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.
Collective Mind infrastructure and repository to crowdsource auto-tuning (c-m...Grigori Fursin
Open access vision publication for this presentation: http://arxiv.org/abs/1308.2410
Designing, analyzing and optimizing applications for rapidly evolving computer systems is often a tedious, ad-hoc, costly and error prone process due to an enormous number of available design and optimization choices combined with complex interactions between all components. Auto-tuning, run-time adaptation and machine learning based techniques have been investigated for more than a decade to address some of these challenges but are still far from the widespread production use. This is not only due to large optimization spaces, but also due to a lack of a common methodology to discover, preserve and share knowledge about behavior of existing computer systems with ever changing interfaces of analysis and optimization tools.
In this talk I presented a new version of the modular, open source Collective Mind Framework and Repository (cTuning.org, c-mind.org/repo) for collaborative and statistical analysis and optimization of program and architecture behavior. Motivated by physics, biology and AI sciences, this framework helps researchers to gradually expose tuning choices, properties and characteristics at multiple granularity levels in existing systems through multiple plugins. These plugins can be easily combined like LEGO to build customized collaborative or private in-house repositories of shared data (applications, data sets, codelets, micro-benchmarks and architecture descriptions), modules (classification, predictive modeling, run-time adaptation) and statistics from multiple program executions. Collected data is continuously analyzed and extrapolated using online learning to predict better optimizations or hardware configurations to effectively balance performance, power consumption and other characteristics.
This approach was initially validated in the MILEPOST project to remove the training phase of a machine learning based self-tuning compiler, and later extended in the Intel Exascale Lab to connect various tuning tools with an in-house customized repository. During this talk, I will demonstrate the auto-tuning using the new version of this framework and off-the-shelf mobile phones while describing encountered challenges and possible solutions.
Classifier Model using Artificial Neural NetworkAI Publications
When it comes to AI and ML, precision in categorization is of the utmost importance. In this research, the use of supervised instance selection (SIS) to improve the performance of artificial neural networks (ANNs) in classification is investigated. The goal of SIS is to enhance the accuracy of future classification tasks by identifying and selecting a subset of examples from the original dataset. The purpose of this research is to provide light on how useful SIS is as a preprocessing tool for artificial neural network-based classification. The work aims to improve the input dataset to ANNs by using SIS, which may help with problems caused by noisy or redundant data. The ultimate goal is to improve ANNs' ability to identify data points properly across a wide range of application areas.
Collective Mind infrastructure and repository to crowdsource auto-tuning (c-m...Grigori Fursin
Open access vision publication for this presentation: http://arxiv.org/abs/1308.2410
Designing, analyzing and optimizing applications for rapidly evolving computer systems is often a tedious, ad-hoc, costly and error prone process due to an enormous number of available design and optimization choices combined with complex interactions between all components. Auto-tuning, run-time adaptation and machine learning based techniques have been investigated for more than a decade to address some of these challenges but are still far from the widespread production use. This is not only due to large optimization spaces, but also due to a lack of a common methodology to discover, preserve and share knowledge about behavior of existing computer systems with ever changing interfaces of analysis and optimization tools.
In this talk I presented a new version of the modular, open source Collective Mind Framework and Repository (cTuning.org, c-mind.org/repo) for collaborative and statistical analysis and optimization of program and architecture behavior. Motivated by physics, biology and AI sciences, this framework helps researchers to gradually expose tuning choices, properties and characteristics at multiple granularity levels in existing systems through multiple plugins. These plugins can be easily combined like LEGO to build customized collaborative or private in-house repositories of shared data (applications, data sets, codelets, micro-benchmarks and architecture descriptions), modules (classification, predictive modeling, run-time adaptation) and statistics from multiple program executions. Collected data is continuously analyzed and extrapolated using online learning to predict better optimizations or hardware configurations to effectively balance performance, power consumption and other characteristics.
This approach was initially validated in the MILEPOST project to remove the training phase of a machine learning based self-tuning compiler, and later extended in the Intel Exascale Lab to connect various tuning tools with an in-house customized repository. During this talk, I will demonstrate the auto-tuning using the new version of this framework and off-the-shelf mobile phones while describing encountered challenges and possible solutions.
Classifier Model using Artificial Neural NetworkAI Publications
When it comes to AI and ML, precision in categorization is of the utmost importance. In this research, the use of supervised instance selection (SIS) to improve the performance of artificial neural networks (ANNs) in classification is investigated. The goal of SIS is to enhance the accuracy of future classification tasks by identifying and selecting a subset of examples from the original dataset. The purpose of this research is to provide light on how useful SIS is as a preprocessing tool for artificial neural network-based classification. The work aims to improve the input dataset to ANNs by using SIS, which may help with problems caused by noisy or redundant data. The ultimate goal is to improve ANNs' ability to identify data points properly across a wide range of application areas.
Genetic Algorithm for optimization on IRIS Dataset REPORT pdfSunil Rajput
Apply the Genetic Algorithm for optimization on a dataset obtained from UCI ML repository.
For Example: IRIS Dataset
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1 Abstract—Autonomous Vehicles (AV) are expected to.docxShiraPrater50
1
Abstract—Autonomous Vehicles (AV) are expected to bring
considerable benefits to society, such as traffic optimization and
accidents reduction. They rely heavily on advances in many
Artificial Intelligence (AI) approaches and techniques. However,
while some researchers in this field believe AI is the core element
to enhance safety, others believe AI imposes new challenges to
assure the safety of these new AI-based systems and applications.
In this non-convergent context, this paper presents a systematic
literature review to paint a clear picture of the state of the art of
the literature in AI on AV safety. Based on an initial sample of
4870 retrieved papers, 59 studies were selected as the result of the
selection criteria detailed in the paper. The shortlisted studies were
then mapped into six categories to answer the proposed research
questions. An AV system model was proposed and applied to
orient the discussions about the SLR findings. As a main result, we
have reinforced our preliminary observation about the necessity
of considering a serious safety agenda for the future studies on AI-
based AV systems.
Keywords: Autonomous vehicles, safety, artificial intelligence,
machine intelligence, machine learning, SLR.
I. INTRODUCTION
Advances in Artificial Intelligence (AI) are one of the key
enablers of the Autonomous Vehicles (AVs) development. In
fact, AVs rely on AI to interpret the environment, understand
its conditions, and make driving-related decisions. Thus, it
basically replicates the human driver actions when driving a
vehicle. In this context, AI applied to AV has become an
important research topic.
AV is a safety-critical system. When operating in an
undesirable way, AV can jeopardize human lives or the
environment in which it operates. It has the potential to threaten
the lives of its own passengers, pedestrians and people in other
vehicles, and damage other transportation system elements (e.g.
other vehicles and transportation infrastructure). Therefore, it is
mandatory to assure AV is safe, mainly when operating on
public roads in which resources will be shared with other
systems (and people).
Although safety is a mandatory characteristic to AV, and
although the researchers seem to agree on the importance of AI
This work was supported in part by the Research, Development and
innovation Center, Ericsson Telecommunication S.A., Brazil.
1Safety Analysis Group from Polytechnic School of University of São Paulo,
São Paulo, Brazil (e-mail: [email protected]).
applied to autonomous vehicles, they seem to disagree on the
AIs impact on AV safety. Many researchers, in special those
related to the AI community and AV manufacturers, advocate
AI as one of the core elements to enhance AV safety. Their
hypothesis is the automation of the driving tasks will lead to a
significant reduction of the car accidents. However, other
researchers, ...
Data Mining Framework for Network Intrusion Detection using Efficient TechniquesIJAEMSJORNAL
The implementation measures the classification accuracy on benchmark datasets after combining SIS and ANNs. In order to put a number on the gains made by using SIS as a strategic tool in data mining, extensive experiments and analyses are carried out. The predicted results of this investigation will have implications for both theoretical and applied settings. Predictive models in a wide variety of disciplines may benefit from the enhanced classification accuracy enabled by SIS inside ANNs. An invaluable resource for scholars and practitioners in the fields of AI and data mining, this study adds to the continuing conversation about how to maximize the efficacy of machine learning methods.
Automating Machine Learning - Is it feasible?Manuel Martín
Facing a machine learning problem for the first time can be overwhelming. Hundreds of methods exist for tackling problems such as classification, regression or clustering. Selecting the appropriate method is challenging, specially if no much prior knowledge is known. In addition, most models require to optimise a number of hyperparameters to perform well. Preparing the data for the learning algorithm is also a labour-intensive process that includes cleaning outliers and imperfections, feature selection, data transformation like PCA and more. A workflow connecting preprocessing methods and predictive models is called a multicomponent predictive system (MCPS). This talk introduces the problem of automating the composition and optimisation of MCPSs and also how they can be adapted in changing environments.
A Novel Feature Selection with Annealing For Computer Vision And Big Data Lea...theijes
Numerous PC vision and medical imaging issues a confronted with gaining from expansive scale datasets, with a huge number of perceptions furthermore, highlights.A novel productive learning plan that fixes a sparsity imperative by continuously expelling variables taking into account a measure and a timetable. The alluring actuality that the issue size continues dropping all through the cycles makes it especially reasonable for enormous information learning. Methodology applies nonexclusively to the advancement of any differentiable misfortune capacity, and discovers applications in relapse, order and positioning. The resultant calculations assemble variable screening into estimation and are amazingly easy to execute. It gives hypothetical assurances of joining and determination consistency. Investigates genuine and engineered information demonstrate that the proposed strategy contrasts exceptionally well and other cutting edge strategies in relapse, order and positioning while being computationally exceptionally effective and adaptable.
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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while some researchers in this field believe AI is the core element
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based AV systems.
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enablers of the Autonomous Vehicles (AVs) development. In
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basically replicates the human driver actions when driving a
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important research topic.
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This work was supported in part by the Research, Development and
innovation Center, Ericsson Telecommunication S.A., Brazil.
1Safety Analysis Group from Polytechnic School of University of São Paulo,
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related to the AI community and AV manufacturers, advocate
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Data Mining Framework for Network Intrusion Detection using Efficient TechniquesIJAEMSJORNAL
The implementation measures the classification accuracy on benchmark datasets after combining SIS and ANNs. In order to put a number on the gains made by using SIS as a strategic tool in data mining, extensive experiments and analyses are carried out. The predicted results of this investigation will have implications for both theoretical and applied settings. Predictive models in a wide variety of disciplines may benefit from the enhanced classification accuracy enabled by SIS inside ANNs. An invaluable resource for scholars and practitioners in the fields of AI and data mining, this study adds to the continuing conversation about how to maximize the efficacy of machine learning methods.
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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.
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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.
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.
In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. 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. The effectiveness of the proposed method is illustrated by means of a numerical example.
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 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.
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.
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.
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Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
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Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems
1. Cite this Chapter as follows:
MLA
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications. IGI Global, 2017. 367-392. Web. 2 Mar. 2017. doi:10.4018/978-1-5225-1908-9.ch017
APA
Kumar, P. S. (2017). PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems. In Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications (pp. 367-392). Hershey, PA: IGI Global. doi:10.4018/978-1-5225-1908-9.ch017
2. Chicago
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." In Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications, 367-392 (2017), accessed March 02, 2017. doi:10.4018/978-1-5225-1908-9.ch017
4.
Editor-in-Chief
Mehdi Khosrow-Pour, DBA
Information Resources Management Association, USA
Associate Editors
Steve Clarke, University of Hull, UK
Murray E. Jennex, San Diego State University, USA
Annie Becker, Florida Institute of Technology, USA
Ari-Veikko Anttiroiko, University of Tampere, Finland
Editorial Advisory Board
Sherif Kamel, American University in Cairo, Egypt
In Lee, Western Illinois University, USA
Jerzy Kisielnicki, Warsaw University, Poland
Amar Gupta, Arizona University, USA
Craig van Slyke, University of Central Florida, USA
John Wang, Montclair State University, USA
Vishanth Weerakkody, Brunel University, UK
6.
Table of Contents
Preface................................................................................................................................................... xx
Volume I
Section 1
Development and Design Methodologies
Chapter 1
Uncertain Static and Dynamic Analysis of Imprecisely Defined Structural Systems............................. 1
S. Chakraverty, National Institute of Technology – Rourkela, India
Diptiranjan Behera, National Institute of Technology – Rourkela, India
Chapter 2
Hierarchical Fuzzy Rule Interpolation and its Application for Hotels Location Selection................... 31
Yanling Jiang, Chongqing University of Science and Technology, China
Shangzhu Jin, Chongqing University of Science and Technology, China
Jun Peng, Chongqing University of Science and Technology, China
Chapter 3
Modified Iterative Methods for Solving Fully Fuzzy Linear Systems................................................... 55
S. A. Edalatpanah, Ayandegan Institute of Higher Education, Tonekabon, Iran
Chapter 4
Comparison of Uncertainties in Membership Function of Adaptive Lyapunov NeuroFuzzy-2 for
Damping Power Oscillations.................................................................................................................. 74
Laiq Khan, COMSATS Institute of Information Technology, Pakistan
Rabiah Badar, COMSATS Institute of Information Technology, Pakistan
Saima Ali, COMSATS Institute of Information Technology, Pakistan
Umar Farid, COMSATS Institute of Information Technology, Pakistan
Chapter 5
Constructing Structural Equation Model Rule-Based Fuzzy System with Genetic Algorithm........... 132
EnDer Su, National Kaohsiung First University of Science and Technology, Taiwan
Thomas W. Knowles, Illinois Institute of Technology, USA
Yu-Gin Fen, National Kaohsiung First University of Science and Technology, Taiwan
7.
Chapter 6
A Novel Approach of Restoration of Digital Images Degraded by Impulse Noise............................. 153
Rashmi Kumari, JJTU, India
Anupriya Asthana, Galgotias University, India
Vikas Kumar, Asia-Pacific Institute of Management, India
Chapter 7
Imprecise Knowledge and Fuzzy Modeling in Materials Domain...................................................... 170
Subhas Ganguly, National Institute Technology Raipur, India
Shubhabrata Datta, Calcutta Institute of Engineering and Management, India
Chapter 8
Assessment of Clinical Decision Support Systems for Predicting Coronary Heart Disease............... 184
Sidahmed Mokeddem, University of Oran 1 Ahmed Ben Bella, Algeria
Baghdad Atmani, University of Oran 1 Ahmed Ben Bella, Algeria
Chapter 9
Early Warning System Framework Proposal Based on Structured Analytical Techniques, SNA,
and Fuzzy Expert System for Different Industries............................................................................... 202
Goran Klepac, University College for Applied Computer Engineering Algebra, Zagreb,
Croatia
Robert Kopal, University College for Applied Computer Engineering Algebra, Zagreb,
Croatia
Leo Mrsic, University College for Applied Computer Engineering Algebra, Zagreb, Croatia
Chapter 10
Stability Enhancement in Multi-Machine Power Systems by Fuzzy-Based Coordinated
AVR-PSS.............................................................................................................................................. 235
Rahmat Khezri, University of Kurdistan, Iran
Hassan Bevrani, University of Kurdistan, Iran
Chapter 11
Fuzzy Finite Element Method in Diffusion Problems......................................................................... 250
S. Chakraverty, National Institute of Technology – Rourkela, India
S. Nayak, National Institute of Technology, India
Chapter 12
A Hybrid Model for Rice Disease Diagnosis Using Entropy Based Neuro Genetic Algorithm......... 273
K. Lavanya, VIT University, Vellore, India
M.A. Saleem Durai, VIT University, Vellore, India
N.Ch.S.N. Iyengar, VIT University, Vellore, India
8.
Chapter 13
A Fuzzy Model with Thermodynamic Based Consequents and a Niching Swarm-Based
Supervisor to Capture the Uncertainties of Damavand Power System................................................ 292
Ahmad Mozaffari, University of Waterloo, Canada
Moein Mohammadpour, Babol University of Technology, Iran
Alireza Fathi, Babol University of Technology, Iran
Mofid Gorji-Bandpy, Babol University of Technology, Iran
Chapter 14
Design of a Hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) Controller for Position and
Angle Control of Inverted Pendulum (IP) Systems............................................................................. 308
Ashwani Kharola, Institute of Technology Management (ITM), India
Chapter 15
Intuitionistic Fuzzy Set Theory with Fair Share CPU Scheduler: A Dynamic Approach................... 321
Supriya Raheja, NorthCap University, India
Chapter 16
Classification of EEG Signals for Motor Imagery Based on Mutual Information and Adaptive
Neuro Fuzzy Inference System............................................................................................................ 347
Shereen A. El-aal, Al-Azhar University, Egypt
Rabie A. Ramadan, Cairo University, Egypt
Neveen Ghali, Al-Azhar University, Egypt
Chapter 17
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems................................... 367
P. Senthil Kumar, Jamal Mohamed College (Autonomous), India
Chapter 18
Fault Detection and Isolation for an Uncertain Takagi-Sugeno Fuzzy System using the Interval
Approach.............................................................................................................................................. 393
Hassene Bedoui, University of Monastir, Tunisia
Atef Kedher, University of Tunis Manar, Tunisia
Kamel Ben Othman, University of Tunis Manar, Tunisia
Section 2
Tools and Technologies
Chapter 19
Fuzzy Expert System to Diagnose Diabetes Using S Weights for S Fuzzy Assessment
Methodology........................................................................................................................................ 418
A. V. Senthil Kumar, Hindusthan College of Arts and Science, India
M. Kalpana, Tamil Nadu Agricultural University, India
9.
Chapter 20
Hybrid Fuzzy Neural Search Retrieval System................................................................................... 443
Rawan Ghnemat, Princess Sumaya University for Technology, Jordan
Adnan Shaout, The University of Michigan – Dearborn, USA
Chapter 21
A Multi-Objective Fuzzy Ant Colony Optimization Algorithm for Virtual Machine Placement....... 459
Boominathan Perumal, VIT University, Vellore, India
Aramudhan M., Perunthalaivar Kamarajar Institute of Engineering and Technology, India
Chapter 22
Fuzzy Adaptive Controller for Uncertain Multivariable Nonlinear Systems with Both Sector
Nonlinearities and Dead-Zones........................................................................................................... 487
Abdesselem Boulkroune, University of Jijel, Algeria
Chapter 23
A Two-Level Fuzzy Value-Based Replica Replacement Algorithm in Data Grids............................. 516
Nazanin Saadat, Science and Research Branch, Islamic Azad University, Iran
Amir Masoud Rahmani, Science and Research Branch, Islamic Azad University, Iran
Chapter 24
A Fuzzy Expert System for Star Classification Based on Photometry................................................ 540
Aida Pakniyat, Kharazmi University, Iran
Rahil Hosseini, Shahr-e-Qods Branch, Islamic Azad University, Iran
Mahdi Mazinai, Shahr-e-Qods Branch, Islamic Azad University, Iran
Chapter 25
Personalized Neuro-Fuzzy Expert System for Determination of Nutrient Requirements................... 551
Priti Srinivas Sajja, Sardar Patel University, India
Jeegar Ashokkumar Trivedi, Sardar Patel University, India
Volume II
Chapter 26
Movie Recommendation System Based on Fuzzy Inference System and Adaptive Neuro Fuzzy
Inference System.................................................................................................................................. 573
Mahfuzur Rahman Siddiquee, North South University, Bangladesh
Naimul Haider, North South University, Bangladesh
Rashedur M. Rahman, North South University, Bangladesh
Chapter 27
Fuzzy Logic-Based Cluster Heads Percentage Calculation for Improving the Performance of the
LEACH Protocol.................................................................................................................................. 609
Omar Banimelhem, Jordan University of Science and Technology, Jordan
Eyad Taqieddin, Jordan University of Science and Technology, Jordan
Moad Y. Mowafi, Jordan University of Science and Technology, Jordan
Fahed Awad, Jordan University of Science and Technology, Jordan
Feda’ Al-Ma’aqbeh, Jordan University of Science and Technology, Jordan
10.
Chapter 28
Evaluation of Human Machine Interface (HMI) on a Digital and Analog Control Room in Nuclear
Power Plants Using a Fuzzy Logic Approach...................................................................................... 628
Pola Lydia Lagari, Purdue University, USA
Antonia Nasiakou, Purdue University, USA
Miltiadis Alamaniotis, Purdue University, USA
Chapter 29
Including Client Opinion and Employee Engagement in the Strategic Human Resource
Management: An Advanced SWOT- FUZZY Decision Making Tool................................................ 647
Rachid Belhaj, Mohammed V University, Morocco
Mohamed Tkiouat, Mohammed V University, Morocco
Chapter 30
An Optimal Fuzzy Load Balanced Adaptive Gateway Discovery for Ubiquitous Internet Access in
MANET............................................................................................................................................... 663
Prakash Srivastava, Madan Mohan Malaviya University of Technology, India
Rakesh Kumar, Madan Mohan Malaviya University of Technology, India
Chapter 31
A Hybrid System Based on FMM and MLP to Diagnose Heart Disease............................................ 682
Swati Aggarwal, NSIT, India
Venu Azad, Government Girls PG College, India
Chapter 32
Strictness Petroleum Prediction System Based on Fuzzy Model........................................................ 715
Senan A. Ghallab, Ain Shams University, Egypt
Nagwa. L. Badr, Ain Shams University, Egypt
Abdel Badeeh Salem, Ain Shams University, Egypt
M. F. Tolba, Ain Shams University, Egypt
Chapter 33
Fuzzy-Based Matrix Converter Drive for Induction Motor................................................................. 738
Chitra Venugopal, University of KwaZulu-Natal, South Africa
Chapter 34
A Fuzzy-Based Calorie Burn Calculator for a Gamified Walking Activity Using Treadmill............. 763
Prabhakar Rontala Subramaniam, University of KwaZulu-Natal, South Africa
Chitra Venugopal, University of KwaZulu-Natal, South Africa
Arun Kumar Sangaiah, VIT University, India
Chapter 35
Application of Fuzzy Logic for Mapping the Agro-Ecological Zones................................................ 782
Bistok Hasiholan Simanjuntak, Satya Wacana Christian University, Indonesia
Sri Yulianto Joko Prasetyo, Satya Wacana Christian University, Indonesia
Kristoko Dwi Hartomo, Satya Wacana Christian University, Indonesia
Hindriyanto Dwi Purnomo, Satya Wacana Christian University, Indonesia
11.
Chapter 36
Prediction of Solar and Wind Energies by Fuzzy Logic Control......................................................... 807
Sanaa Faquir, University Sidi Mohamed Ben Abdallah, Morocco
Ali Yahyaouy, University Sidi Mohamed Ben Abdallah, Morocco
Hamid Tairi, University Sidi Mohamed Ben Abdallah, Morocco
Jalal Sabor, Ecole Nationale Superieure d’Arts et Metiers (ENSAM), Morocco
Chapter 37
Enhancement of Turbo-Generators Phase Backup Protection Using Adaptive Neuro Fuzzy
Inference System.................................................................................................................................. 835
Mohamed Salah El-Din Ahmed Abdel Aziz, Dar Al-Handasah (Shair and partners), Egypt
Mohamed Elsamahy, The Higher Institute of Engineering, El-Shorouk Academy, Egypt
Mohamed A. Moustafa Hassan, Cairo University, Egypt
Fahmy M. A. Bendary, Benha University, Egypt
Chapter 38
Fuzzy Rule Based Environment Monitoring System for Weather Controlled Laboratories Using
Arduino................................................................................................................................................ 855
S. Sasirekha, SSN College of Engineering, India
S. Swamynathan, Anna University, India
Chapter 39
Fuzzy Labeled Transition Refinement Tree: Application to Stepwise Designing Multi Agent
Systems................................................................................................................................................ 873
Sofia Kouah, University of Constantine 2, Algeria University of Oum El Bouaghi, Algeria
Djamel-Eddine Saidouni, University of Constantine 2, Algeria
Chapter 40
Rule-Based Systems for Medical Diagnosis........................................................................................ 906
V. S. Giridhar Akula, Methodist College of Engineering and Technology, India
Section 3
Utilization and Application
Chapter 41
Implementation of Fuzzy Technology in Complicated Medical Diagnostics and Further
Decision............................................................................................................................................... 935
A. B. Bhattacharya, University of Kalyani, India
Arkajit Bhattacharya, M. G. M. Medical College and Hospital, India
Chapter 42
Intelligent Decision Making and Risk Analysis of B2c E-Commerce Customer Satisfaction............ 969
Masoud Mohammadian, University of Canberra, Australia
12.
Chapter 43
Fuzzy Logic Based Approach for Power System Fault Section Analysis............................................ 987
Neeti Dugaya, Sagar Institute of Research, Technology and Science, India
Smita Shandilya, Sagar Institute of Research, Technology and Science, India
Chapter 44
Some Recent Defuzzification Methods.............................................................................................. 1003
Harendra Kumar, Gurukula Kangari University, India
Chapter 45
Application of Fuzzy Expert System in Medical Treatment............................................................. 1020
Kajal Ghosal, Chronic Disease and Oncological Homeopathic Consultant, India
Partha Haldar, Jadavpur University, India
Goutam Sutradhar, Jadavpur University, India
Chapter 46
Predicting Uncertain Behavior and Performance Analysis of the Pulping System in a Paper
Industry Using PSO and Fuzzy Methodology................................................................................... 1070
Harish Garg, Indian Institute of Technology-Roorkee, India
Monica Rani, Indian Institute of Technology-Roorkee, India
S.P. Sharma, Indian Institute of Technology-Roorkee, India
Chapter 47
Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM
Problems............................................................................................................................................ 1110
John Robinson P., Bishop Heber College (Autonomous), India
Henry Amirtharaj E. C., Bishop Heber College (Autonomous), India
Volume III
Chapter 48
A Fuzzy-Based Approach to Support Decision Making in Complex Military Environments.......... 1150
Timothy P. Hanratty, US Army Research Laboratory, Aberdeen Proving Ground, USA
E. Allison Newcomb, Towson University, USA
Robert J. Hammell II, Towson University, USA
John T. Richardson, US Army Research Laboratory, Aberdeen Proving Ground, USA
Mark R. Mittrick, US Army Research Laboratory, Aberdeen Proving Ground, USA
Chapter 49
Nonlinear System Identification of Smart Buildings......................................................................... 1183
Soroush Mohammadzadeh, University of Oklahoma, USA
Yeesock Kim, Worcester Polytechnic Institute (WPI), USA
13.
Chapter 50
Fuzzy Logic-Based Intelligent Control System for Active Ankle Foot Orthosis.............................. 1203
M. Kanthi, Manipal University, India
Chapter 51
Knowledge Representation Using Fuzzy XML Rules in Web-Based Expert System for Medical
Diagnosis........................................................................................................................................... 1237
Priti Srinivas Sajja, Sardar Patel University, India
Chapter 52
Improvement of JXTA-Overlay P2P Platform: Evaluation for Medical Application and
Reliability........................................................................................................................................... 1268
Yi Liu, Fukuoka Institute of Technology (FIT), Japan
Shinji Sakamoto, Fukuoka Institute of Technology (FIT), Japan
Keita Matsuo, Fukuoka Prefectural Fukuoka Technical High School, Japan
Makoto Ikeda, Fukuoka Institute of Technology (FIT), Japan
Leonard Barolli, Fukuoka Institute of Technology (FIT), Japan
Fatos Xhafa, Technical University of Catalonia, Spain
Chapter 53
Bio-Inspired Computing through Artificial Neural Network............................................................. 1285
Nilamadhab Dash, C. V. Raman College of Engineering, India
Rojalina Priyadarshini, C. V. Raman College of Engineering, India
Brojo Kishore Mishra, C. V. Raman College of Engineering, India
Rachita Misra, C. V. Raman College of Engineering, India
Chapter 54
Trust Calculation Using Fuzzy Logic in Cloud Computing.............................................................. 1314
Rajanpreet Kaur Chahal, Panjab University, India
Sarbjeet Singh, Panjab University, India
Chapter 55
Fuzzy Decision Support System for Coronary Artery Disease Diagnosis Based on Rough Set
Theory................................................................................................................................................ 1367
Noor Akhmad Setiawan, Universitas Gadjah Mada, Indonesia
Chapter 56
Artificial Intelligent Approaches for Prediction of Longitudinal Wave Velocity in Rocks............... 1385
A. K. Verma, Indian School of Mines, India
T. N. Singh, Indian Institute of Technology, India
Sachin Maheshwar, Indian School of Mines, India
14.
Chapter 57
An Adaptive Path Planning Based on Improved Fuzzy Neural Network for Multi-Robot
Systems.............................................................................................................................................. 1396
Zhiguo Shi, University of Science and Technology, China
Huan Zhang, University of Science and Technology, China
Jingyun Zhou, University of Science and Technology, China
Junming Wei, Australian National University, Australia
Chapter 58
Information Systems on Hesitant Fuzzy Sets.................................................................................... 1425
Deepak D., National Institute of Technology Calicut, India
Sunil Jacob John, National Institute of Technology Calicut, India
Chapter 59
Artificial Intelligence Methods and Their Applications in Civil Engineering.................................. 1453
Gonzalo Martínez-Barrera, Universidad Autónoma del Estado de México, Mexico
Osman Gencel, Bartin University, Turkey
Ahmet Beycioglu, Düzce University, Turkey
Serkan Subaşı, Düzce University, Turkey
Nelly González-Rivas, Joint Center for Research in Sustainable Chemistry (CCIQS), Mexico
Chapter 60
Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic
Trapezoidal Fuzzy MAGDM Problems............................................................................................. 1478
John P. Robinson, Bishop Heber College, India
Chapter 61
A Study on Hybridization of Intelligent Techniques in Bioinformatics............................................ 1518
Peyakunta Bhargavi, Sri Padmavati Mahila University, India
S. Jyothi, Sri Padmavati Mahila University, India
D. M. Mamatha, Sri Padmavati Mahila Univeristy, India
Chapter 62
Dynamic Behaviour and Crack Detection of a Multi Cracked Rotating Shaft using Adaptive
Neuro-Fuzzy-Inference System: Vibration Analysis of Multi Cracked Rotating Shaft..................... 1540
Rajeev Ranjan, Haldia Institute of Technology, India
Section 4
Organizational and Social Implications
Chapter 63
Modeling Conflict Dynamics: System Dynamic Approach............................................................... 1553
Janez Usenik, University of Maribor, Slovenia
Tit Turnsek, Landscape Governance College Grm, Slovenia
15.
Chapter 64
Fuzzy Opinion: Detection of Opinion Based on SentiWordNet Dictionary by Using Fuzzy
Logic.................................................................................................................................................. 1576
Mohamed Amine Boudia, Dr. Tahar Moulay University of Saida, Algeria
Reda Mohamed Hamou, Dr. Tahar Moulay University of Saida, Algeria
Abdelmalek Amine, Dr. Tahar Moulay University of Saida, Algeria
Chapter 65
Adjust Fuzzy Model Parameters for Head Election in Wireless Sensor Network Protocols............. 1596
Walaa Abd el Aal Afifi, ISSR-Cairo University, Egypt
Hesham Ahmed Hefny, ISSR-Cairo University, Egypt
Chapter 66
Bidder Selection in Public Procurement using a Fuzzy Decision Support System........................... 1620
Vjekoslav Bobar, University of Belgrade, Serbia
Ksenija Mandic, University of Belgrade, Serbia
Milija Suknovic, University of Belgrade, Serbia
Chapter 67
Fuzzy Dynamic Load Balancing in Virtualized Data Centers of SaaS Cloud Provider.................... 1643
Md. S. Q. Zulkar Nine, North South University, Bangladesh
Abul Kalam Azad, North South University, Bangladesh
Saad Abdullah, North South University, Bangladesh
Rashedur M. Rahman, North South University, Bangladesh
Section 5
Emerging Trends
Chapter 68
Emerging Application of Fuzzy Expert System in Medical Domain................................................ 1667
A. V. Senthil Kumar, Hindusthan College of Arts and Science, India
M. Kalpana, Tamil Nadu Agricultural University, India
Chapter 69
Fuzzy Critical Path Method Based on a New Approach of Ranking Fuzzy Numbers Using
Centroid of Centroids......................................................................................................................... 1690
N. Ravi Shankar, GITAM University, India
B. Pardha Saradhi, Dr. L.B. College, India
S. Suresh Babu, GITAM University, India
Chapter 70
MAGDM-Miner: A New Algorithm for Mining Trapezoidal Intuitionistic Fuzzy Correlation
Rules.................................................................................................................................................. 1708
John P. Robinson, Bishop Heber College, India
Henry Amirtharaj, Bishop Heber College, India
16.
Chapter 71
Advances in QoS/E Characterization and Prediction for Next Generation Mobile Communication
Systems.............................................................................................................................................. 1739
Charalampos N. Pitas, National Technical University of Athens, Greece
Apostolos G. Fertis, SMA und Partner AG, Zurich, Switzerland
Dimitris E. Charilas, National Technical University of Athens, Greece
Athanasios D. Panagopoulos, National Technical University of Athens, Greece
Index....................................................................................................................................................xxii
18. 368
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems
are the parameters of the transportation problem. Efficient algorithms have been developed for solving
transportationproblemswhenthecostcoefficients,thedemandandsupplyquantitiesareknownprecisely.
In the history of mathematics, Hitchcock (1941) originally developed the basic transportation prob-
lem. Charnes and Cooper (1954) developed the stepping stone method which provides an alternative
way of determining the simplex method information. Appa (1973) discussed several variations of the
transportation problem. Arsham et al. (1989) proposed a simplex type algorithm for general transporta-
tion 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 infor-
mation 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 program-
ming 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) pro-
posed 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 find-
ing 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 transpor-
tation problems in which supplies and demands are trapezoidal fuzzy numbers. Hadi Basirzadeh (2011)
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20. 389
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems
Values of µ Z
c( ) at different values of c can be determined using equations given below:
µ Z
c
for c
c
for c
for c( ) =
≤
−
≤ ≤
≤ ≤
−
0 104
104
64
104 168
1 168 184
248
,
,
,
cc
for c
for c
64
184 248
0 248
,
,
≤ ≤
≥
By using the proposed method a decision maker has the following advantages:
1. The proposed method gives the optimal solution in terms of mixed fuzzy numbers. Moreover, the
proposed method gives the opportunity to the decision maker to solve all the types of FTP;
2. The proposed method is computationally very simple and easy to understand.
7. CONCLUSION
On the basis of the present study, it can be concluded that the type-1, type-2 and type-4 FTP which can
be solved by the existing methods (Pandian and Natarajan (2010), Dinagar and Palanivel (2009), Rani,
Gulathi, and Kumar (2014), Hadi Basirzadeh (2011), Gani and Razak (2006)) can also be solved by
the proposed method. However, it is much easier to apply the proposed method as compared to all the
Figure 1. Graphical representation of type-3 fuzzy transportation cost
21. 390
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems
existing methods. Also, new method and new multiplication operation on TrFN is proposed to compute
the optimal objective values in terms of trapezoidal fuzzy number which are very simple and easy to
understand and it can be easily applied by decision maker to solve type-1 and type-3 FTP. The proposed
method gives the optimal solution in terms of mixed fuzzy numbers. Hence the proposed method gives
the opportunity to the decision maker to solve all the types of FTP and computationally very simple
when compared to all the existing methods.
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This work was previously published in PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems edited by
Deng-Feng Li, pages 121-146, copyright year 2016 by IGI Publishing (an imprint of IGI Global).