Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In this article, we propose a new approach to solve intuitionistic fuzzy assignment
problem. Classical assignment problem deals with deterministic cost. In practical
situations it is not easy to determine the parameters. The parameters can be modeled
to fuzzy or intuitionistic fuzzy parameters. This paper develops an approach based on
diagonal optimal algorithm to solve an intuitionistic fuzzy assignment problem. A new
ranking procedure based on combined arithmetic mean is used to order the
intuitionistic fuzzy numbers so that Diagonal optimal algorithm [22] can be applied to
solve the intuitionistic fuzzy assignment problem. To illustrate the effectiveness of the
algorithm numerical examples were given..
Here is the first set of notes for the first class in Analysis of Algorithm. I added a dedicatory for my dear Fabi... she has showed me what real idealism is....
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In this article, we propose a new approach to solve intuitionistic fuzzy assignment
problem. Classical assignment problem deals with deterministic cost. In practical
situations it is not easy to determine the parameters. The parameters can be modeled
to fuzzy or intuitionistic fuzzy parameters. This paper develops an approach based on
diagonal optimal algorithm to solve an intuitionistic fuzzy assignment problem. A new
ranking procedure based on combined arithmetic mean is used to order the
intuitionistic fuzzy numbers so that Diagonal optimal algorithm [22] can be applied to
solve the intuitionistic fuzzy assignment problem. To illustrate the effectiveness of the
algorithm numerical examples were given..
Here is the first set of notes for the first class in Analysis of Algorithm. I added a dedicatory for my dear Fabi... she has showed me what real idealism is....
These are my note in the class of probabilistic analysis for the "average case" input. The look at:
1.- The use of the indicator function
2.- Enforcing the "Uniform Assumption"
At the end, we look at the application of the insertion sort average case.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
Symbolic Computation via Gröbner BasisIJERA Editor
The purpose of this paper is to find the orthogonal projection of a rational parametric curve onto a rational parametric surface in 3-space. We show that the orthogonal projection problem can be reduced to the problem of finding elimination ideals via Gröbnerbasis. We provide a computational algorithm to find the orthogonal projection, and include a few illustrative examples. The presented method is effective and potentially useful for many applications related to the design of surfaces and other industrial and research fields.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
Optimum Solution of Quadratic Programming Problem: By Wolfe’s Modified Simple...IJLT EMAS
In this paper, an alternative approach to the Wolfe’s
method for Quadratic Programming is suggested. Here we
proposed a new approach based on the iterative procedure for
the solution of a Quadratic Programming Problem by Wolfe’s
modified simplex method. The method sometimes involves less or
at the most an equal number of iteration as compared to
computational procedure for solving NLPP. We observed that
the rule of selecting pivot vector at initial stage and thereby for
some NLPP it takes more number of iteration to achieve
optimality. Here at the initial step we choose the pivot vector on
the basis of new rules described below. This powerful technique
is better understood by resolving a cycling problem.
The Analysis of Performance Measures of Generalized Trapezoidal Fuzzy Queuing...IJERA Editor
The purpose of this research paper was to propose a method which can be utilized to determine the different types of performance measures on the basis of the crisp values for the fuzzy queuing model which has an unreliable server and where the rate of arrival, the rate of service, the rate of breakdown and the rate of repair are all expressed as the fuzzy numbers. In this case the inter arrival time, the time of service, the rates of breakdown and the rates of repair are all triangular functions and are also expressed as the Trapezoidal fuzzy numbers. The main intent is to transform the fuzzy inter arrival time, the time of service, the rates of breakdown and the rates of repair into the crisp values by using the Ranking function method. Then the crisp values are applied in the classical formulas for the performance measure. In the fuzzy environment the ranking fuzzy numbers are very helpful in making the decisions. The ranking function method is one of the most reliable method, is simpler to apply in comparison to other methods and can be utilized to solve the different types of queuing problems. In this research paper a numerical example is also provided for both the triangular and the trapezoidal fuzzy number so that a practical insight into the problem can be provided.
Quadratic Programming : KKT conditions with inequality constraintsMrinmoy Majumder
In the case of Quadratic Programming for optimization, the objective function is a quadratic function. One of the techniques for solving quadratic optimization problems is KKT Conditions which is explained with an example in this tutorial.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
Addiction and Suicide Prevention - December 2012 Dawn Farm
“Addiction and Suicide Prevention” was presented on Tuesday December 18, 2012; by Raymond Dalton, MA; Dawn Farm therapist. There is an alarmingly high prevalence of suicide among people with addiction and people in early recovery. This program will raise awareness of the signs of suicidal thinking and describe ways to offer support and obtain help for people who may be contemplating suicide. Viewers will learn how to recognize suicidal thinking, reach out and offer support to others contemplating suicide, obtain help when suicidal thoughts are present, and access local and national suicide prevention and intervention resources. This program is part of the Dawn Farm Education Series, a FREE, annual workshop series developed to provide accurate, helpful, hopeful, practical, current information about chemical dependency, recovery, family and related issues. The Education Series is organized by Dawn Farm, a non-profit community of programs providing a continuum of chemical dependency services. For information, please see http://www.dawnfarm.org/programs/education-series.
These are my note in the class of probabilistic analysis for the "average case" input. The look at:
1.- The use of the indicator function
2.- Enforcing the "Uniform Assumption"
At the end, we look at the application of the insertion sort average case.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
Symbolic Computation via Gröbner BasisIJERA Editor
The purpose of this paper is to find the orthogonal projection of a rational parametric curve onto a rational parametric surface in 3-space. We show that the orthogonal projection problem can be reduced to the problem of finding elimination ideals via Gröbnerbasis. We provide a computational algorithm to find the orthogonal projection, and include a few illustrative examples. The presented method is effective and potentially useful for many applications related to the design of surfaces and other industrial and research fields.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
Optimum Solution of Quadratic Programming Problem: By Wolfe’s Modified Simple...IJLT EMAS
In this paper, an alternative approach to the Wolfe’s
method for Quadratic Programming is suggested. Here we
proposed a new approach based on the iterative procedure for
the solution of a Quadratic Programming Problem by Wolfe’s
modified simplex method. The method sometimes involves less or
at the most an equal number of iteration as compared to
computational procedure for solving NLPP. We observed that
the rule of selecting pivot vector at initial stage and thereby for
some NLPP it takes more number of iteration to achieve
optimality. Here at the initial step we choose the pivot vector on
the basis of new rules described below. This powerful technique
is better understood by resolving a cycling problem.
The Analysis of Performance Measures of Generalized Trapezoidal Fuzzy Queuing...IJERA Editor
The purpose of this research paper was to propose a method which can be utilized to determine the different types of performance measures on the basis of the crisp values for the fuzzy queuing model which has an unreliable server and where the rate of arrival, the rate of service, the rate of breakdown and the rate of repair are all expressed as the fuzzy numbers. In this case the inter arrival time, the time of service, the rates of breakdown and the rates of repair are all triangular functions and are also expressed as the Trapezoidal fuzzy numbers. The main intent is to transform the fuzzy inter arrival time, the time of service, the rates of breakdown and the rates of repair into the crisp values by using the Ranking function method. Then the crisp values are applied in the classical formulas for the performance measure. In the fuzzy environment the ranking fuzzy numbers are very helpful in making the decisions. The ranking function method is one of the most reliable method, is simpler to apply in comparison to other methods and can be utilized to solve the different types of queuing problems. In this research paper a numerical example is also provided for both the triangular and the trapezoidal fuzzy number so that a practical insight into the problem can be provided.
Quadratic Programming : KKT conditions with inequality constraintsMrinmoy Majumder
In the case of Quadratic Programming for optimization, the objective function is a quadratic function. One of the techniques for solving quadratic optimization problems is KKT Conditions which is explained with an example in this tutorial.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
Addiction and Suicide Prevention - December 2012 Dawn Farm
“Addiction and Suicide Prevention” was presented on Tuesday December 18, 2012; by Raymond Dalton, MA; Dawn Farm therapist. There is an alarmingly high prevalence of suicide among people with addiction and people in early recovery. This program will raise awareness of the signs of suicidal thinking and describe ways to offer support and obtain help for people who may be contemplating suicide. Viewers will learn how to recognize suicidal thinking, reach out and offer support to others contemplating suicide, obtain help when suicidal thoughts are present, and access local and national suicide prevention and intervention resources. This program is part of the Dawn Farm Education Series, a FREE, annual workshop series developed to provide accurate, helpful, hopeful, practical, current information about chemical dependency, recovery, family and related issues. The Education Series is organized by Dawn Farm, a non-profit community of programs providing a continuum of chemical dependency services. For information, please see http://www.dawnfarm.org/programs/education-series.
قائمة العشرة الأوائل لأخبار التكنولوجيا في مايو 2013MOTC Qatar
نحن نقرأ ونطلع على الأخبار المتعلقة بالتكنولوجيا والإنترنت لنوفر عليكم العناء في البحث عن آخر وأهم التطورات في هذا المجال. قائمة الأخبار لهذا الشهر تلقي الضوء على الأخبار التي كانت أكثر لفتا لأنظارنا. نتمنى أن تستمتعوا بالاطلاع على هذه الأخبار والتطورات، ولا تترددوا في مشاركتنا آرائكم ووجهات نظركم بالنسبة لآخر أخبار التكنولوجيا والإنترنت التي لفتت انتباهكم.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Antonin Léonard - Blogueur, Stratégiste, Co-Fondateur de la communauté OuiSha...TechnoArk
Présenté le 31 janvier 2014 lors de la Conférence TechnoArk 2014 à Sierre (CH) - "Internet, vecteur de l'économie du partage"-> www.technoark.ch/conference
Solving Fuzzy Maximal Flow Problem Using Octagonal Fuzzy NumberIJERA Editor
In this paper a general fuzzy maximal flow problem is discussed . A crisp maximal flow problem can be solved
in two methods : linear programming modeling and maximal flow algorithm . Here I tried to fuzzify the
maximal flow algorithm using octagonal fuzzy numbers introduced by S.U Malini and Felbin .C. kennedy [26].
By ranking the octagonal fuzzy numbers it is possible to compare them and using this we convert the fuzzy
valued maximal flow algorithm to a crisp valued algorithm . It is proved that a better solution is obtained when
it is solved using fuzzy octagonal number than when it is solved using trapezoidal fuzzy number . To illustrate
this a numerical example is solved and the obtained result is compared with the existing results . If there is no
uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp
maximal flow problems.
Solving Fuzzy Maximal Flow Problem Using Octagonal Fuzzy NumberIJERA Editor
In this paper a general fuzzy maximal flow problem is discussed . A crisp maximal flow problem can be solved
in two methods : linear programming modeling and maximal flow algorithm . Here I tried to fuzzify the
maximal flow algorithm using octagonal fuzzy numbers introduced by S.U Malini and Felbin .C. kennedy [26].
By ranking the octagonal fuzzy numbers it is possible to compare them and using this we convert the fuzzy
valued maximal flow algorithm to a crisp valued algorithm . It is proved that a better solution is obtained when
it is solved using fuzzy octagonal number than when it is solved using trapezoidal fuzzy number . To illustrate
this a numerical example is solved and the obtained result is compared with the existing results . If there is no
uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp
maximal flow problems.
A GENERALIZED SAMPLING THEOREM OVER GALOIS FIELD DOMAINS FOR EXPERIMENTAL DESIGNcscpconf
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
A Generalized Sampling Theorem Over Galois Field Domains for Experimental Des...csandit
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
KEY
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A PROBABILISTIC ALGORITHM OF COMPUTING THE POLYNOMIAL GREATEST COMMON DIVISOR...ijscmcj
In the earlier work, subresultant algorithm was proposed to decrease the coefficient growth in the Euclidean algorithm of polynomials. However, the output polynomial remainders may have a small factor which can be removed to satisfy our needs. Then later, an improved subresultant algorithm was given by representing the subresultant algorithm in another way, where we add a variant called 𝜏 to express the small factor. There was a way to compute the variant proposed by Brown, who worked at IBM. Nevertheless, the way failed to determine each𝜏 correctly.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Existence and Controllability Result for the Nonlinear First Order Fuzzy Neut...ijfls
In this paper, we devoted study the existence and controllability for the nonlinear fuzzy neutral integrodifferential equations with control system in E_N. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous and compactly supported interval fuzzy number. The results are obtained by using the contraction principle theorem. An example to illustrate the theory.
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called 𝜏 and gave a way to compute the variant. Nevertheless, the way failed to determine every 𝜏 correctly.
In this paper, we will give a probabilistic algorithm to determine the variant 𝜏 correctly in most cases by adding a few steps instead of computing 𝑡(𝑥) when given 𝑓(𝑥) and𝑔(𝑥) ∈ ℤ[𝑥], where 𝑡(𝑥) satisfies that 𝑠(𝑥)𝑓(𝑥) + 𝑡(𝑥)𝑔(𝑥) = 𝑟(𝑥), here 𝑡(𝑥), 𝑠(𝑥) ∈ ℤ[𝑥]
A LEAST ABSOLUTE APPROACH TO MULTIPLE FUZZY REGRESSION USING Tw- NORM BASED O...ijfls
A least absolute approach to multiple fuzzy regression using Tw-norm based arithmetic operations is
discussed by using the generalized Hausdorff metric and it is investigated for the crisp input- fuzzy output
data. A comparative study based on two data sets are presented using the proposed method using shape
preserving operations with other existing method.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
User_42751212015Module1and2pagestocompetework.pdf
User_42751212015Module1and2pagestocompetework_1.pdf
User_42751212015Module2Homework(CIS330).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].
Directions: Please complete each of the following exercises. Please read the instructions carefully.
For all “short programming assignments,” include source code files in your submission.
1. Short programming assignment. Combine the malloc2D function of program 3.16 with the adjacency matrix code of program 3.18 to write a program that allows the user to first enter the count of vertices, and then enter the graph edges. The program should then output the graph with lines of the form:
There is an edge between 0 and 3.
2. Short programming assignment. Modify your program for question 2.1 so that after the adjacency matrix is created, it is then converted to an adjacency list, and the output is generated from the list.
3. Short programming assignment. Modify program 4.7 from the text, overloading the == operator to work for this ADT using a friend function.
4. Is the ADT given in program 4.7 a first-class ADT? Explain your answer.
5. Suppose you are given the source code for a C++ class, and asked if the class shown is an ADT. On what factors would your decision be based?
6. How does using strings instead of simple types like integers alter the O-notation of operations?
User_42751212015Module1Homework(CIS330)Corrected (1).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].
Directions: Please refer to your textbook to complete the following exercises.1. Refer to page 12 of your text to respond to the following:Show the contents of the id array after each union operation when you use the quick find algorithm (Program I.I) to solve the connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of times the program accesses the id array for each input pair.2. Refer to page 12 of your text to respond to the following:Show the contents of the id array after each union operation when you use the quick union algorithm (Program I.I) to solve the connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of times the program accesses the id array for each input pair.3. Refer to figures 1.7 and 1.8 on pages 16 and 17 of the text. Give the contents of the id array after each union operation for the weighted quick union algorithm running on the examples corresponding to figures 1.7 and 1.84. For what value is N is 10N lg N>2N2 ...
A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretabi...IJECEIAES
In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binaryreal Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The approach is tested on two control examples: a single input single output (SISO) system and a multivariable (MIMO) system.
Similar to International Journal of Engineering Research and Development (20)
A Novel Method for Prevention of Bandwidth Distributed Denial of Service AttacksIJERD Editor
Distributed Denial of Service (DDoS) Attacks became a massive threat to the Internet. Traditional
Architecture of internet is vulnerable to the attacks like DDoS. Attacker primarily acquire his army of Zombies,
then that army will be instructed by the Attacker that when to start an attack and on whom the attack should be
done. In this paper, different techniques which are used to perform DDoS Attacks, Tools that were used to
perform Attacks and Countermeasures in order to detect the attackers and eliminate the Bandwidth Distributed
Denial of Service attacks (B-DDoS) are reviewed. DDoS Attacks were done by using various Flooding
techniques which are used in DDoS attack.
The main purpose of this paper is to design an architecture which can reduce the Bandwidth
Distributed Denial of service Attack and make the victim site or server available for the normal users by
eliminating the zombie machines. Our Primary focus of this paper is to dispute how normal machines are
turning into zombies (Bots), how attack is been initiated, DDoS attack procedure and how an organization can
save their server from being a DDoS victim. In order to present this we implemented a simulated environment
with Cisco switches, Routers, Firewall, some virtual machines and some Attack tools to display a real DDoS
attack. By using Time scheduling, Resource Limiting, System log, Access Control List and some Modular
policy Framework we stopped the attack and identified the Attacker (Bot) machines
Hearing loss is one of the most common human impairments. It is estimated that by year 2015 more
than 700 million people will suffer mild deafness. Most can be helped by hearing aid devices depending on the
severity of their hearing loss. This paper describes the implementation and characterization details of a dual
channel transmitter front end (TFE) for digital hearing aid (DHA) applications that use novel micro
electromechanical- systems (MEMS) audio transducers and ultra-low power-scalable analog-to-digital
converters (ADCs), which enable a very-low form factor, energy-efficient implementation for next-generation
DHA. The contribution of the design is the implementation of the dual channel MEMS microphones and powerscalable
ADC system.
Influence of tensile behaviour of slab on the structural Behaviour of shear c...IJERD Editor
-A composite beam is composed of a steel beam and a slab connected by means of shear connectors
like studs installed on the top flange of the steel beam to form a structure behaving monolithically. This study
analyzes the effects of the tensile behavior of the slab on the structural behavior of the shear connection like slip
stiffness and maximum shear force in composite beams subjected to hogging moment. The results show that the
shear studs located in the crack-concentration zones due to large hogging moments sustain significantly smaller
shear force and slip stiffness than the other zones. Moreover, the reduction of the slip stiffness in the shear
connection appears also to be closely related to the change in the tensile strain of rebar according to the increase
of the load. Further experimental and analytical studies shall be conducted considering variables such as the
reinforcement ratio and the arrangement of shear connectors to achieve efficient design of the shear connection
in composite beams subjected to hogging moment.
Gold prospecting using Remote Sensing ‘A case study of Sudan’IJERD Editor
Gold has been extracted from northeast Africa for more than 5000 years, and this may be the first
place where the metal was extracted. The Arabian-Nubian Shield (ANS) is an exposure of Precambrian
crystalline rocks on the flanks of the Red Sea. The crystalline rocks are mostly Neoproterozoic in age. ANS
includes the nations of Israel, Jordan. Egypt, Saudi Arabia, Sudan, Eritrea, Ethiopia, Yemen, and Somalia.
Arabian Nubian Shield Consists of juvenile continental crest that formed between 900 550 Ma, when intra
oceanic arc welded together along ophiolite decorated arc. Primary Au mineralization probably developed in
association with the growth of intra oceanic arc and evolution of back arc. Multiple episodes of deformation
have obscured the primary metallogenic setting, but at least some of the deposits preserve evidence that they
originate as sea floor massive sulphide deposits.
The Red Sea Hills Region is a vast span of rugged, harsh and inhospitable sector of the Earth with
inimical moon-like terrain, nevertheless since ancient times it is famed to be an abode of gold and was a major
source of wealth for the Pharaohs of ancient Egypt. The Pharaohs old workings have been periodically
rediscovered through time. Recent endeavours by the Geological Research Authority of Sudan led to the
discovery of a score of occurrences with gold and massive sulphide mineralizations. In the nineties of the
previous century the Geological Research Authority of Sudan (GRAS) in cooperation with BRGM utilized
satellite data of Landsat TM using spectral ratio technique to map possible mineralized zones in the Red Sea
Hills of Sudan. The outcome of the study mapped a gossan type gold mineralization. Band ratio technique was
applied to Arbaat area and a signature of alteration zone was detected. The alteration zones are commonly
associated with mineralization. The alteration zones are commonly associated with mineralization. A filed check
confirmed the existence of stock work of gold bearing quartz in the alteration zone. Another type of gold
mineralization that was discovered using remote sensing is the gold associated with metachert in the Atmur
Desert.
Reducing Corrosion Rate by Welding DesignIJERD Editor
The paper addresses the importance of welding design to prevent corrosion at steel. Welding is
used to join pipe, profiles at bridges, spindle, and a lot more part of engineering construction. The
problems happened associated with welding are common issues in these fields, especially corrosion.
Corrosion can be reduced with many methods, they are painting, controlling humidity, and also good
welding design. In the research, it can be found that reducing residual stress on the welding can be
solved in corrosion rate reduction problem.
Preheating on 500oC and 600oC give better condition to reduce corosion rate than condition after
preheating 400oC. For all welding groove type, material with 500oC and 600oC preheating after 14 days
corrosion test is 0,5%-0,69% lost. Material with 400oC preheating after 14 days corrosion test is 0,57%-0,76%
lost.
Welding groove also influence corrosion rate. X and V type welding groove give better condition to reduce
corrosion rate than use 1/2V and 1/2 X welding groove. After 14 days corrosion test, the samples with
X welding groove type is 0,5%-0,57% lost. The samples with V welding groove after 14 days corrosion test is
0,51%-0,59% lost. The samples with 1/2V and 1/2X welding groove after 14 days corrosion test is 0,58%-
0,71% lost.
Router 1X3 – RTL Design and VerificationIJERD Editor
Routing is the process of moving a packet of data from source to destination and enables messages
to pass from one computer to another and eventually reach the target machine. A router is a networking device
that forwards data packets between computer networks. It is connected to two or more data lines from different
networks (as opposed to a network switch, which connects data lines from one single network). This paper,
mainly emphasizes upon the study of router device, it‟s top level architecture, and how various sub-modules of
router i.e. Register, FIFO, FSM and Synchronizer are synthesized, and simulated and finally connected to its top
module.
Active Power Exchange in Distributed Power-Flow Controller (DPFC) At Third Ha...IJERD Editor
This paper presents a component within the flexible ac-transmission system (FACTS) family, called
distributed power-flow controller (DPFC). The DPFC is derived from the unified power-flow controller (UPFC)
with an eliminated common dc link. The DPFC has the same control capabilities as the UPFC, which comprise
the adjustment of the line impedance, the transmission angle, and the bus voltage. The active power exchange
between the shunt and series converters, which is through the common dc link in the UPFC, is now through the
transmission lines at the third-harmonic frequency. DPFC multiple small-size single-phase converters which
reduces the cost of equipment, no voltage isolation between phases, increases redundancy and there by
reliability increases. The principle and analysis of the DPFC are presented in this paper and the corresponding
simulation results that are carried out on a scaled prototype are also shown.
Mitigation of Voltage Sag/Swell with Fuzzy Control Reduced Rating DVRIJERD Editor
Power quality has been an issue that is becoming increasingly pivotal in industrial electricity
consumers point of view in recent times. Modern industries employ Sensitive power electronic equipments,
control devices and non-linear loads as part of automated processes to increase energy efficiency and
productivity. Voltage disturbances are the most common power quality problem due to this the use of a large
numbers of sophisticated and sensitive electronic equipment in industrial systems is increased. This paper
discusses the design and simulation of dynamic voltage restorer for improvement of power quality and
reduce the harmonics distortion of sensitive loads. Power quality problem is occurring at non-standard
voltage, current and frequency. Electronic devices are very sensitive loads. In power system voltage sag,
swell, flicker and harmonics are some of the problem to the sensitive load. The compensation capability
of a DVR depends primarily on the maximum voltage injection ability and the amount of stored
energy available within the restorer. This device is connected in series with the distribution feeder at
medium voltage. A fuzzy logic control is used to produce the gate pulses for control circuit of DVR and the
circuit is simulated by using MATLAB/SIMULINK software.
Study on the Fused Deposition Modelling In Additive ManufacturingIJERD Editor
Additive manufacturing process, also popularly known as 3-D printing, is a process where a product
is created in a succession of layers. It is based on a novel materials incremental manufacturing philosophy.
Unlike conventional manufacturing processes where material is removed from a given work price to derive the
final shape of a product, 3-D printing develops the product from scratch thus obviating the necessity to cut away
materials. This prevents wastage of raw materials. Commonly used raw materials for the process are ABS
plastic, PLA and nylon. Recently the use of gold, bronze and wood has also been implemented. The complexity
factor of this process is 0% as in any object of any shape and size can be manufactured.
Spyware triggering system by particular string valueIJERD Editor
This computer programme can be used for good and bad purpose in hacking or in any general
purpose. We can say it is next step for hacking techniques such as keylogger and spyware. Once in this system if
user or hacker store particular string as a input after that software continually compare typing activity of user
with that stored string and if it is match then launch spyware programme.
A Blind Steganalysis on JPEG Gray Level Image Based on Statistical Features a...IJERD Editor
This paper presents a blind steganalysis technique to effectively attack the JPEG steganographic
schemes i.e. Jsteg, F5, Outguess and DWT Based. The proposed method exploits the correlations between
block-DCTcoefficients from intra-block and inter-block relation and the statistical moments of characteristic
functions of the test image is selected as features. The features are extracted from the BDCT JPEG 2-array.
Support Vector Machine with cross-validation is implemented for the classification.The proposed scheme gives
improved outcome in attacking.
Secure Image Transmission for Cloud Storage System Using Hybrid SchemeIJERD Editor
- Data over the cloud is transferred or transmitted between servers and users. Privacy of that
data is very important as it belongs to personal information. If data get hacked by the hacker, can be
used to defame a person’s social data. Sometimes delay are held during data transmission. i.e. Mobile
communication, bandwidth is low. Hence compression algorithms are proposed for fast and efficient
transmission, encryption is used for security purposes and blurring is used by providing additional
layers of security. These algorithms are hybridized for having a robust and efficient security and
transmission over cloud storage system.
Application of Buckley-Leverett Equation in Modeling the Radius of Invasion i...IJERD Editor
A thorough review of existing literature indicates that the Buckley-Leverett equation only analyzes
waterflood practices directly without any adjustments on real reservoir scenarios. By doing so, quite a number
of errors are introduced into these analyses. Also, for most waterflood scenarios, a radial investigation is more
appropriate than a simplified linear system. This study investigates the adoption of the Buckley-Leverett
equation to estimate the radius invasion of the displacing fluid during waterflooding. The model is also adopted
for a Microbial flood and a comparative analysis is conducted for both waterflooding and microbial flooding.
Results shown from the analysis doesn’t only records a success in determining the radial distance of the leading
edge of water during the flooding process, but also gives a clearer understanding of the applicability of
microbes to enhance oil production through in-situ production of bio-products like bio surfactans, biogenic
gases, bio acids etc.
Gesture Gaming on the World Wide Web Using an Ordinary Web CameraIJERD Editor
- Gesture gaming is a method by which users having a laptop/pc/x-box play games using natural or
bodily gestures. This paper presents a way of playing free flash games on the internet using an ordinary webcam
with the help of open source technologies. Emphasis in human activity recognition is given on the pose
estimation and the consistency in the pose of the player. These are estimated with the help of an ordinary web
camera having different resolutions from VGA to 20mps. Our work involved giving a 10 second documentary to
the user on how to play a particular game using gestures and what are the various kinds of gestures that can be
performed in front of the system. The initial inputs of the RGB values for the gesture component is obtained by
instructing the user to place his component in a red box in about 10 seconds after the short documentary before
the game is finished. Later the system opens the concerned game on the internet on popular flash game sites like
miniclip, games arcade, GameStop etc and loads the game clicking at various places and brings the state to a
place where the user is to perform only gestures to start playing the game. At any point of time the user can call
off the game by hitting the esc key and the program will release all of the controls and return to the desktop. It
was noted that the results obtained using an ordinary webcam matched that of the Kinect and the users could
relive the gaming experience of the free flash games on the net. Therefore effective in game advertising could
also be achieved thus resulting in a disruptive growth to the advertising firms.
Hardware Analysis of Resonant Frequency Converter Using Isolated Circuits And...IJERD Editor
-LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region[5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits.
Simulated Analysis of Resonant Frequency Converter Using Different Tank Circu...IJERD Editor
LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region [5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits. The supported simulation
is done through PSIM 6.0 software tool
Amateurs Radio operator, also known as HAM communicates with other HAMs through Radio
waves. Wireless communication in which Moon is used as natural satellite is called Moon-bounce or EME
(Earth -Moon-Earth) technique. Long distance communication (DXing) using Very High Frequency (VHF)
operated amateur HAM radio was difficult. Even with the modest setup having good transceiver, power
amplifier and high gain antenna with high directivity, VHF DXing is possible. Generally 2X11 YAGI antenna
along with rotor to set horizontal and vertical angle is used. Moon tracking software gives exact location,
visibility of Moon at both the stations and other vital data to acquire real time position of moon.
“MS-Extractor: An Innovative Approach to Extract Microsatellites on „Y‟ Chrom...IJERD Editor
Simple Sequence Repeats (SSR), also known as Microsatellites, have been extensively used as
molecular markers due to their abundance and high degree of polymorphism. The nucleotide sequences of
polymorphic forms of the same gene should be 99.9% identical. So, Microsatellites extraction from the Gene is
crucial. However, Microsatellites repeat count is compared, if they differ largely, he has some disorder. The Y
chromosome likely contains 50 to 60 genes that provide instructions for making proteins. Because only males
have the Y chromosome, the genes on this chromosome tend to be involved in male sex determination and
development. Several Microsatellite Extractors exist and they fail to extract microsatellites on large data sets of
giga bytes and tera bytes in size. The proposed tool “MS-Extractor: An Innovative Approach to extract
Microsatellites on „Y‟ Chromosome” can extract both Perfect as well as Imperfect Microsatellites from large
data sets of human genome „Y‟. The proposed system uses string matching with sliding window approach to
locate Microsatellites and extracts them.
Importance of Measurements in Smart GridIJERD Editor
- The need to get reliable supply, independence from fossil fuels, and capability to provide clean
energy at a fixed and lower cost, the existing power grid structure is transforming into Smart Grid. The
development of a smart energy distribution grid is a current goal of many nations. A Smart Grid should have
new capabilities such as self-healing, high reliability, energy management, and real-time pricing. This new era
of smart future grid will lead to major changes in existing technologies at generation, transmission and
distribution levels. The incorporation of renewable energy resources and distribution generators in the existing
grid will increase the complexity, optimization problems and instability of the system. This will lead to a
paradigm shift in the instrumentation and control requirements for Smart Grids for high quality, stable and
reliable electricity supply of power. The monitoring of the grid system state and stability relies on the
availability of reliable measurement of data. In this paper the measurement areas that highlight new
measurement challenges, development of the Smart Meters and the critical parameters of electric energy to be
monitored for improving the reliability of power systems has been discussed.
Study of Macro level Properties of SCC using GGBS and Lime stone powderIJERD Editor
One of the major environmental concerns is the disposal of the waste materials and utilization of
industrial by products. Lime stone quarries will produce millions of tons waste dust powder every year. Having
considerable high degree of fineness in comparision to cement this material may be utilized as a partial
replacement to cement. For this purpose an experiment is conducted to investigate the possibility of using lime
stone powder in the production of SCC with combined use GGBS and how it affects the fresh and mechanical
properties of SCC. First SCC is made by replacing cement with GGBS in percentages like 10, 20, 30, 40, 50 and
by taking the optimum mix with GGBS lime stone powder is blended to mix in percentages like 5, 10, 15, 20 as
a partial replacement to cement. Test results shows that the SCC mix with combination of 30% GGBS and 15%
limestone powder gives maximum compressive strength and fresh properties are also in the limits prescribed by
the EFNARC.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
Have you ever wanted a Ruby client API to communicate with your web service? Smithy is a protocol-agnostic language for defining services and SDKs. Smithy Ruby is an implementation of Smithy that generates a Ruby SDK using a Smithy model. In this talk, we will explore Smithy and Smithy Ruby to learn how to generate custom feature-rich SDKs that can communicate with any web service, such as a Rails JSON API.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
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GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Elevating Tactical DDD Patterns Through Object Calisthenics
International Journal of Engineering Research and Development
1. International Journal of Engineering Research and Development
e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com
Volume 9, Issue 7 (January 2014), PP. 40-49
Solution of Fuzzy Maximal Flow Network Problem Based
on Generalized Trapezoidal Fuzzy Numbers with Rank
and Mode
M. K. Alam1, M. K. Hasan2
1
Lecturer in Mathematics, Department of Mathematics and Statistics, Bangladesh University of Business and
Technology, Dhaka, Bangladesh.
2
Assistant Professor of Mathematics, Department of Mathematics and Statistics, Bangladesh University of
Business and Technology, Dhaka, Bangladesh.
Abstract:- Network-flow problems can be solved by several methods. Labeling techniques can be used to solve
wide variety of network problems. A new algorithm to find the fuzzy maximal flow between source and sink
was proposed by Kumar et el. [19]. They have represented normal triangular fuzzy numbers as network flow. It
is not possible to restrict the membership function to the normal form and proposed the concept of generalized
fuzzy numbers in many cases [8]. Generalized trapezoidal fuzzy numbers for solving the maximal flow network
problems have been used by Kumar [21]. In this paper, we have modified the existing algorithm to find fuzzy
maximal network flow between source and sink for generalized trapezoidal fuzzy number. Ranking and mode
function to find the highest flow for maximum flow path of generalized trapezoidal fuzzy number has been
applied. A numerical example has been solved by the proposed algorithm and the other results are discussed.
Mathematica programs have been applied for various arithmetic operations.
Keywords:- Mode and Ranking function, Normal Trapezoidal Fuzzy Numbers, Generalized Trapezoidal Fuzzy
Numbers, Fuzzy Maximal Flow Problem, Fuzzy Residue.
I.
INTRODUCTION
In 1965 Zadeh [30] introduced the concept of fuzzy set theory. Fuzzy set can provided solution to
vast range of scientific problems. When the estimation of a system coefficient is imprecise and only
some vague knowledge about the actual value of the parameters is available, it may be convenient to
represent some or all of them with fuzzy numbers [30]. Fuzzy numbers are fuzzy subsets of the set of real
numbers satisfying some additional conditions. Arithmetic operations on fuzzy numbers have also been
developed according to the extension principle based on interval arithmetic [24]. Fuzzy numbers allow us to
make
the
mathematical
model
of
logistic
variable
or
fuzzy
environment.
Opposite and reverse fuzzy numbers have not been shown by Dubois [13] and Yager [29] on the
sense of group structure. Some of the interesting arithmetic works on fuzzy numbers are discussed by Dubois
[14]. Arithmetic behavior of trapezoidal fuzzy numbers is not widely discussed in the literature. The aims
of this paper to stimulate the inclusion of trapezoidal fuzzy numbers in applied engineering and scientific
problems by extending the concept of traditional algebra into fuzzy set theory, which is described by Bansal [3].
A method for ranking of generalized trapezoidal fuzzy numbers is studied by Chen [9]. Abbasbandy [1] has
introduced a new approach for ranking of trapezoidal fuzzy numbers based on the rank, mode, left and right
spreads at some-levels of trapezoidal fuzzy numbers.
The maximum flow problem is one of basic problems for combinatorial optimization in weighted
directed graphs. In the real life situation very useful models in a number of practical contexts including
communication networks, oil pipeline systems, power systems, costs, capacities and demands are constructed by
the base of maximal flow network problem. Fulkerson [15] provided the maximal flow problem and solved by
the simplex method for the linear programming. The maximal flow problem have been solved by Ford [14]
using augmenting path algorithm. This algorithm has been used to solve the crisp maximal flow problems [2],
[4], [26]. Fuzzy numbers represent the parameters of maximal flow problems. Kim [17] is one of the first
introducer on this subject. Chanas [5], [6], [7] approached this problem using minimum costs technique. An
algorithm for a network with crisp stricter was presented by Chanas in their first paper. In their second paper
they proposed that the flow was a real number and the capacities have upper and lower bounds had been
discussed [6]. In their third paper, they had also studied the integer flow and proposed an algorithm [8]. Intervalvalued versions of the max-flow min cut theorem and Karp-Edmonds algorithm was developed by Diamond
[11]. Some times it arise uncertain environment. The network flow problems using fuzzy numbers were
investigated by Liu [23]. Generalized fuzzy versions of maximum flow problem were considered by Ji [16]
40
2. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
with respect to arc capacity as fuzzy variables. A new algorithm to find fuzzy maximal flow between source and
sink is proposed by Kumar et al. [19] with the help of ranking function.
In this paper the existing algorithm [19] have been modified to find fuzzy maximal flow between
source and sink by representing all the parameters considered as generalized trapezoidal fuzzy numbers. To
illustrate the modified algorithm, a numerical example is solved. If there is no uncertainty about the flow
between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.
But when we face same rank more than one arc then we have applied mode function for selected maximal flow
path. In section 2 we have discussed some basic definitions, ranking function, mode function and arithmetic
operations for interval and generalized trapezoidal fuzzy numbers. In section 3 we have proposed an algorithm
for solving fuzzy maximal flow problems. In section 4 we have applied the proposed algorithm over a numerical
example. In section 5 and 6 we have discussed results and conclusion respectively.
II.
PRELIMINARIES
In this section some basic definitions, ranking function, mode function and arithmetic operations are
reviewed
1.1.
Definition [13]: Let 𝑋 be a universal classical set of objects and a characteristic function 𝜇 𝐴 of a
classical set 𝐴 ⊆ 𝑋 assigns a value either 0 or 1 i.e.
1 if 𝑥 ∈ 𝐴
𝜇𝐴 𝑥 =
.
0 if 𝑥 ∉ 𝐴
This function can be generalized to a function 𝜇 𝐴 such that the value assigned to the element of the
universal set 𝑋 fall within a specified range unit interval 0,1 i.e. 𝜇 𝐴 : 𝑋 → 0,1 . The assigned values indicate
the membership grade of the element in the set 𝐴. The function 𝜇 𝐴 is called membership function and the set
𝐴 = 𝑥, 𝜇 𝐴 𝑥 ; 𝑥 ∈ 𝑋 defined by 𝜇 𝐴 𝑥 for all 𝑥 ∈ 𝑋 is called fuzzy set.
1.2.
Remark: Throughout this paper we shall write fuzzy set 𝜇.
1.3.
Definition [18]: Suppose 𝜇 is a fuzzy set. Then for any 𝛼 ∈ 0,1 , the level set (or 𝜶 𝒄𝒖𝒕) of 𝜇 is
denoted by 𝜇 𝛼 and defined by 𝜇 𝛼 = 𝑥 ∈ 𝑋: 𝜇 𝑥 ≥ 𝛼 .
1.4.
Definition: [27] The special significance is fuzzy sets that are defined on the set ℝ of real number is
membership functions of these sets, which have the form 𝜇: ℝ → 0,1 is called fuzzy number if the following
axioms are satisfies:
𝜇 must be normal fuzzy set i.e. there exist 𝑥 ∈ ℝ; 𝜇 𝑥 = 1
𝜇 𝛼 must be closed interval of real number, for every 𝛼 ∈ 0,1
the support of 𝜇 must be bounded and compact i.e. 𝑥 ∈ ℝ; 𝜇 𝑥 > 0 is bounded and compact.
Fuzzy number is denoted by 𝐹 ℝ .
1.5.
Remark: Every fuzzy number is convex fuzzy sets. Also a fuzzy set 𝜇 is convex if for all 𝑥, 𝑦 ∈ 𝑋;
𝜇 𝑘𝑥 + 1 − 𝑘 𝑦 ≥ min 𝜇 𝑥 , 𝜇 𝑦 , for all 𝑘 ∈ 0, 1 .
1.6.
Arithmetic Operations
In this section, we shall define addition and subtraction between two intervals.
Let 𝑎, 𝑏 and 𝑐, 𝑑 be two closed interval, then
Addition: 𝑎, 𝑏 + 𝑐, 𝑑 = 𝑎 + 𝑐, 𝑏 + 𝑑 , Additive inverse: − 𝑎, 𝑏 = −𝑏, −𝑎
Subtraction: 𝑎, 𝑏 − 𝑐, 𝑑 = 𝑎, 𝑏 + − 𝑐, 𝑑 = 𝑎, 𝑏 + −𝑑, −𝑐 = 𝑎 − 𝑑, 𝑏 − 𝑐
1.7.
Definition: [10] A fuzzy number 𝐴 = 𝑎, 𝑏, 𝑐, 𝑑 is said to be a trapezoidal fuzzy numbers if its
membership function is given by
0 ; −∞ < 𝑥 ≤ 𝑎
𝑥− 𝑎
; 𝑎≤ 𝑥< 𝑏
𝑏− 𝑎
1 ; 𝑏 ≤ 𝑥 ≤ 𝑐 , where 𝑎, 𝑏, 𝑐, 𝑑 ∈ ℝ
𝜇 𝑥 =
𝑥− 𝑑
; 𝑐< 𝑥≤ 𝑑
𝑐− 𝑑
0 ; 𝑑≤ 𝑥<∞
.
1.8.
Definition: [10] A fuzzy number 𝐴 = 𝑎, 𝑏, 𝑐, 𝑑; 𝑤 is said to be a generalized trapezoidal fuzzy
number if its membership function is given by
41
3. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
𝜇 𝑥 =
0 ; −∞ < 𝑥 ≤ 𝑎
𝑤 𝑥− 𝑎
; 𝑎≤ 𝑥< 𝑏
𝑏− 𝑎
𝑤 ; 𝑏≤ 𝑥≤ 𝑐
𝑤 𝑥− 𝑑
; 𝑐< 𝑥≤ 𝑑
𝑐− 𝑑
0 ; 𝑑≤ 𝑥<∞
where 𝑎, 𝑏, 𝑐, 𝑑 ∈ ℝ and 𝑤 ∈ 0, 1
Arithmetic Operations
In this subsection, arithmetic operations between two generalized trapezoidal fuzzy number, defined on
universal set of real numbers ℝ, are reviewed by Chen [10].
Let 𝐴 = 𝑎1 , 𝑏1 , 𝑐1 , 𝑑1 ; 𝑤1 and 𝐵 = 𝑎2 , 𝑏2 , 𝑐2 , 𝑑2 ; 𝑤2 be two generalized trapezoidal fuzzy numbers then
𝐴 + 𝐵 = 𝑎1 + 𝑎2 , 𝑏1 + 𝑏2 , 𝑐1 + 𝑐2 , 𝑑1 + 𝑑2 ; min 𝑤1 , 𝑤2
𝐴 − 𝐵 = 𝑎1 − 𝑑2 , 𝑏1 − 𝑐2 , 𝑐1 − 𝑏2 , 𝑑1 − 𝑎2 ; min 𝑤1 , 𝑤2
1.9.
Ranking function
A convenient method for comparing of fuzzy number is by use of ranking function [22]. A ranking
function ℜ: 𝐹 ℝ → ℝ, where 𝐹 ℝ is set of all fuzzy numbers defined on set of real numbers, which maps each
fuzzy number in to a real number. Let 𝐴 = 𝑎1 , 𝑏1 , 𝑐1 , 𝑑1 ; 𝑤1 and 𝐵 = 𝑎2 , 𝑏2 , 𝑐2 , 𝑑2 ; 𝑤2 be two
generalized trapezoidal fuzzy numbers then
𝑤 𝑎 + 𝑏 + 𝑐 + 𝑑
𝑤 𝑎 + 𝑏 + 𝑐 + 𝑑
ℜ 𝐴 = 1 1 1 1 1 and ℜ 𝐵 = 2 2 2 2 2 .
4
4
Mathematica function for rank calculation:
𝒛[[𝟓]] ∗ (𝒛[[𝟏]] + 𝒛[[𝟐]] + 𝒛[[𝟑]] + 𝒛[[𝟒]])
𝒓𝒂[𝐳_]: =
𝟒
1.9.1. If ℜ 𝐴 > 𝑅 𝐵 then we say 𝐴 ≻ 𝐵
1.9.2. If ℜ 𝐴 < 𝑅 𝐵 then we say 𝐴 ≺ 𝐵
1.9.3. If ℜ 𝐴 = ℜ 𝐵 then we say 𝐴 ≈ 𝐵
1.10.
Mode function
When two generalized fuzzy number 𝐴 ≈ 𝐵 with respect to ranking function then we will apply mode
function for maximum flow position. A mode function 𝑀: 𝐹 ℝ → ℝ, where 𝐹 ℝ is set of all fuzzy numbers
defined on set of real numbers, which maps each fuzzy number in to a real number [20]. Let
𝐴 = 𝑎1 , 𝑏1 , 𝑐1 , 𝑑1 ; 𝑤1 and 𝐵 = 𝑎2 , 𝑏2 , 𝑐2 , 𝑑2 ; 𝑤2 be two generalized trapezoidal fuzzy numbers then
𝑀 𝐴 =
𝑤 1 𝑏 1 + 𝑐1
2
and
𝑀 𝐵 =
𝑤 2 𝑏 2 + 𝑐2
2
Mathematica function for mode calculation,
III.
.
𝑚𝑜𝑑[z_]: =
𝑧[[5]]∗(𝑧[[2]]+𝑧[[3]])
2
ALGORITHM
Chen has proposed that it is not possible to control the membership function to the normal form, in
some case [8]. He also proposed the concept of generalize fuzzy numbers. The normal form of trapezoidal
fuzzy number ware used by various papers for solving real life problems. In this paper, we will use generalized
trapezoidal fuzzy number for network flow. In the section the maximal flow network problem is modified to
find fuzzy maximal flow between sources and sink for generalized trapezoidal fuzzy numbers. The proposed
algorithm is direct extension of existing algorithm [26], [25]. The fuzzy maximal flow algorithm is based on
finding breakthrough paths with net positive flow between the source and sink nodes. Consider arc 𝑖, 𝑗 with
initial fuzzy capacities 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 and fuzzy residuals capacities (or remaining fuzzy capacities) 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 .
For a node 𝑗 that receives flow from node 𝑖, we will a label 𝜇𝑎 𝑗 , 𝑖 , where 𝜇𝑎 𝑗 is the fuzzy flow from node 𝑖 to
𝑗. The step of algorithm for generalized trapezoidal fuzzy number are summarized as follows:
1.11.
Step 1 For all arcs 𝑖, 𝑗 , set the residual fuzzy capacity is equal to initial fuzzy capacity i.e.,
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 = 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 . Let 𝜇𝑎1 = ∞, ∞, ∞, ∞; 1 and label the source node 1 with ∞, ∞, ∞, ∞; 1 , − . Set
𝑖 = 1, and go to step 2.
1.12.
Step 2 Determine 𝑆 𝑖 , the set of unlabeled nodes 𝑗 that can be reached directly from node 𝑖 by arcs with
positive residuals capacity (i.e., 𝜇𝑐 𝑖𝑗 is non-negative fuzzy number for each 𝑗 ∈ 𝑆 𝑖 ). If 𝑆 𝑖 = ∅ then go to step 4,
otherwise go to step 3.
1.13.
Step 3 Determine 𝑘 ∈ 𝑆 𝑖 such that
max ℜ 𝜇𝑐 𝑖𝑗 = ℜ 𝜇𝑐 𝑖𝑘
𝑗 ∈𝑆 𝑖
42
4. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
Set 𝜇𝑎 𝑘 = 𝜇𝑐 𝑖𝑘 and label node 𝑘 with 𝜇𝑎 𝑘 , 𝑖 . If 𝑘 = 𝑛, the sink node has been labeled, and a breakthrough path
is found, then go to step 5. Otherwise go to step 2.
Again, if max 𝑗 ∈𝑆 𝑖 ℜ 𝜇𝑐 𝑖𝑗 is more than one fuzzy flow then we have applied mode test for maximal flow
according to maximal rank test.
Mathematica program for breakthrough path according to rank and mode
1.14.
Seep 4 If 𝑖 = 1, no breakthrough is possible, then go to step 6. Otherwise, let 𝑟 be the node that has
been labeled immediately before current node 𝑖 and remove 𝑖 from the set of nodes adjacent to 𝑟. Set 𝑖 = 𝑟 and
go to step 2.
1.15.
Step 5 Let 𝑁 𝑝 = 1, 𝑘1 , 𝑘2 , … … … , 𝑛 define the nodes of the 𝑝 𝑡ℎ breakthrough path from source node
1 to sink node 𝑛. Then the maximal flow along the path is completed as 𝜇 𝑝 = min 𝜇1 , 𝜇 𝑘 1 , 𝜇 𝑘 2 , … … … , 𝜇 𝑛 .
Mathematica function for maximal flaw for a path is 𝑓𝑙𝑜𝑤 = {𝑟[𝑓01], 𝑟[𝑓12], 𝑟[𝑓24], 𝑟[𝑓45]}; 𝑓𝜇𝑎 =
Min[𝑓𝑙𝑜𝑤]. The residual capacity of each arc along the breakthrough path is decreased by 𝜇 𝑝 in the direction of
the flow and increased by 𝜇 𝑝 in the reverse direction i.e. for nodes 𝑖 and 𝑗 on the path, the residual flow id
change from the current 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 to
1.15.1. Case 1 We shall compute 𝜇𝑐 𝑖𝑗 − 𝜇 𝑝 , 𝜇𝑐 𝑗𝑖 + 𝜇 𝑝 if the flow is from 𝑖 to 𝑗.
1.15.2. Case 2 We shall compute 𝜇𝑐 𝑖𝑗 + 𝜇 𝑝 , 𝜇𝑐 𝑗𝑖 − 𝜇 𝑝 if the flow is from 𝑗 to 𝑖.
Mathematica function for residual capacity calculation
43
5. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
1.16.
Step 6 In the step we will determine flow and residue.
1.16.1. Given that total numbers of breakthrough paths are m. Then we get total flow of a network by
determining: 𝐹 = 𝜇1 + 𝜇2 + 𝜇3 + ⋯ + 𝜇 𝑚 , where m is the number of iteration.
Mathematica function for total flow calculation
1.16.2. Using the initial and final fuzzy residuals of arc 𝑖, 𝑗 are
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 and
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 respectively, the
fuzzy optimal flow in arc 𝑖, 𝑗 is computed as follows: Let 𝛼, 𝛽 = 𝜇𝑐 𝑖𝑗 − 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 − 𝜇𝑐 𝑗𝑖 . If ℜ 𝛼 > 0
then the fuzzy optimal flow from 𝑖 to 𝑗 is 𝛼. Otherwise, if ℜ 𝛽 > 0 then the fuzzy optimal flow from 𝑗 to 𝑖 is
𝛽.
Mathematica function for decision flow direction
IV.
ILLUSTRATIVE EXAMPLE
In this section the proposed algorithm is illustrated by solving a numerical example.
Example Consider the network shown in the figure 1. We will find out the fuzzy maximal flow between source
node 1 and destination node 5.
Iteration 1: Set the initial fuzzy residual 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 equal to the initial fuzzy capacity
flow from the given network according to Mathematica:
44
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 . Input of all
6. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
Remarks: First four entries of each vector represents trapezoidal fuzzy number and fifth entry is value
of 𝑤 for generalize trapezoidal fuzzy number. We have used “,” in replace of “;” for calculation in Mathematica.
Also we have used “{}” in replace of “[[ ]]” for fuzzy number to calculation in Mathematica. Also 𝐨𝐟𝛍 and 𝐟𝛍
represent initial and residual flow respectively. Any bold Mathematica texts are input and other texts are output.
In Mahtematica 𝐫𝐚𝐟𝛍 represents rank test function, 𝐦𝐨𝐟𝛍 represents mode test function, 𝐫𝐞𝐬𝐞𝐝𝐮𝐞 represents
residue function, 𝐭𝐨𝐭𝐚𝐥𝐟𝐥𝐨𝐰 represents flow addition function and 𝐟𝐥𝐨𝐰𝐝𝐢𝐫𝐞𝐜𝐭𝐢𝐨𝐧 represents flow direction
function.
Step 1: Set f01={Infinity,Infinity,Infinity,Infinity,1} in Mathematica format i.e.
{∞,∞,∞,∞,1} and label node 1 with (f01,-). Set 𝑖 = 1.
Step 2: 𝑆1 = 2, 3, 4 ≠ 𝜑.
Step 3: We are calculating maximum ranking of the generalized trapezoidal fuzzy number using Mathematica
program which defined raf𝝁 in section 3.3.
so, set 𝑘 = 2 and 𝜇𝑎2 = 𝜇𝑐12 = fμ12 = 0,7,22,38; .7 and label node 2 with fμ12, 1 . Set 𝑖 = 2 and repeat
step 2.
Step 2: 𝑆2 = 4, 5 .
Step 3: raf[f24,f25,f0]
theri ranks are {16.25,16.25,0}, maximum rank are both at 1st {8,12,20,25,1.} and 2n position
{12,20,38,60,0.5} so we need mode test. mof [f24,f25,f0]
their mods are {16.,14.5,0}, maximum mode is 1st position which is {8,12,20,25,1.}
so set 𝑘 = 4 and 𝜇𝑎4 = 𝜇𝑐24 = fμ24 = 8,12,20,25; 1 . Now label node 4 with fμ24,2 . Set 𝑖 = 4 and
repeat step 2.
Step 2: 𝑆4 = 3,5 .
Step 3: raf [f43,f45,f0] output: theri ranks are {45.,45.,0} maximum rank are both 1st {20,40,60,80,0.9}
and 2n position {30,150,180,240,0.3} so we need mode test. mof [f43,f45,f0] output: their mods are
{45.,49.5,0} maximum mode is 2nd position which is {30,150,180,240,0.3}.
so, set 𝑘 = 5 and 𝜇𝑎5 = 𝜇𝑐45 = fμ45 = 30, 150, 180, 240; .3 . Now label sink node 5 with fμ45,4 . We
have reached the sink node 5, and so a breakthrough path is found. Go to step 5.
Step 5: The breakthrough path is 1 → 2 → 4 → 5 and 𝑁1 = 1,2,4,5 ,
Mathematica script:
45
7. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
We have calculated the fuzzy residual capacities along path 𝑁1 are (using Mathematica program which
has defined residue in section 3.5):
Input for residue
Output for residue
Update network flow as follows:
Iteration 2
Repeating the procedure described in iteration 1, at the starting node 1, the obtained breakthrough path
is 1 → 4 → 3 → 5 and 𝑁2 = 1,4,3,5 . 𝜇2 = [[8, 10, 20, 35; .6]].
Iteration 3
Repeating the procedure described in iteration 1, the obtained breakthrough path is
1 → 3 → 5 and 𝑁3 = 1,3,5 . 𝜇2 =[[2, 7, 15, 20; .5]]
46
8. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
Iteration 4
Step 6: Now we calculate Fuzzy maximal flow.
Fuzzy maximal flow in the network is 𝐹 = 𝑓 𝑎1 + 𝑓 𝑎1 + 𝑓 𝑎1 = [ 10,24,57,93; 0.5 ]. The initial and final
fuzzy residuals of arc 𝑖, 𝑗 are
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 and
𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 respectively, the fuzzy optimal flow in arc 𝑖, 𝑗 is
computed as follows: Let 𝛼, 𝛽 = 𝜇𝑐 𝑖𝑗 − 𝜇𝑐 𝑖𝑗 , 𝜇𝑐 𝑗𝑖 − 𝜇𝑐 𝑗𝑖 . If ℜ 𝛼 > 0 then the fuzzy optimal flow from 𝑖
to 𝑗 is 𝛼. Otherwise, if ℜ 𝛽 > 0 then the fuzzy optimal flow from 𝑗 to 𝑖 is 𝛽
47
9. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
2.
Results and Discussion
0 ; −∞ < 𝑥 ≤ 10
0.5 𝑥 − 10
; 10 ≤ 𝑥 < 24
14
0.5 ; 24 ≤ 𝑥 ≤ 57
𝜇𝐹 𝑥 =
0.5 𝑥 − 93
; 57 < 𝑥 ≤ 93
36
0 ; 93 ≤ 𝑥 < ∞
where, 𝑥 represent the amount of flow.
V.
CONCLUSION
In this paper, we have proposed algorithm for solving the fuzzy maximal (optimal) flow problems
occurring in real life situation and we have shown that the flows are represented by using generalized
trapezoidal fuzzy numbers. Kumar and Kaur [23] have solved fuzzy maximal flow problems using generalized
trapezoidal fuzzy numbers. But they apply only ranking function for maximal flow path. To demonstrate the
proposed new algorithm, we have solved a numerical example and obtain results are discussed. In the algorithm
of the paper, we have used ranking function also used mode function when ranking function fails for chose the
path of the flow, we have also used some Mathematica program for all mathematical calculation of these
numerical example. In future, we can solve the other network problems by extending this proposed algorithm.
REFERENCES
[1].
[2].
[3].
[4].
Abbasbandy S., Hajjari T., “A new approach for ranking of trapezoidal fuzzy numbers”, Computers
and Mathematics with Applications, 57 (2009), pp. 413-419
Ahuja R. K., Magnanti T. L. and Orlin J. B., Network Flows, Theory and Algorithm, Prentice Hall,
New Jersey (1993)
Bansal A., “Trapezoidal Fuzzy Numbers (a,b,c,d): Arithmetic Behavior”, International Journal of
Physical and Mathematical Science, (2011), pp. 39-44.
Bazarra M. S., Jarvis J. J. and Sherali H. D., Linear Programming and Network Flows, 2nd Edition,
Wiley, New York, (1990)
48
10. Solution of Fuzzy Maximal Flow Network Problem Based on Generalized…
[5].
[6].
[7].
[8].
[9].
[10].
[11].
[12].
[13].
[14].
[15].
[16].
[17].
[18].
[19].
[20].
[21].
[22].
[23].
[24].
[25].
[26].
[27].
[28].
[29].
[30].
Chanas S. and Kolodziejczyk W, “Maximum Flow in a Network with fuzzy arc capacities”, Fuzzy Sets
and Systems, 8: (1982), pp. 165-173
Chanas S. and Kolodziejczyk W, “Real-valued Flow in a Network with fuzzy arc capacities”, Fuzzy
Sets and Systems, 13: (1984), pp. 139-151
Chanas S. and Kolodziejczyk W, “Integer Flow in Network with Fuzzy Capacity Constrains”,
Networks, 16: (1986), pp. 17-31
Chen S. H “Operations of Fuzzy Numbers with function principal”, Tamkang Journal of Management
Sciences, 6 (1985), pp. 13-25
Chen S. J., Chen, S. M. “Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy
numbers”, Applied Intelligence, 26 (2007), pp. 1-11
Chen S. M. and Chen J. H., “Fuzzy risk analysis based on ranking generalized fuzzy numbers with
different heights and different spreads”, Expert Systems with Applications, vol. 36, (2009), pp. 68336842.
Diamond A., “A Fuzzy Max-Flow Min-Cut Theorem”, Fuzzy Sets and Systems, 119: (2001), pp. 139148
Dubois D., Prade H. “Fuzzy real algebra Some results”, Fuzzy Sets Syatems, 2 (1979), pp. 327-349
Dubois D., Prade H, Fuzzy Sets and Systems Theory and Applications, New
York/London/Toronto/Sydney/San Francisco; (1980)
Ford L. R. and Fulkerson D. R., “Maximal Flow Through a network”, Canadian Journal of
Mathematics, vol. 8, (1956), pp. 399-401
Fulkerson D. R. and Dantzig G. B., “Computation of Maximum Flow in Network”, Naval Research
Logistics Quarterly, vol. 2, (1955), pp. 277-283
Ji X., Yang L. and Shao Z., “Chance Constrained Maximum Flow Problem with Arc Capacities”,
Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, 4114: (2006), pp. 11-19
Kim K. and Roush F., “Fuzzy Flows on Network”, Fuzzy Sets and Systems, 8: (1982), pp 35-38
Klir, George J. and Yuan, Bo, Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice, Hall of
India Private Limited, New Delhi-110 001, (1997)
Kumar A., Bhatia N. and Kaur M. “A new approach for solving fuzzy maximal flow problems”,
Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, 5908 (2009), pp. 278-286
Kumar A., Singh P., Kaur A. and Kaur P., “Ranking of generalized Trapezoidal Fuzzy Numbers Based
on Rank, Mode, Fivergence and Spread”, Turkish Journal of Fuzzy Systems, Vol. 1, No. 2 (2010), pp.
141-152
Kumar A. and Kaur M. “An Algorithm for Solving Fuzzy Maximal Flow Problems Using Generalized
Trapezoidal Fuzzy Numbers”, International Journal of Applied Science and Engineering, 8, 2 (2010),
pp. 109-118
Liou, T. S. and Wang, M. J. “Ranking fuzzy numbers with integral value”, Fuzzy Sets and Systems,
50(1): (1992), pp. 247-255
Liu S. T. and Kao C., “Network Flow Problems with Fuzzy Arc Lengths”, IEEE Transactions on
Systems, Man and Cybernetics, 34: (2004), pp. 765-769
Moore R. E., Methods and Applications of Interval Analysis. SIAM, Philadelphia, 1979
Taha H. A., operational Research: An Introduction, Prentice-Hall, New Jersey, (2003)
Taha H. A., Operation Research: An Introduction; Eighth Edition, New Dhelhi-110 001, (2006)
Thaker P. A., Shelar D. S. and Thaker S. P., “Solving Fuzzy Linear Programming Problem”,
Proceedings of the World Corld Congress on Engineering, London, U.K., Vol II, (2009) pp. 978-988
Stephen Wolfram, The Mathematica Book: 5th Edition, Cambridge (2003)
Yager R., “On Solving Fuzzy Mathematical Relationships”, Information Control, 41 (1979) 29-55
Zadeh, L., “Fuzzy sets”, Information and Control, 8, (1965), pp. 338–353
49