Fuzzy Sets and Interactive Multiobjective Optimization

✍ Scribed by Masatoshi Sakawa (auth.)

• Publisher: Springer US
• Year: 1993
• Tongue: English
• Leaves: 319
• Series: Applied Information Technology
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-6
Fundamentals of Fuzzy Set Theory....Pages 7-35
Fuzzy Linear Programming....Pages 36-90
Fuzzy Nonlinear Programming....Pages 91-148
Interactive Multiobjective Linear Programming with Fuzzy Parameters....Pages 149-173
Interactive Multiobjective Nonlinear Programming with Fuzzy Parameters....Pages 174-197
Interactive Computer Programs....Pages 198-224
Some Applications....Pages 225-246
Further Research Directions....Pages 247-273
Back Matter....Pages 274-308

✦ Subjects

Mathematics, general; Computer Science, general