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Fuzzy Sets and Interactive Multiobjective Optimization : Applied Information Technology - Masatoshi Sakawa

Fuzzy Sets and Interactive Multiobjective Optimization

Applied Information Technology

Hardcover

Published: 28th February 1993
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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.

Introductionp. 1
Introduction and historical remarksp. 1
Organization of the bookp. 4
Fundamentals of Fuzzy Set Theoryp. 7
Fuzzy setsp. 7
Extension principlep. 17
Fuzzy numbersp. 22
Fuzzy decisionp. 32
Fuzzy Linear Programmingp. 36
Linear programming and fuzzy linear programmingp. 36
Multiobjective linear programmingp. 43
Interactive multiobjective linear programmingp. 61
Fuzzy multiobjective linear programmingp. 67
Interactive fuzzy multiobjective linear programmingp. 81
Fuzzy Nonlinear Programmingp. 91
Nonlinear programming and fuzzy nonlinear programmingp. 91
Multiobjective nonlinear programmingp. 103
Interactive multiobjective nonlinear programmingp. 117
Fuzzy multiobjective nonlinear programmingp. 128
Interactive fuzzy multiobjective nonlinear programmingp. 134
Interactive Multiobjective Linear Programming With Fuzzy Parametersp. 149
Problem formulation and solution conceptsp. 151
Interactive programmingp. 154
Interactive fuzzy programmingp. 160
Interactive Multiobjective Nonlinear Programming With Fuzzy Parametersp. 174
Problem formulation and solution conceptsp. 175
Interactive nonlinear programmingp. 178
Interactive fuzzy nonlinear programmingp. 186
Interactive Computer Programsp. 198
Illustrative examples with computer outputsp. 207
Installation of PC versions for linear modelsp. 223
Some Applicationsp. 225
Packaging system in automated warehousesp. 225
Pass scheduling for hot tandem millsp. 233
Regional planningp. 241
Further Research Directionsp. 247
Multiobjective possibilistic programmingp. 247
Multiobjective programming with fuzzy variables and parametersp. 255
Fuzzy multiobjective 0-1 programming through neural computationp. 262
Fuzzy regression analysisp. 266
Appendix: Hyperplane Methods and Trade-Offsp. 274
Referencesp. 289
Indexp. 305
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306443374
ISBN-10: 0306443376
Series: Applied Information Technology
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 308
Published: 28th February 1993
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 25.4 x 17.8  x 1.91
Weight (kg): 1.84