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Fuzzy Stochastic Multiobjective Programming

Author: Masatoshi Sakawa

Publisher: Springer Science & Business Media

Published: 2011-02-03

Total Pages: 268

ISBN-13: 144198402X

Although studies on multiobjective mathematical programming under uncertainty have been accumulated and several books on multiobjective mathematical programming under uncertainty have been published (e.g., Stancu-Minasian (1984); Slowinski and Teghem (1990); Sakawa (1993); Lai and Hwang (1994); Sakawa (2000)), there seems to be no book which concerns both randomness of events related to environments and fuzziness of human judgments simultaneously in multiobjective decision making problems. In this book, the authors are concerned with introducing the latest advances in the field of multiobjective optimization under both fuzziness and randomness on the basis of the authors’ continuing research works. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is devoted to mathematical preliminaries, which will be used throughout the remainder of the book. Starting with basic notions and methods of multiobjective programming, interactive fuzzy multiobjective programming as well as fuzzy multiobjective programming is outlined. In Chapter 3, by considering the imprecision of decision maker’s (DM’s) judgment for stochastic objective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochastic programming is developed. In Chapter 4, through the consideration of not only the randomness of parameters involved in objective functions and/or constraints but also the experts’ ambiguous understanding of the realized values of the random parameters, multiobjective programming problems with fuzzy random variables are formulated. In Chapter 5, for resolving conflict of decision making problems in hierarchical managerial or public organizations where there exist two DMs who have different priorities in making decisions, two-level programming problems are discussed. Finally, Chapter 6 outlines some future research directions.

Multi-Objective Stochastic Programming in Fuzzy Environments

Author: Biswas, Animesh

Publisher: IGI Global

Published: 2019-03-22

Total Pages: 420

ISBN-13: 1522583025

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It is frequently observed that most decision-making problems involve several objectives, and the aim of the decision makers is to find the best decision by fulfilling the aspiration levels of all the objectives. Multi-objective decision making is especially suitable for the design and planning steps and allows a decision maker to achieve the optimal or aspired goals by considering the various interactions of the given constraints. Multi-Objective Stochastic Programming in Fuzzy Environments discusses optimization problems with fuzzy random variables following several types of probability distributions and different types of fuzzy numbers with different defuzzification processes in probabilistic situations. The content within this publication examines such topics as waste management, agricultural systems, and fuzzy set theory. It is designed for academicians, researchers, and students.

Linear and Multiobjective Programming with Fuzzy Stochastic Extensions

Author: Masatoshi Sakawa

Publisher: Springer Science & Business Media

Published: 2013-11-29

Total Pages: 347

ISBN-13: 1461493994

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Although several books or monographs on multiobjective optimization under uncertainty have been published, there seems to be no book which starts with an introductory chapter of linear programming and is designed to incorporate both fuzziness and randomness into multiobjective programming in a unified way. In this book, five major topics, linear programming, multiobjective programming, fuzzy programming, stochastic programming, and fuzzy stochastic programming, are presented in a comprehensive manner. Especially, the last four topics together comprise the main characteristics of this book, and special stress is placed on interactive decision making aspects of multiobjective programming for human-centered systems in most realistic situations under fuzziness and/or randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is a concise and condensed description of the theory of linear programming and its algorithms. Chapter 3 discusses fundamental notions and methods of multiobjective linear programming and concludes with interactive multiobjective linear programming. In Chapter 4, starting with clear explanations of fuzzy linear programming and fuzzy multiobjective linear programming, interactive fuzzy multiobjective linear programming is presented. Chapter 5 gives detailed explanations of fundamental notions and methods of stochastic programming including two-stage programming and chance constrained programming. Chapter 6 develops several interactive fuzzy programming approaches to multiobjective stochastic programming problems. Applications to purchase and transportation planning for food retailing are considered in Chapter 7. The book is self-contained because of the three appendices and answers to problems. Appendix A contains a brief summary of the topics from linear algebra. Pertinent results from nonlinear programming are summarized in Appendix B. Appendix C is a clear explanation of the Excel Solver, one of the easiest ways to solve optimization problems, through the use of simple examples of linear and nonlinear programming.

Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty

Author: Shi-Yu Huang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 425

ISBN-13: 940092111X

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Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

A Fuzzy/stochastic Multiobjective Linear Programming Method

Author: Bruno Urli

Publisher:

Published: 1990

Total Pages: 17

ISBN-13:

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Fuzzy Sets and Interactive Multiobjective Optimization

Author: Masatoshi Sakawa

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 319

ISBN-13: 1489916334

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The main characteristics of the real-world decision-making problems facing humans today are multidimensional and have multiple objectives including eco nomic, environmental, social, and technical ones. Hence, it seems natural that the consideration of many objectives in the actual decision-making process re quires multiobjective approaches rather than single-objective. One ofthe major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. Although multiobjective optimization problems differ from single objective optimization problems only in the plurality of objective functions, it is significant to realize that multiple objectives are often noncom mensurable and conflict with each other in multiobjective optimization problems. With this ob servation, in multiobjective optimization, the notion of Pareto optimality or effi ciency has been introduced instead of the optimality concept for single-objective optimization. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected from among the set of Pareto optimal or efficient solutions. Therefore, the question is, how does one find the preferred point as a compromise or satisficing solution with rational pro cedure? This is the starting point of multiobjective optimization. To be more specific, the aim is to determine how one derives a compromise or satisficing so lution of a decision maker (DM), which well represents the subjective judgments, from a Pareto optimal or an efficient solution set.

Study on Stochastic Multiobjective Optimization Problems

Author: Taghreed A. Hassanin

Publisher: LAP Lambert Academic Publishing

Published: 2014-02-20

Total Pages: 180

ISBN-13: 9783659505300

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This book introduces an efficient approach for treating Stochastic Multiobjective Programming Problem (SMP) through the probability maximization model, we introduced stochastic goals to consider the ambiguous judgments of the DM and proposed an interactive stochastic approach based on reference point satisficing method as a fusion of stochastic approaches and deterministic ones to derive a satisficing solution for the DM from the efficient solutions obtained. Also, this book introduces an optimization approach for solving Fuzzy Multiobjective Linear Programming Problem (FMOLP) problems with fuzzy goals in objective functions and constraints. This approach is based on the improvement of a compromise model for solving FMOLP by improving the objectives by altering their membership functions using the principle of the ARP Method, which guarantee the feasibility. This book presents a comparative study between the stochastic approach and the fuzzy approach for treating single and multiobjective objective linear/nonlinear programming problems.

Fuzzy Multi-Criteria Decision Making

Author: Cengiz Kahraman

Publisher: Springer Science & Business Media

Published: 2008-08-09

Total Pages: 591

ISBN-13: 0387768130

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This work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more. Each of the 22 chapters includes practical applications along with new developments/results. This book may be used as a textbook in graduate operations research, industrial engineering, and economics courses. It will also be an excellent resource, providing new suggestions and directions for further research, for computer programmers, mathematicians, and scientists in a variety of disciplines where multicriteria decision making is needed.

Interactive Multiobjective Decision Making Under Uncertainty

Author: Hitoshi Yano

Publisher: CRC Press

Published: 2017-02-03

Total Pages: 296

ISBN-13: 1498763553

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Recently, many books on multiobjective programming have been published. However, only a few books have been published, in which multiobjective programming under the randomness and the fuzziness are investigated. On the other hand, several books on multilevel programming have been published, in which multiple decision makers are involved in hierarchical decision situations. In this book, we introduce the latest advances in the field of multiobjective programming and multilevel programming under uncertainty. The reader can immediately use proposed methods to solve multiobjective programming and multilevel programming, which are based on linear programming or convex programming technique. Organization of each capter is summarized as follows. In Chapter 2, multiobjective programming problems with random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 3, multiobjective programming problems with fuzzy random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which not only the uncertainty of fuzzy random variables but also the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 4, multiobjective multilevel programming is discussed, and the interactive algorithms are developed to obtain a satisfactory solution, in which the hierarchical decision structure of multiple decision makers is reflected. In Chapter 5, two kinds of farm planning problems are solved by applying the proposed method, in which cost coefficients of crops are expressed by random variables.

Intelligent Computing

Author: Kohei Arai

Publisher: Springer

Published: 2018-11-01

Total Pages: 1165

ISBN-13: 3030011747

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This book, gathering the Proceedings of the 2018 Computing Conference, offers a remarkable collection of chapters covering a wide range of topics in intelligent systems, computing and their real-world applications. The Conference attracted a total of 568 submissions from pioneering researchers, scientists, industrial engineers, and students from all around the world. These submissions underwent a double-blind peer review process. Of those 568 submissions, 192 submissions (including 14 poster papers) were selected for inclusion in these proceedings. Despite computer science’s comparatively brief history as a formal academic discipline, it has made a number of fundamental contributions to science and society—in fact, along with electronics, it is a founding science of the current epoch of human history (‘the Information Age’) and a main driver of the Information Revolution. The goal of this conference is to provide a platform for researchers to present fundamental contributions, and to be a premier venue for academic and industry practitioners to share new ideas and development experiences. This book collects state of the art chapters on all aspects of Computer Science, from classical to intelligent. It covers both the theory and applications of the latest computer technologies and methodologies. Providing the state of the art in intelligent methods and techniques for solving real-world problems, along with a vision of future research, the book will be interesting and valuable for a broad readership.