This document presents an article from the International Journal of Fuzzy System Applications that proposes a new method called the PSK method for solving type-1 and type-3 fuzzy transportation problems. In transportation problems, supplies, demands, and costs are usually certain values, but the article considers problems where these values may be uncertain and represented by fuzzy numbers like triangular or trapezoidal fuzzy numbers. The PSK method transforms the fuzzy transportation problem into a crisp one using an existing ranking procedure so that conventional solution methods can be applied. The method differs from solving certain transportation problems only in the allocation step. The PSK method and a new operation for multiplying trapezoidal fuzzy numbers are proposed to find an optimal solution with both crisp and fuzzy components
Hosein Naseri received his B.Eng. in Mechanical Engineering from K.N. Toosi University of Technology in 2013. He is currently a member of the Mechatronic Mechanisms Laboratory and associate researcher at the Nasir Virtual Reality Laboratory. His research interests include signal processing, traffic modeling, and inertial navigation systems. He has participated in projects such as developing driving simulators and a new gyro-free inertial navigation system.
Recent developments in metamodel based robust black-box simulation optimizati...Nader Ale Ebrahim
In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model’s output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state-of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.
This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport called conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.
The well-known Vehicle Routing Problem (VRP) consist of assigning routeswith a set
ofcustomersto different vehicles, in order tominimize the cost of transport, usually starting from a central
warehouse and using a fleet of fixed vehicles. There are numerousapproaches for the resolution of this kind of
problems, being the metaheuristic techniques the most used, including the Genetic Algorithms (AG). The
number of approachesto the different parameters of an AG (selection, crossing, mutation...) in the literature is
such that it is not easy to take a resolution of a VRP problem directly. This paper aims to simplify this task by
analyzing the best known approaches with standard VRP data sets, and showing the parameter configurations
that offer the best results.
October 2021: Top Read Articles in Soft Computingijsc
Soft computing is likely to play an important role in science and engineering in the future. The successful applications of soft computing and the rapid growth suggest that the impact of soft computing will be felt increasingly in coming years. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. This Open access peer-reviewed journal serves as a platform that fosters new applications for all scientists and engineers engaged in research and development in this fast growing field.
This document provides an overview of several research articles on the topic of neutrosophic multi-criteria decision making. It introduces concepts like neutrosophic quadruple numbers and algebras. It also summarizes decision making methods like bipolar neutrosophic TOPSIS and ELECTRE that can handle indeterminate information. Further, it discusses hybrid models involving neutrosophic sets, soft sets, and rough sets applied to decision making problems. Finally, it outlines approaches to nonlinear programming and multi-criteria group decision making under neutrosophic number environments.
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A Hybrid method of face detection based on Feature Extraction using PIFR and ...IJERA Editor
This document presents a hybrid method for face detection based on feature extraction using partial feature extraction (PIFR) and feature optimization using teacher-learning based optimization (TLBO). The proposed method extracts texture features from face images using PIFR. The extracted features are then optimized for selection and improvement using the TLBO algorithm. The optimized features are classified using a support vector machine to detect faces. The method is tested on Google face image databases in MATLAB, achieving a detection ratio of 95%, higher than PIFR alone. The paper concludes the proposed method provides better face detection performance than PIFR through feature optimization.
Hosein Naseri received his B.Eng. in Mechanical Engineering from K.N. Toosi University of Technology in 2013. He is currently a member of the Mechatronic Mechanisms Laboratory and associate researcher at the Nasir Virtual Reality Laboratory. His research interests include signal processing, traffic modeling, and inertial navigation systems. He has participated in projects such as developing driving simulators and a new gyro-free inertial navigation system.
Recent developments in metamodel based robust black-box simulation optimizati...Nader Ale Ebrahim
In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model’s output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state-of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.
This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport called conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.
The well-known Vehicle Routing Problem (VRP) consist of assigning routeswith a set
ofcustomersto different vehicles, in order tominimize the cost of transport, usually starting from a central
warehouse and using a fleet of fixed vehicles. There are numerousapproaches for the resolution of this kind of
problems, being the metaheuristic techniques the most used, including the Genetic Algorithms (AG). The
number of approachesto the different parameters of an AG (selection, crossing, mutation...) in the literature is
such that it is not easy to take a resolution of a VRP problem directly. This paper aims to simplify this task by
analyzing the best known approaches with standard VRP data sets, and showing the parameter configurations
that offer the best results.
October 2021: Top Read Articles in Soft Computingijsc
Soft computing is likely to play an important role in science and engineering in the future. The successful applications of soft computing and the rapid growth suggest that the impact of soft computing will be felt increasingly in coming years. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. This Open access peer-reviewed journal serves as a platform that fosters new applications for all scientists and engineers engaged in research and development in this fast growing field.
This document provides an overview of several research articles on the topic of neutrosophic multi-criteria decision making. It introduces concepts like neutrosophic quadruple numbers and algebras. It also summarizes decision making methods like bipolar neutrosophic TOPSIS and ELECTRE that can handle indeterminate information. Further, it discusses hybrid models involving neutrosophic sets, soft sets, and rough sets applied to decision making problems. Finally, it outlines approaches to nonlinear programming and multi-criteria group decision making under neutrosophic number environments.
March 2021: Top Read Articles in Soft Computingijsc
Soft computing is likely to play an important role in science and engineering in the future. The successful applications of soft computing and the rapid growth suggest that the impact of soft computing will be felt increasingly in coming years. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. This Open access peer-reviewed journal serves as a platform that fosters new applications for all scientists and engineers engaged in research and development in this fast growing field.
A Hybrid method of face detection based on Feature Extraction using PIFR and ...IJERA Editor
This document presents a hybrid method for face detection based on feature extraction using partial feature extraction (PIFR) and feature optimization using teacher-learning based optimization (TLBO). The proposed method extracts texture features from face images using PIFR. The extracted features are then optimized for selection and improvement using the TLBO algorithm. The optimized features are classified using a support vector machine to detect faces. The method is tested on Google face image databases in MATLAB, achieving a detection ratio of 95%, higher than PIFR alone. The paper concludes the proposed method provides better face detection performance than PIFR through feature optimization.
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This document summarizes a paper that compares image mining and data mining techniques. Image mining is the process of extracting meaningful information from images using techniques from data mining and machine learning. While data mining uses structured data, image mining works with unstructured visual data from images. The paper explores the differences between the two fields, such as image mining having to first extract features from images before applying data mining algorithms, while data mining works directly with structured data. It also discusses challenges that are unique to image mining like the need for large training datasets and computational complexity of computer vision algorithms.
In solving real life transportation problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. So, in this paper, we consider a transportation problem having uncertainty and hesitation in supply, demand and costs. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TrIFNs) to deal with uncertainty and hesitation. We propose a new method called PSK method for finding the intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem in single stage. Also the new multiplication operation on TrIFN is proposed to find the optimal object value in terms of TrIFN. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.
This document provides citation information for a chapter titled "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems" published in the book "Fuzzy Systems: Concepts, Methodologies, Tools, and Applications". It lists the citation in MLA, APA, and Chicago format. The chapter discusses using the PSK method to solve type-1 and type-3 fuzzy transportation problems.
IICET 2015 - i-manager's International Conference on Engineering and Technolo...imanconference
The purpose of IICET 2015 is to provide a platform for researchers, engineers, academics and industrial professionals to present their recent research work and to explore future trends in various areas of engineering and technology and enrich their insight on in-depth research in the field of Engineering. IICET 2015 will feature Keynote lectures by eminent Academics and various technical sessions with paper presentations.
IICET 2015 is organized by i-manager Publications (www.imanagerpublications.com) which has made its marked milestone of a triumphant decade in Academic Publishing. All articles will undergo a rigorous review process by the Technical committees. Proceedings of the Conference will be submitted for possible inclusion into IEEE Xplore as well as other Abstracting and Indexing (A&I) databases. Extended version of selected papers will be published in i-manager’s Journals. i-manager’s Journals are listed in ProQuest, EBSCO, Index Copernicus, Ulrich Directories, Cabell’s Directories, Google Scholar, Indian Citation Index, Global Impact Factor, Cite Factor etc.
This thesis presents a novel hierarchical reinforcement learning framework called Reinforcement Learning Optimal Control (RLOC) for controlling nonlinear dynamical systems. RLOC operates at two levels: 1) It uses optimal control to learn local linear models and controllers. 2) A high-level reinforcement learning agent uses these controllers as actions and learns how to combine them to maximize long-term reward. The framework demonstrates that a small number of local controllers can solve global nonlinear control problems, providing a model for how the brain bridges low-level control and high-level action selection. Evaluation on benchmark problems shows RLOC competes with state-of-the-art control methods in computational cost and solution quality.
International Journal of Distributed and Parallel systems (IJDPS)ijdpsjournal
International Journal of Distributed and Parallel systems (IJDPS)
ISSN: 0976-9757[Online]; 2229-3957[Print]
https://airccse.org/journal/ijdps/ijdps.html
International Journal of Distributed and Parallel systems (IJDPS)
https://www.academia.edu/69752775/International_Journal_of_Distributed_and_Parallel_systems_IJDPS_
Application Of Single-Server Queue System In Performance Analysis Of Shuttle ...Tracy Drey
This document summarizes a study that analyzed the performance of shuttle bus operations at the Federal University of Technology Akure (FUTA) using a single-server queue system model. The study found that the shuttle bus system had a 93% performance level, indicating it was able to meet student demand. The methodology involved modeling the shuttle bus system as a single-server M/M/1 queue, where arrivals and services follow a Poisson process. Key concepts discussed include Poisson processes, Laplace transforms, and modeling queue systems. The study replicates the methodology of a similar prior study at FUTA to analyze shuttle bus performance.
Use of Evolutionary Polynomial Regression (EPR) for Prediction of Total Sedim...CSCJournals
This study presents the use of Evolutionary Polynomial Regression (EPR) in predicting the total sediment load of ten selected rivers in Malaysia. EPR is a data-driven hybrid technique, based on evolutionary computing. In order to apply the method, the extensive database of the Department of Irrigation and Drainage (DID), Ministry of Natural Resources & Environment, Malaysia was sought, and unrestricted access was granted. The EPR technique produced greatly improved results compared to other previous sediment load methods. A robustness study was performed in order to confirm the generalisation ability of the developed EPR model, and a sensitivity analysis was also conducted to determine the relative importance of model inputs. The performance of the EPR model demonstrates its predictive capability and generalisation ability to solve highly nonlinear problems of river engineering applications, such as sediment.
In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer’s over time work, unexpected failures in machine, seasonal changesandmanymore. Tocountertheseproblems,dependingonthenatureoftheparameters, theTPisclassifiedintotwocategoriesnamelytype-2andtype-4fuzzytransportationproblems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992)isusedtotransformthetype-2andtype-4FTPsintoacrisponesothattheconventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.
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This paper presents a new topology for a delta modulation technique used to improve the power factor of AC-DC converters. The new topology uses novel algorithms to generate PWM control signals for the converter transistors. Simulation results show the new topology yields sinusoidal input current in phase with the input voltage without DC offset. It also provides constant output voltage regulation through voltage control of the reference current. The varying switching frequency is improved over other delta modulation techniques. The new topology offers better stability performance compared to other delta modulation variants or modulation methods.
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International Journal of Engineering (IJE) Volume (4) Issue (3)CSCJournals
The document summarizes the design and simulation of a multiband cross dipole antenna based on triangular and quadratic Koch curve fractals.
[1] The antenna was designed and analyzed using the method of moments technique. It was simulated using NEC software and found to operate at 0.543 GHz, 2 GHz, and 6.5 GHz with acceptable bandwidth.
[2] The radiation characteristics and reflection coefficient were described. The gain was also calculated in three planes.
[3] The antenna exhibits multiband behavior due to its fractal geometry, making it suitable for various wireless applications while maintaining a small size and low profile.
The document describes the International Journal of Computer Science and Information Technology (IJCSIT). It provides information on the scope, topics of interest, editorial board, submission guidelines, and review process of the journal. The IJCSIT is a peer-reviewed scientific journal that publishes original research on computer science and information systems fields. It accepts various types of papers and has an international editorial board.
The document describes the International Journal of Computer Science and Information Technology (IJCSIT). It provides information on the scope, topics of interest, editorial board, submission guidelines, and review process of the journal. The IJCSIT is a peer-reviewed scientific journal that publishes original research on computer science and information systems fields. It accepts various types of papers and has an international editorial board.
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Optimization, Learning Algorithms and Applications.pdfMan_Ebook
This document provides information about a conference titled "First International Conference, OL2A 2021" that was held from July 19-21, 2021 in Bragança, Portugal. It discusses the conference's organization, including its editors, scientific committee members, and topics. The conference focused on optimization, learning algorithms, and applications. It received 134 submissions and selected 52 accepted papers, including 39 full papers.
In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. A new relevant numerical example is also included.
In solving real life assignment problem, we often face the state of uncertainty as well as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, computationally a simple method is proposed to find the optimal solution for an unbalanced assignment problem under intuitionistic fuzzy environment. In conventional assignment problem, cost is always certain. This paper develops an approach to solve the unbalanced assignment problem where the time/cost/profit is not in deterministic numbers but imprecise ones. In this assignment problem, the elements of the cost matrix are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the AP . Finally, the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.
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In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. A new relevant numerical example is also included.
In solving real life assignment problem, we often face the state of uncertainty as well as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, computationally a simple method is proposed to find the optimal solution for an unbalanced assignment problem under intuitionistic fuzzy environment. In conventional assignment problem, cost is always certain. This paper develops an approach to solve the unbalanced assignment problem where the time/cost/profit is not in deterministic numbers but imprecise ones. In this assignment problem, the elements of the cost matrix are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the AP . Finally, the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.
In conventional assignment problem, cost is always certain. In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. There is no systematic approach for finding an optimal solution for mixed intuitionistic fuzzy assignment problem. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is not in deterministic numbers but imprecise ones. The solution procedure of mixed intuitionistic fuzzy assignment problem is proposed to find the optimal assignment and also obtain an optimal value in terms of triangular intuitionistic fuzzy numbers. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.
In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. In conventional assignment problem, cost is always certain. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is considered real, fuzzy and an intuitionistic fuzzy numbers. Ranking procedure of Annie Varghese and Sunny Kuriakose [4] is used to transform the mixed intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the assignment problem. The method is illustrated by a numerical example. The proposed method is very simple and easy to understand. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.
In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy Vogel’s Approximation method is proposed to find an initial basic feasible solution in terms of triangular intuitionistic fuzzy numbers. The solution procedure is illustrated with suitable numerical example.
In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic Fuzzy Vogel’s Approximation Method is proposed to find an initial basic feasible solution. Intuitionistic Fuzzy Modified Distribution Method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The solution procedure is illustrated with suitable numerical example.
There are several algorithms, in literature, for obtaining the fuzzy optimal solution of fuzzy transportation problems (FTPs). To the best of the author's knowledge, in the history of mathematics, no one has been able to solve transportation problem (TP) under four different uncertain environment using single method in the past years. So, in this chapter, the author tried to categories the TP under four different environments and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs), and trapezoidal fuzzy numbers (TrFNs) to solve the TP. A new method, namely, PSK (P. Senthil Kumar) method for finding a fuzzy optimal solution to fuzzy transportation problem (FTP) is proposed. Practical usefulness of the PSK method over other existing methods is demonstrated with four different numerical examples. To illustrate the PSK method different types of FTP is solved by using the PSK method and the obtained results are discussed.
In solving real life assignment problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representations for the data. So, in this paper, the authors consider the assignment problem having uncertainty and hesitation in cost/time/profit. They formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. The authors propose a new method called PSK (P.Senthil Kumar) method for finding the intuitionistic fuzzy optimal cost/time/profit for fully intuitionistic fuzzy assignment problem (FIFAP). The proposed method gives the optimal object value in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.
In conventional transportation problem (TP), supplies, demands and costs are always certain. This paper develops an approach to solve the unbalanced transportation problem where as all the parameters are not in deterministic numbers but imprecise ones. Here, all the parameters of the TP are considered to the triangular intuitionistic fuzzy numbers (TIFNs). The existing ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy transportation problem (UIFTP) into a crisp one so that the conventional method may be applied to solve the TP. The occupied cells of unbalanced crisp TP that we obtained are as same as the occupied cells of UIFTP.
On the basis of this idea the solution procedure is differs from unbalanced crisp TP to UIFTP in allocation step only. Therefore, the new method and new multiplication operation on triangular intuitionistic fuzzy number (TIFN) is proposed to find the optimal solution in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful.
In this article, two methods are presented, proposed method 1 and proposed method 2. Proposed method 1 is based on linear programming technique and proposed method 2 is based on modified distribution method. Both of the methods are used to solve the balanced and unbalanced intuitionistic fuzzy transportation problems. The ideas of the proposed methods are illustrated with the help of real life numerical examples which is followed by the results and discussion and comparative study is given. The proposed method is computationally very simple when compared to the existing methods, it is shown to be and easier form of evaluation when compared to current methods.
In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian’s (2014) method is reviewed. Finally, the comparative study, results and discussion are given.
This document presents a method for solving an assignment problem where the costs are triangular intuitionistic fuzzy numbers rather than certain values. It introduces the concepts of intuitionistic fuzzy sets and triangular intuitionistic fuzzy numbers, and defines operations and a ranking method for comparing them. The paper formulates the intuitionistic fuzzy assignment problem mathematically as an optimization problem that minimizes the total intuitionistic fuzzy cost while satisfying constraints that each job is assigned to exactly one machine. It describes using an intuitionistic fuzzy Hungarian method to solve this type of assignment problem.
This document presents a systematic approach for solving mixed intuitionistic fuzzy transportation problems. It begins with definitions of fuzzy sets, intuitionistic fuzzy sets, and triangular intuitionistic fuzzy numbers. It then formulates an intuitionistic fuzzy transportation problem and proposes a mixed intuitionistic fuzzy zero point method to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. Finally, it provides the computational procedure and illustrates the method with a numerical example.
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Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a0 = cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...PsychoTech Services
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PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems
1.
2. Abbas Al-Refaie, University of Jordan, Jordan
Ahmad Taher Azar, Benha University, Egypt
P. Balasubramaniam, Gandhigram Rural University, India
Zeungnam Bien, UNIST, Korea
Asli Celikyilmaz, University of California-Berkeley, USA
Keeley Crockett, Manchester Metropolitan University, UK
Ali Ebrahimnejad, Islamic Azad University, Iran
K. Honda, Osaka Prefecture University, Japan
Jun-ichi Horiuch, Kitami Institute of Technology, Japan
Richard Jensen, The University of Wales, Aberystwyth, UK
Erich Peter Klement, Johannes Kepler University, Austria
Rudolf Kruse, Otto-von-Guericke-Universität Magdeburg, Germany
Salim Labiod, University of Jijel, Algeria
Yongming Li, Shaanxi Normal University, China
T. Warren Liao, Louisiana State Univeristy, USA
Pawan Lingras, Saint Mary’s University, Canada
Peide Liu, Shandong University, China
Yan-Jun Liu, Liaoning University of Technology, China
Yeh Ching Nee, National University of Singapore, Singapore
Jianbin Qiu, Harbin Institute of Technology, China
Chai Quek, Nanyang Technological University, Singapore
Elisabeth Rakus-Andersson, Blekinge Institute of Technology, Sweden
Soheil Salahshour, Islamic Azad University Mobarakeh Branch, Iran
Ismail Burhan Turksen, TOBB Economy and Technology University, Turkey
Pandian Vasant, Universiti Teknologi PETRONAS, Malaysia
Michael Voskoglou, Graduate Technological Educational Institute (T.E.I.), Greece
Hsiao-Fan Wang, National Tsing Hua University, China
Mao-Jiun J. Wang, National Tsing Hua University, Taiwan
Frank Werner, Otto-von-Guericke University, Germany
Chien-Wei Wu, National Taiwan University of Science and Technology, Taiwan
Tai-Shi Wu, National Taipei University, Taiwan
Zeshui Xu, PLA University of Science and Technology, China
Mesut Yavuz, Shenandoah University, USA
Gaofeng Yu, Sanming University, China
International Editorial Review Board
EDITOR-IN-CHIEF
Deng-Feng Li, Fuzhou University, China
INTERNATIONAL ADVISORY BOARD
Ronald R. Yager, Iona College, USA
Lotfi A. Zadeh, California University at Berkeley, USA
Hans-Jürgen Zimmermann, European Laboratory for Intelligent Techniques Engineering, Inform GmbH, Germany
ASSOCIATE EDITORS
Mark Burgin, UCLA, USA
Mingzhi Chen, Fuzhou University, China
Volume 5 • Issue 4 • October-December 2016 • ISSN: 2156-177X • eISSN: 2156-1761
An official publication of the Information Resources Management Association
International Journal of Fuzzy System Applications
5. International Journal of Fuzzy System Applications
Volume 5 • Issue 4 • October-December 2016
122
for general transportation problems. An Introduction to Operations Research Taha (2008) deals the
transportation problem.
In today’s real world problems such as in corporate or in industry many of the distribution
problems are imprecise in nature due to variations in the parameters. To deal quantitatively with
imprecise information in making decision, Zadeh (1965) introduced the fuzzy set theory and has
applied it successfully in various fields. The use of fuzzy set theory becomes very rapid in the field of
optimization after the pioneering work done by Bellman and Zadeh (1970). The fuzzy set deals with
the degree of membership (belongingness) of an element in the set. In a fuzzy set the membership
value (level of acceptance or level of satisfaction) lies between 0 and 1 where as in crisp set the
element belongs to the set represent 1 and the element not belongs to the set represent 0.
Due to the applications of fuzzy set theory, several authors like Oheigeartaigh (1982) presented
an algorithm for solving transportation problems where the availabilities and requirements are fuzzy
sets with linear or triangular membership functions. Chanas et al. (1984) presented a fuzzy linear
programming model for solving transportation problems with fuzzy supply, fuzzy demand and crisp
costs. Chanas et al. (1993) formulated the fuzzy transportation problems in three different situations and
proposed method for solving the formulated fuzzy transportation problems. Chanas and Kuchta (1996)
proposed the concept of the optimal solution for the transportation problem with fuzzy coefficients
expressed as fuzzy numbers, and developed an algorithm for obtaining the optimal solution.
Chanas and Kuchta (1998) developed a new method for solving fuzzy integer transportation
problem by representing the supply and demand parameters as L-R type fuzzy numbers. Saad and
Abbas (2003) proposed an algorithm for solving the transportation problems under fuzzy environment.
Liu and Kao (2004) presented a method for solving fuzzy transportation problems based on extension
principle. Chiang (2005) proposed a method to find the optimal solution of transportation problems
with fuzzy requirements and fuzzy availabilities. Gani and Razak (2006) obtained a fuzzy solution
for a two stage cost minimizing fuzzy transportation problem in which availabilities and requirements
are trapezoidal fuzzy numbers using a parametric approach. Das and Baruah (2007) discussed Vogel’s
approximation method to find the fuzzy initial basic feasible solution of fuzzy transportation problem
in which all the parameters (supply, demand and cost) are represented by triangular fuzzy numbers.
Li et al. (2008) proposed a new method based on goal programming approach for solving fuzzy
transportation problems with fuzzy costs.
Chen et al. (2008) proposed the methods for solving transportation problems on a fuzzy network.
Lin (2009) used genetic algorithm for solving transportation problems with fuzzy coefficients.
Dinagar and Palanivel (2009) investigated the transportation problem in fuzzy environment using
trapezoidal fuzzy numbers. De and Yadav (2010) modified the existing method (Kikuchi 2000) by
using trapezoidal fuzzy numbers instead of triangular fuzzy numbers. Pandian et al. (2010) proposed
a new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem where all the
parameters are trapezoidal fuzzy numbers. Mohideen and Kumar (2010) did a comparative study on
transportation problem in fuzzy environment. Sudhakar et al. (2011) proposed a different approach for
solving two stage fuzzy transportation problems in which supplies and demands are trapezoidal fuzzy
numbers. Hadi Basirzadeh (2011) discussed an approach for solving fuzzy transportation problem
where all the parameters are trapezoidal fuzzy numbers. Gani et al. (2011) presented simplex type
algorithm for solving fuzzy transportation problem where all the parameters are triangular fuzzy
numbers. Nasseri and Ebrahimnejad (2011) did sensitivity analysis on linear programming problems
with trapezoidal fuzzy variables.
Biswas and Modak (2012) studied using fuzzy goal programming technique to solve multi-
objective chance constrained programming problems in a fuzzy environment. Saati et al. (2012)
presented a two-fold linear programming model with fuzzy data. Ebrahimnejad (2012) discussed
cost efficiency measures with trapezoidal fuzzy numbers in data envelopment analysis based on
ranking functions: application in insurance organization and hospital. Rani et al. (2014) presented a
method for unbalanced transportation problems in fuzzy environment taking all the parameters are
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8. Reference to this paper should be made as follows:
MLA
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems." IJFSA 5.4 (2016): 121-146. Web. 16 Mar. 2017.
doi:10.4018/IJFSA.2016100106
APA
Kumar, P. S. (2016). PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems. International Journal of Fuzzy System Applications
(IJFSA), 5(4), 121-146. doi:10.4018/IJFSA.2016100106
Chicago
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems," International Journal of Fuzzy System Applications
(IJFSA) 5 (2016): 4, accessed (March 16, 2017),
doi:10.4018/IJFSA.2016100106
9. International Journal of Fuzzy System Applications
Volume 5 • Issue 4 • October-December 2016
144
REFERENCES
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Arsham, H., & Kahn, A. B. (1989). A simplex-type algorithm for general transportation problems: An alternative
to stepping-stone. The Journal of the Operational Research Society, 40(6), 581–590. doi:10.1057/jors.1989.95
Basirzadeh, H. (2011). An approach for solving fuzzy transportation problem. Applied Mathematical Sciences,
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Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17,:
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P. Senthil Kumar is an Assistant Professor in PG and Research Department of Mathematics at Jamal Mohamed
College (Autonomous), Tiruchirappalli, Tamil Nadu, India. He has six years of teaching experience. He received
his BSc, MSc and MPhil from Jamal Mohamed College, Tiruchirappalli in 2006, 2008, 2010 respectively. He
completed his BEd in Jamal Mohamed College of Teacher Education in 2009. He completed PGDCA in 2011
in the Bharathidasan University and PGDAOR in 2012 in the Annamalai University, Tamil Nadu, India. He has
submitted his PhD thesis in the area of intuitionistic fuzzy optimisation technique to the Bharathidasan University
in 2015. He has published many research papers in referred national and international journals like Springer, IGI
Global, etc. He also presented his research in Elsevier Conference Proceedings (ICMS-2014), MMASC-2012, etc.
His areas of interest include operations research, fuzzy optimisation, intuitionistic fuzzy optimisation, numerical
analysis and graph theory, etc.