatch effects and simulation proposed. results. Finally the conclusion of this brief is presented. Other approaches to implement in CMOS technologies the Gaussian function in weak inversion operation [3,4] or as a piece-wise linear 767 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Hybrid Robot Controller Based On Neural Network Compensator Farnaz Sabahi , M.M.Fateh ,A.A.Gharehvici Abstract— In the framework of hybrid position / froce control process, we used a perceptron network with the extended backpropagation learning algorithm to adjust the parameters of the network. The underlying control system, here a robot, represents a non-linear system with an uncertainty related to it. In the proposed method a perceptron network is used as an approximator for modeling uncertain parts of robot dynamic but we assumed there is known parts through human knowledge and experience. Neural network parameter matrices are updated online with no initial offline training using the error as the objective function. The controller guarantees stability for any arbitrary initial values of neural network parameters and any unknown-but-bounded disturbances. Simulation is dealt with the hybrid control scheme in the Cartesian coordinates of the work space especially from the view point of tracking not only force but also position by citing an example of two degree of freedom robot. Keywords—Neural Network, Hybrid Position/Force Control, Uncertainty. interacting with its environment is called force control. I. INTRODUCTION Spong et.al [16] presented an excellent work, which T HE major difficulty associated to robot control is dealing with uncertainty in its model. The traditional representation requires a well-structured and well- triggered off many researches about robot force control. The most common methods of force control are hybrid position/force control [10], where either a position or a defined model.Even if the structure is known, numerical force is controlled along each task space direction, and model usually become inefficient as the complexity impedance control [17], that force is controlled indirectly increases. Moreover,there may be a lot of by means of closed-loop position control . uncertainties,unpredictable dynamics and other unknown Various applications have been made in the area of phenomena that can not be mathematically robot force control using neural network. Among the modeled.Therefor, when a system can not be modeled pioneering papers are the studies done by Jung et. al with traditional methods then neural network is a [2,11]. They used special properties concerning inertia suitable tool that offers an efficient mathematical and friction matrices, and used standard backpropagation method in handling many problems like those of stated algorithm to train the network to achieve zero error. above. Marques et.al [18] discussed the hybrid impedance In the last decades ,some neural network methods to control approach with an inverse dynamic controller and model the dynamic of robot have been suggested.In this a neural network compensator of manipulator. This work filed,Kawato presented in his paper [15] many researchs was extended by Tian etal [9] .The paper is considered that are about the use of neural network as a robot the control of the constrained robotic manipulators and controller. the solution of a reduced model is obtained through a During many tasks, robot makes contact with nonlinear transformation and using neural network just environment. The problem of controlling robot when for force loop in hybrid control manner. Walter and coworkers [13], developed two neural network algorithm for visuo_motor control of an industrial robot based on F.Sabahi is with the Electrical Engineering Department, Shahrood visual information provided by two camera ,the robot University of Technology(corresponding author to provide e-mail: learns to position its end effector without an external Farnaz_Sabahi@ yahoo.com). M.M.Fateh is with the Electrical Engineering Department, teacher (self organizing algorithm). Shahrood University of Technology Most of methods mentioned above focused on A.A.Gharehvici is with the Electrical Engineering Department, offline training or they have assumed no part of the robot Shahrood University of Technology dynamic to be known. Besides that, most of neural 773 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Neuro-Fuzzy Approach for Trajectory Tracking of Two-Link Robot Manipulators Matineh Shaker1,*, Caro Lucas1, 2, Amir Homayoun Jafari3 1 Control and Intelligent Processing Center of Excellence, Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran 2 Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran 3 Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran. m.shaker@ece.ut.ac.ir Abstract: This paper presents a neuro-fuzzy scheme for controlling rigid robot manipulators. The proposed control strategy consists of two modules. In first module, RBFN model from the dynamical equations of the plant is acquired to approximate the nonlinear relation between inputs and outputs of the system. In second step, after the neural model obtained, by assigning suitable membership functions, setting heuristic fuzzy rules, and applying gradient descent method for optimization, the fuzzy controller is obtained. Simulations performed on a two-link robot manipulator illustrate the methods and exhibit its performance. The results confirm the accuracy and robustness of controller. Keywords: MIMO systems, Radial basis function network, Fuzzy systems, PID control, Fuzzy control 1 Introduction On the other hand, fuzzy theory presents Robot is one of the most important machines for outstanding capabilities in the area of controlling industrial automation. They can be applied in nonlinear multi input- multi output (MIMO) hazardous environments to substitute manual systems. In many works like those presented in [4] labors for routine works [1]. To make the robots and [5], fuzzy controllers are used for adaptive more effective, their motion trajectory should be control of robot manipulator and the results manipulated. confirm that fuzzy theory is a reliable method for However, robot manipulators have complex control action. nonlinear dynamical structures and this makes the In this work, we proposed a neuro-fuzzy system control action difficult. Also, there are some kinds that incorporates the human-like reasoning style of of uncertainties in nonlinear models of robot fuzzy systems through the use of fuzzy sets and a manipulators. Some of them are uncertainties in linguistic model. The main strength of neuro-fuzzy the parameters of the system and some others are systems is that they are general function not modeled and are due to external disturbances approximators with the ability to interpret IF- like noise and friction. To encounter these THEN rules. In other words, we have used the problems, the use of some techniques of soft advantages of both neural networks and fuzzy modeling has great importance. Simulation results systems in our integrated system. To do this, first obtained from works in [2] and [3], have verified of all, we obtain a neural model of the plant using that artificial neural networks are convenient in Radial Basis Function Network (RBFN). Then we modeling the nonlinear systems with poorly known applied our fuzzy controller to the system and gain dynamics. satisfactory results. The scheme is evaluated through two experiments. First, we compared the 779 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Chattering Elimination with Fuzzy Sliding Mode Control in Parallel Robots M. Dehghani F. Shabaninia Dept. of Elec. Eng. Dept. of Elec. Eng. Shiraz University Shiraz University Dehghani.mehdi@hotmail.com Shabani@shirazu.ac.ir Abstract - Accuracy of tracking and robustness are very important specifications in control of parallel robots. Classical control methods could not satisfy these requirements in parallel robots, simultaneously. Sliding mode control solves problems of accurate tracking, but it is not robust enough because of influence of chattering phenomena. Implementation of fuzzy logic in sliding mode enhances robustness. In this paper, by use of dynamic model of Delta parallel robot and considering uncertainty with dynamic parameters, the fuzzy sliding mode control is applied to this parallel robot. Simulation results and comparison of them with sliding mode control results show the advantages of applying fuzzy logic in control methods. Keywords: parallel robot, fuzzy logic, sliding mode control, chattering phenomena. kg) along trajectories about 200mm long [5], [6], 1 Introduction [7] and [8]. Today, some types of Delta robots are constructed which are able to move heavy objects The idea of design of parallel robots has been (figure 2). regarded since 1947 when D. Stewart designed In this paper dynamic based control of Delta robot flight simulator based on his parallel robot [1]. Then which involves uncertainty in parameters will be other types of parallel robots were designed [2]. In performed using fuzzy sliding mode control. early 80’s Delta parallel robot was presented by Raymond Clavel (figure 1), [3]. The basic idea behind the design of Delta robot is the use of parallelograms. A parallelogram allows an input link to remain at the fixed orientation with respect to the output link [4]. The disadvantage of Delta robots are limited workspace and complex kinematic of them. Because of the appropriate characteristics of Delta parallel robot such as accuracy, high velocity and rigidity, limited workspace can be neglected [3]. These robots are used in quick operations such as picking up and placing light objects (from 10 gr to 1 Figure 1 - The Clavel’s Delta robot 785 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Meta-Level Control of Snake Robots S. Hasanzadeh A.-R. Akbarzadeh-T. M.-R. Akbarzadeh-T. Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad shahirhasandadeh@yahoo.com alytootoonchi@gmail.com akbarzadeh@ieee.org Abstract: In this paper, a new fuzzy logic controller (FLC) for navigation of a snake robot is proposed. This FLC is used as high level controller of a novel control architecture. The objective of this control architecture is to guide the snake robot from an initial configuration to a final position. Simple rules in dynamic equations of motion of 2D snake robot moving with serpentine gait are utilized to form a fuzzy inference system. Other parts of the control architecture are a PID as low level controller and a desired orientation generator unit. In order to verify capability of the proposed control architecture to guide snake robot from any initial configuration to desired final position, simulations are carried out using SimMechanic toolbox of MATLAB software. Keywords: snake robot, locomotion, fuzzy logic controller, serpentine gait. applying soft computing methods for the control, particularly fuzzy controllers. 1. Introduction Two broad classes of control methods have been Despite having challenges in the area of control used with snake robots. The first class can be and inefficiency in locomotion due to high friction described as trajectory-tracking control. It uses snake-like robots have attracted the attention of predefined gait patterns, usually computed as sine researchers for applications not suitable for waves that are tracked with a feedback controller wheeled and legged robots. Applications such as [1, 2]. Typically, the control is open-loop: the set ruins of collapsed buildings or narrow passages points of the joints are calculated and sent to the are good examples where snake robot may be motor controllers without any form of feedback used. Snake-like robots are advantageous over (the only feedback present in the system is the one wheeled vehicles for terrainability, traction, used by the PID controller). universal penetration capabilities, high adaptability and task shapability due to kinematic The other class can be described as online gait redundancies. They also offer graceful generation control. In this case, gaits (motion degradation and increasing reliability when made mode of snake robot) are not predefined in modular. Other application areas of snake robots advance, but generated online during locomotion. are maintenance and condition monitoring of These approaches can, therefore, better deal with complex technical structures and plants, such as perturbations and irregular terrains. Most of these airplane motors, pipelines and nuclear power approaches are model-based, i.e. they rely on a stations. kinematic [3, 4, 5] or dynamic [6, 7] model of the robot’s locomotion in order to design control laws The two main challenges of snake robots over for the gait generation. wheeled mechanisms are difficulty in analyzing and synthesizing snakelike locomotion Another new control method is using central mechanisms as well as its control. This paper pattern generators (CPGs). In this method hopes to contribute to these challenges by locomotion in vertebrates is controlled by CPGs, which are networks of neurons that can produce 793 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Gait Planning, Complete Dynamic Modeling and Online Neural Network Control of a Biped Robot Department of Mechanical Engineering K. N. Toosi Univ. of Technology S. Ali A. Moosavian S. Hossein Sadati Amir Takhmar Mansoor Alghooneh moosavian@kntu.ac.ir sadati@kntu.ac.ir takhmar@sina.kntu.ac.ir alghooneh@gmail.com Abstract: Control of biped robots based on designated smooth and stable trajectories is a challenging problem that is the focus of this paper. A desired trajectory for the lower body will be designed to alleviate the impacts due to contact with the ground. This is obtained by fitting proper polynomials at appropriate break points. Then, the upper body motion is planned based on the Zero Moment Point (ZMP) criterion to provide a stable motion for the biped robot. Next, dynamics equations will be obtained for both single support phase (SSP) and double support phase (DSP). Finally, the online Neural Network Control (NNC) approach is applied for both SSP and DSP. Obtained results show the successful performance of this kind of controller on a biped robot. Keywords: biped robots, stability, gait planning, neural network controller According to the synergy method, the nonlinear 1 Introduction differential equations for the upper body motion Control of biped robots requires appropriate gait are obtained and solved by the iteration method. planning that satisfies stable walking. One of the To obtain the nominal required torques or the earliest criteria to investigate the stability of such required torques for the control of biped robots, it systems is Zero Moment Point (ZMP) criterion, is necessary to obtain theirs dynamic equations. [1-2]. The ZMP is a point where the horizontal The dynamic equations of biped robots are components of the resultant moment of all external different in each phase and because of the forces, including gravity and inertial forces, complexity of equations in DSP, the most of becomes zero. According to the ZMP criterion if researchers have only investigated these robots in that point is inside the support polygon, the robot SSP, [5, 6]. To track planned trajectories, various will be stable, otherwise the robot will tend to tip control strategies have been suggested and over. The support polygon is defined as the foot implemented on the biped robot, [5,6,7,8,10]. supporting exterior on the ground. Goswami has Among different controllers, the Sliding Mode introduced the Foot Rotation Indicator (FRI) Control (SMC) is a suitable control approach that criterion, [3]. This corresponds to a point where ensures good tracking despite parameter the net ground reaction force would exert to keep uncertainties, [5, 8, 10]. The two CTM and SMC the foot stationary. According to this criterion if have been applied for the single support phase the FRI point is inside the support polygon, the (SSP) of a 5 DOF biped robot without active feet, robot will be stable, otherwise the robot will tend where SMC results in a better performance to tip over. The FRI criterion has been introduced compared to CTM, [5]. However, SMC only for the SSP. The upper body motion has been experiences chattering problem that is due to used to compensate the stability of biped robots. switching process and may even cause instability, Vukobratovic has used the prescribed synergy so some researcher has tried to eliminate method to obtain the upper body motion, [4]. chattering problem in the control of a biped robot, 805 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A Bio-inspired Genetic Algorithm Applied to a Constrained Optimization Problem in Power Systems H. R. Abdolmohammadi S. Jafari M. R. Rajati M. E. Nazari abdolmohammadi2000@yahoo.com sajadjafari83@gmail.com mohammadreza.rajati@gmail.com nazari_bati@yahoo.com Abstract: In this paper, an improved genetic algorithm is proposed to solve the economic dispatch (ED) problem for co- generation systems. The proposed algorithm is a novel bio-inspired Genetic Algorithm. This algorithm seems to be efficient in finding global optimum in the economic dispatch problem. Furthermore, it provides a suitable framework for future extension to other optimization algorithms. Keywords: Genetic Algorithm, Economic Dispatch. each author adds some new feature to arrive to the 1 Introduction optimal solution. For example [1] solves the CHP economic dispatch problem based on the separability Economic dispatch (ED) is used to determine the of the objective function of the problem. The optimal schedule of on-line generating outputs so as separability, defined by the authors, is the fact that to meet the load demand at the minimum operating the objective function is the sum of the cost cost. Recently, co-generation units have played an functions of separate units, and most of the increasingly important role in the utility industry. constraints are linked to one specific unit. In this Co-generation units can provide not only electrical method, a two-level strategy was adopted. The lower power but also heat to the customers. For most level solves the economic dispatch problems of the cogeneration units, the heat production capacities individual units for given power and heat lambdas, depend on the power generation and vice versa. and the upper level updates the lambda’s by Some complications arise in Combined Heat and sensitivity coefficients. The procedure is repeated Power (CHP) systems because the dispatch has to until the heat and power demands are met. Ref. [2] find the set points of power and heat production with does a physical interpretation of the feasibility region the minimum fuel cost such that both demands were for the CHP units, and then solves the problem in matched, indeed, the CHP units should operate in a two layers, one for heat and the other for power. Ref. bounded power vs. heat plane [1–9]. Basically, the [3] uses the same method as [2] but adds a steam dispatch problem can be formulated as an turbine working at full capacity. A new algorithm for optimization problem with a quadratic objective combined heat and power economic dispatch function and linear constraints. Such problems can (CHPED) problem was proposed in [4]. In this be solved with a general-purpose package that is algorithm the problem was decomposed into heat and designed to solve quadratic programming problems, power dispatch sub-problems. The two sub-problems but the computational effort increases at least were connected by the heat-power feasible region quadratically with the increasing number of units. constraints of co-generation units. The analysis and The literature reports basically the traditional method interpretation of the connection have led to the to solve the ED problem adapted for CHP plants development of the two-layer algorithm in which the based on Lagrangian relaxation [1], [2]. However, outer layer used the Lagrangian relaxation technique to solve the power dispatch, and the inner layer used 813 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Reactive power planning in Distribution Systems using A Reinforcement learning method Mehdi Ahrari Nouri ,Alireza Seifi m_ahrarinouri@yahoo.com , seifi@shirazu.ac.ir T T Ms Student Assistance Professor Department of Electric Engineering Department of Electric Engineering Shiraz University Shiraz University Shiraz (Iran) Shiraz (Iran) Abstract: This work presents a new algorithm RL approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses RL for sizing and sitting of capacitors in radial distribution feeders. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9- bus radial distribution feeder along with a 34-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem. Keywords:Reactive Power Planning, Reinforcement Learning, Radial Distribution Feeder approaches to identify the sensitive nodes by the 1 Introduction levels of effect on the system losses. Ref. [4] adopted an equivalent circuit of a lateral branch to Capacitors are widely installed in distribution simplify the distribution loss analysis, which systems for reactive power compensation to obtained the capacitor operational strategies achieve power and energy loss reduction, voltage according to the reactive load duration curve and regulation, system capacity release, power flow sensitivity index. Moreover, optimal capacitor control, improving system stability and power planning based on the fuzzy algorithm was factor correction. Capacitor planning must implemented to present the imprecise nature of its determine the optimal site and size of capacitors to parameters or solutions in practical distribution be installed on the buses of a radial distribution systems [5-7]. Several investigations have recently system. Many approaches have been proposed to applied AI techniques to resolve the optimal solve the capacitor planning problem. For instance, capacitor planning problem due to the growing [1] formulated the problem as a mixed integer popularity of AI. Refs. [8, 9] presented a solution programming problem that incorporated power methodology based on a simulated annealing (SA) flows and voltage constraints. The problem was technique. Ref. [10] applied the tabu search decomposed into a master problem and a slave technique to determine the optimal capacitor problem to determine the sitting of the capacitors, planning in Chiang et al's [8] distribution system, and the types as well as size of the capacitors and compared the results of the TS with the SA. In placed on the system. Refs [2,3] proposed heuristic Refs.[11-12], genetic algorithms (GA) were 835 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Accuracy-based Classifier Systems for EEG Classification of Schizophrenic Patients M. Sabeti*, M. H. Sadreddini*, G. W. Price+ * Department of Computer Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran + School of Psychiatry and Clinical Neuroscience, University of Western Australia, Perth, Australia sabeti@shirazu.ac.ir Abstract: In this paper, EEG signals of twenty schizophrenic patients and twenty age-matched healthy subjects are analyzed with objective of classification two groups. In this case, Fuzzy Accuracy-based Classifier System (F-XCS) is used to automatically generate fuzzy if-then rules for discrimination healthy and schizophrenic subjects. Several features including AR model coefficients, band power and fractal dimension are extracted from EEG signals. First, the F-XCS is applied where a randomly generated initial population of fuzzy if-then rules is evolved by typical genetic operations such as selection, crossover and mutation. Second, a heuristic procedure for improving the performance of F- XCS is applied and result of adding this heuristic procedure is analyzed. The motivation behind this approach is that F- XCS will be capable of generating compact, high performance rule sets which are general and accurate. Keywords: EEG, Schizophrenic, Fuzzy, Classification. had to lack a generative rule that is to be as random 1 Introduction as possible. They found that schizophrenic patients were more inclined to be repetitive. Pressman et al. Schizophrenia is a mental disorder from which 1% [6] showed lack of synchronization alternation of the whole population suffer. According to the ability in the schizophrenic patients during diagnostic criteria of the American Psychiatry working memory task. They indicated a difference Association [1], patients show some characteristic in brain activity, especially in frontal and temporal symptoms including delusions, hallucinations or channels. Paulus et al. [7] carried out a simple disorganized speech. Recently, much attention has choice task consisting of predicting 500 random been paid to analysis of EEG signals of right or left appearances of a stimulus in order to schizophrenic patients. In some research [2, 3], obtain binary response in patients with nonlinear methods have been applied to EEG schizophrenia and control group. After applying signals of the two groups of schizophrenic patients mutual and cross-mutual information, they showed and control participants. The results showed that the response sequences generated by patients differences in dynamic process between the two exhibited a higher degree of interdependency than mentioned groups. Hornero et al. [4] asked the those in control group. participants to press space bar key randomly to generate time series. The results obtained showed 2 Data Acquisition that the time series generated by schizophrenic patients had a lower complexity than the control Twenty patients with schizophrenia and twenty group. In an interesting test, for random number age-matched control participants participated in generation [5], participants were asked to choose a this study. They were recruited from the Center for number from one to ten several times. Numbers Clinical Research in Neuropsychiatry, Perth, 865 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Reflecting on the Fuzzy process of Self-organized Learning Hamid Sepehr (PhD) Department of Education and Psychology, Yazd University hsepehr@yazduni.ac.ir Abstract : This paper presents the findings of two action research projects involving learning and self-organization by two distinct groups of learners. They include English-speaking primary school children and Farsi-speaking university students. Focusing on recordings of process information it discusses the generally fuzzy nature of the self- organized learning. The findings seem to support a multi-valence - as opposed to the traditional bi-valence approach to the study of learning. The analysis of the process information also depicts a non-linear – as opposed to linear - character for the way learning and self-organization develops. The study of the process of learning also shows a simple causal model to be ineffective in evaluating the influence of different factors in development of learning and stresses the need for alternative and more ‘fuzzy’ approaches such as ‘coherence’ or ‘synchronicity’ to confront the challenges in this field. Fuzzy Cognitive Maps may also be useful in mapping the complex relationship between different modalities of learning. Introduction Learning is placed at the heart of any design for models have not sufficiently attended to mapping improvement and change. It is at times described the actual processes people choose to engage in as the central theme in psychology (Schultz & while learning (Marton & Saljo 1976, 1997, Schultz 1987). In the past few decades, Entwistle 2002). Self-management, self- educational research and theory has shifted its directedness, self-regulation and self- focus from ‘teaching’ to ‘learning’. Learning organization are among the concepts most may also be the most researched topic within the widely used (eg Ginnis 1992, Westwood 1990). field of ‘fuzzy logic’ application (e.g. Kosko Such approaches have strengthened a ‘systems’ 1994, p 205). Much of the ‘fuzzy logic’ literature view of man as active and ever-searching on learning is in the domain of artificial learner. intelligence and machine learning (eg Russo & Self-Organization as a dynamic control Jain 2000). However, applications within process has been proposed and studied in many humanities, psychology and education are not domains (Schultz & Schultz 1987, Lovelock rare. 1978, Camzine et al 2003). An approach to Traditional models of learning have ‘learning’ as a process of ‘self-organization’ has generally followed a linear and single-mode path been proposed by Thomas and Harri-Augstein focusing on isolated and disperse aspects of (1985). With roots in psychological as well as learning (Driscoll 1994). Mechanistic cybernetic theories, their theory suggests that all models have reduced the role of awareness and effective learning is achieved when a person is have stressed conditioning. Less attention has consciously engaged in a process of generating been paid to Human Learning as a useful feedback to himself/herself. They see the developmental and multi-modal process. process as personal, ‘conversational’ and Although the developmental models have reflective (Harri-Augstein & Thomas 1991). attempted to describe the mechanisms of Self-organized learning (as opposed to ‘other- development in given domains (e.g. cognitive, organised learning’) as a process of human and emotional, social, etc.) they have not gone far organizational development has been used enough in studying the interrelationship between widely to help overcome difficulties and to raise such domains (op cit & Ho 2001). The cognitive effectiveness in diverse areas of learning in life 877 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran A New Method for Automatic Border Detection in IVUS Images and 3D Visualization of the Segmented Frames Z.Najafi1, A.Taki1, 2, S.K.Setarehdan1, R.Zoroofi1, N.Navab2 1 Faculty of Electrical and Computer Engineering, University of Tehran, Tehran, Iran 2 Computer Aided Medical Procedures (CAMP) - TU Munich, Germany z.najafi@ece.ut.ac.ir, arashtaki@dpimail.net, ksetareh@ece.ut.ac.ir, rzoroofi@ece.ut.ac.ir, navab@ cs.tum.edu Abstract: In this paper, an effective method for automated extraction of the lumen and media–adventitia borders in intravascular ultrasound (IVUS) images is presented. The method is based on non-parametric deformable models. The calcified deposits within an IVUS image appear as bright regions between the two extracted borders and obstruct the penetration of ultrasound, a phenomenon known as “acoustic shadowing”. We have visualized the segmented frames and highlighted the calcified regions in the 3D representation of IVUS images. The proposed method is evaluated using 70 IVUS frames from 7 different patients. Statistical analyses of the results demonstrate a high accuracy rate of the automatically extracted boundaries compared to those manually identified by expert. Keywords: Deformable models, IVUS, Border detection, 3D Visualization. different border optimization algorithms such as 1 Introduction dynamic programming, graph searching, simulated annealing, solution of partial differential equations, Intravascular Ultrasound (IVUS) is a catheter- and genetic algorithms have been applied to the based medical imaging technique. Using a IVUS images in these articles [4], [5]. Recent specially designed ultrasound catheter it provides approaches are mostly based on the active contours real-time tomographic images of the arterial wall together with minimizing an energy or cost that shows the morphology and histological function which guides a snake towards the vessel properties of the cross-section of the vessel. IVUS borders. not only provides a quantitative assessment of the The active contours used in the previous vessels' wall but also introduces information about approaches are mostly based on a kind of the nature of atherosclerotic lesions as well as the parametric deformable model. However, plaque shape and size [1], [2]. The first step for parametric deformable models have two main plaque characterization in IVUS images is limitations. First, in situations where the initial segmentation. Nevertheless, it is a difficult, model and desired object boundary differ greatly in subjective and time-consuming procedure to size and shape, the model must be re- manually perform segmentation. Therefore, there parameterized dynamically to faithfully recover the is an increasing interest in developing automatic object boundary. The second limitation is that it tissue segmentation algorithms for IVUS images has difficulty dealing with topological adaptation [3]. such as splitting or merging model parts, a useful Several algorithms for lumen and media- property for recovering either multiple objects or Adventitia contours detection have been reported objects with unknown topology [6]. in the past decade. Various edge detection and In this work, we have focused on the development contour identification techniques together with and validation of an automated method based on 891 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Breast Cancer Detection from FNA Using SVM and RBF Classifier Majid Iranpour , Sanaz Almassi , Morteza Analoui Computer Department , Iran University science & Technology Majid.iranpoor@comp.iust.ac.ir , Sanazalmassi@comp.iust.ac.ir , Analoui@iust.ac.ir Abstract: In this paper, we consider the benefits of applying support vector machines (SVMs) and radial basis function (RBF) for breast cancer detection. The Wisconsin diagnosis breast cancer (WDBC) dataset is used in the classification experiments; the dataset was generated from fine needle aspiration (FNA) samples through image processing. The 1-norm C-SVM (L1-SVM) and 2-norm C-SVM (L2-SVM) are applied, for which the grid search based on gradient descent based on validation error estimate (GDVEE) are developed to improve the detection accuracy. Experimental results demonstrate that SVM classifiers with the proposed automatic parameter tuning systems and the RBF classifier can be used as one of most efficient tools for breast cancer detection, with the detection accuracy up to 98%. Keywords: Breast cancer detection, Parameter tuning, Radial basis function networks, Support vector machines. the University of Wisconsin, Madison, applied image processing techniques to derive the WDBC 1 Introduction dataset directly from digital scans of FNA slides, and then employed machine learning techniques to Worldwide, breast cancer is the most common differentiate benign from malignant samples, form of cancer and the second most common cause which could be the earliest study of machine of cancer deaths in females, which affects learning application to breast cancer detection. approximately 10% of all women at some stage of Later, several works on computational intelligence their life in the western world. Breast cancer may were developed in the area of breast cancer, be detected via a cautious study of clinical history, including the multilayer perceptron [1], radial basis physical examination and imaging with either function (RBF) networks [2], fuzzy classifiers mammography or ultrasound. However, definitive [3,6], clustering algorithms [4], evolutionary diagnosis of a breast mass can only be established computation [5], principal component analysis [6], through fine-needle aspiration (FNA) biopsy, core and different kernel-based methods [7]. needle biopsy or excisional biopsy. Among these Support vector machines (SVMs) are highly methods, FNA is the easiest and fastest method of successful in solving various nonlinear and non- obtaining a breast biopsy, and is effective for separable problems in machine learning, In women who have fluid-filled cysts. FNA uses a addition to the original C-SVM learning method needle smaller than those used for blood tests to proposed by Cortes and Vapnik [8] in 1995. remove fluid, cells, and small fragments of tissue In order to use SVM, one needs to decide the value for examination under a microscope. Research of the regularization parameter (C for C-SVM) and works on the Wisconsin diagnosis breast cancer the kernel function before training the SVM (WDBC) data grew out of the desire of Dr. classifier. Thus, choosing a suitable kernel function Wolberg to diagnose breast masses accurately is imperative to the success of the learning process, based solely on FNA. Previously, researchers from 911 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Fuzzy Learning Automata: A Novel Approach For Multimodal Function Optimization Seyed-Hamid Zahiri Department of Electrical Engineering, Faculty of Engineering, Birjand University, Birjand, Iran shzahiri@yahoo.com Abstract: The concept of fuzzy learning automata (LA) has been introduced to construct a novel algorithm for optimizing the multimodal complex functions. In this approach a fuzzy controller is designed to change the internal LA parameters adaptively while the search process is executing by LA. The proposed algorithm has been tested on different kinds of benchmark functions. The experimental results show more powerfulness and effectiveness of the proposed algorithm in comparison to other function optimization algorithms based on the LA. The proposed algorithm can be considered as an effective search and optimization algorithm and may be utilized for wide range of engineering tasks like data mining, pattern recognition, image processing, adaptive control, power systems, and other optimization problems. Keywords: Fuzzy controller, learning automata, function optimization, reinforcement algorithm. control [2], signal processing [3], power systems 1 Introduction [4], and pattern recognition [5]). Over the years many researches on the LA based Function optimization is an important task which function optimization techniques were reported. A deals with finding the minimum (or maximum) stochastic automata model was adopted by Shapiro value of a function in the search space. Many and Nerendra [6] to find an optimal solution for engineering tasks, such as pattern recognition, data multimodal performance criteria. Thathachar and clustering, image processing, power systems, and Sastry [7] proposed Pursuit algorithm to improve design of integrated circuits, can be consider as the convergence rate of LA based function optimization ( or multiobjective optimization) optimization. Also an automata model was problems. proposed by Oommen and Lanctôt [8], using Different kinds of gradient, heuristic, evolutionary discritized Pursuit algorithm. Obaidat et al [9] and swarm intelligence based algorithms have been developed an algorithm for fast convergence of reported in the literature. Learning Automata (LA) learning automata. Beigy and Meybodi [10] is another approach which has been utilized for proposed a continuous action-set automaton for function optimization. Learning automata (LA) is function optimization. They studied the referred to an automaton acting in an unknown convergence properties of their algorithm random environment which improves its theoretically and experimentally. Also Zeng and performance to obtain an optimal action. An action Lui [11] presented a method for optimizing is applied to a random environment and the continuous functions using LA. Their method random environment evaluates the applied action enhances local search in interesting regions or and gives fitness to the selected action of automata. intervals and reduces the whole searching space by The response of the environment is used by removing useless regions. automata to select its next action. This procedure is All aforesaid algorithms have some internal continued to reach the optimal action. LA has parameters with very important influence on the been used in several tasks of engineering problems search process of the method. Obviously an (for example graph partitioning [1] adaptive intelligent schedule for controlling these 937 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Gait Recognition Based on Human Leg Gesture Classification Jaber Roohi, Hadi Sadoghi Yazdi Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran E-mail: sadoghi@sttu.ac.ir Abstract: This paper presents a human gait recognition system based on a leg gesture separation. Main innovation in this paper includes gait recognition using leg gesture classification which gives a high precision recognition system. Five state of leg in human gait are extracted after background estimation and human detection in the scene. Leg gestures are classified over directional chain code of bottom part of silhouette contour. A spatio-temporal data base namely Energy Halation Image (EHI) is constructed over bottom part of human silhouette from train film sequence for five leg gestures separately. Eigen space of energy halation is applied to multilayer perceptron neural network. Five neural network system recognize people but with medium recognition rate. A neuro-fuzzy fusion technique is used for obtaining high recognition rate. Experimental results is performed over a suitable data base include 20 samples for eight person which each sample have 100 frames approximately. 99% recognition rate of the proposed system is obtained over 10 samples test patterns. Keywords: Human leg gesture separation; Gait recognition; Background estimation; Spatio- temporal data base; Neural network classifier; Neuro-fuzzy based classifier fusion. 1. Introduction has been identified as a major health issue in Australia [5]. In [6] automatic recognition of young-old gait types H UMAN GAIT is an important subject in various researches. Some of them attend to gait as a biometric feature in human identification problem [1]. Human gait recognition has attracted growing attention in video-based applications from their respective gait-patterns has been studied using support vector machine. Ageing influences gait patterns causing constant threats to control of locomotors balance. [2, 3]. Recent research has shown that individuals have Biomechanical analysis of gait has been successfully distinctive and special ways of walking and that human applied in human clinical gait analysis [7]. With regards gait recognition has many advantages as human gait is a to gait recognition, a major early result from Psychology biometric feature that may be captured from a great is by Johansson [8], who used point light displays to distance and gait has the advantage of being unobtrusive. demonstrate the ability of humans to rapidly distinguish Various applications exist for gait analysis as designing human locomotion from other motion patterns. Cutting of suitable recessed tactile surface [4]. and Kozlowski [9] showed that this ability also extends Tactile ground surface indicators installed on to recognition of friends. sidewalks help visually impaired people walk safely. The Identification of people by analysis of gait patterns visually impaired distinguish the indicators by stepping extracted from video has recently become a popular into its convexities and following them. However, these research problem. However, the conditions under which indicators sometimes cause the nonvisually impaired to the problem is “solvable” are not understood or stumble. In [4] have been studied effects of these characterized as are mentioned in [3]. The biggest indicators by comparing the kinematics and kinetic limitation in human motion analysis is the underlying variables of walking on paths with and without difficulty of tracking the human body for subsequent indicators. interpretation [10, and 11]. Another interest for gait identification is that of reflect So, we propose new approach without body parts gait degeneration due to ageing that might have closer tracking which fall into motion-based category. Main linkage to the causes of falls. This would help to innovation of the proposed method includes gait undertake appropriate measures to prevent falls. Like in recognition based of leg gesture classification. Leg many other developed countries, falls in older population gesture studies have various applications. In this among, some interest work indicates importance of leg gesture 949 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬
    • First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran 29-31 Aug 2007 Intelligent Systems Scientific Society of Iran Road Detection from High Resolution Satellite Imagery Using Texture Parameters in Neural Network M. Mokhtarzade PhD Student, K.N Toosi University of Technology, Geodesy and Geomatics Faculty (m_mokhtarzade@yahoo.com) H. Ebadi Assistant Professor, K.N Toosi University of Technology, Geodesy and Geomatics Faculty (Ebadi@kntu.ac.ir) M.J.Valadan Zoej Associate Professor, K.N Toosi University of Technology, Geodesy and Geomatics Faculty (ValadanZouj@kntu.ac.ir) Abstract: In this paper, neural networks are applied on high resolution IKONOS images for road detection. It was tried to optimize neural network's functionality using a variety of texture parameters with different window sizes and gray level numbers. Both the source image and pre-classified image were used for texture parameter extraction. The obtained results were compared in terms of road and background detection accuracy. It was concluded that using texture parameters from the source image could improve road detection ability of the neural networks, while using the results of texture analysis of the pre-classified image develops the background detection accuracy. Keywords: Road detection, texture parameters, co-occurrence matrix, neural networks, back propagation. A comprehensive review on the proposed 1 Introduction methods for road extraction could be found in [1] where these methods are categorized from High resolution commercial satellite lunches have different aspects and a broad reference list is made available imagery at resolutions close to presented. The idea of geometrical and that of aerial photographs, which can then be used topological analysis of high resolution binary in wide variety of applications such as preparing images for automatic vectorization of segmented and updating maps. road networks was presented in [2]. In [3] a new Extraction of the road networks was mostly fuzzy segmentation method is proposed for road carried out manually by the operators so far. detection in high resolution satellite images that However, considerable skill was necessary for needed only a few number of road samples. such operations, efficiency was never very high, Recently, the idea of using contextual information and this method is costly and time consuming. for improving segmentation process of road Road detection can be considered as the first step regions have been tested by many researchers. As in road extraction process and is defined as the a good example of exploiting texture information process of assigning a value to each pixel that can in road extraction, the research presented in [4] be used as a criterion to extinguish road and non- could be mentioned. Also, in [5], the road pixels. effectiveness of angular texture signature was Vigorous methods have been proposed for evaluated to discriminate between parking lots automatic and semi-automatic extraction of road and roads using high resolution satellite images. networks from satellite images. Recently, these In the present research, road detection is performed on high-resolution pan-sharpened methods are more focused on high resolution RGB Ikonos satellite images, using texture satellite images due to their outstanding parameters in artificial neural network characteristics in mapping from space. algorithms. At first, road detection has been performed using only spectral information. Then 955 ‫ﻫﺸﺘﻤﻴﻦ ﻛﻨﻔﺮاﻧﺲ ﺳﻴﺴﺘﻤﻬﺎي ﻫﻮﺷﻤﻨﺪ ، 9-7 ﺷﻬﺮﻳﻮر 6831 ، داﻧﺸﮕﺎه ﻓﺮدوﺳﻲ ﻣﺸﻬﺪ‬