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Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys pp 171–226Cite as

Fuzzy Multiobjective and Multilevel Optimization

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 52))

Abstract

In this chapter, for handling and tackling the imprecise nature of human judgments, multiobjective optimization in a fuzzy environment is discussed. Starting with several basic definitions involving fuzzy sets, Bellman and Zadeh’s approach to decision making in a fuzzy environment, called fuzzy decision, is outlined. Fundamental notions and methods of multiobjective, and interactive multiobjective programming are briefly reviewed. Then multiobjective linear programming and interactive multiobjective linear programming, both incorporating fuzzy goals of the decision maker (DM), are explained in detail by putting special emphasis on Pareto optimality. Multiobjective linear programming problems with fuzzy parameters, which reflect the experts’ ambiguous or fuzzy understanding of the nature of the parameters in the problem-formulation process, are also formulated. By extending the usual Pareto optimality concepts, interactive decision-making methods, both without and with the fuzzy goals of the D M, for deriving a satisficing solution for the DM efficiently from an extended Pareto optimal solution set are presented. Finally, attention is focused on two-level linear programming problems and an interactive fuzzy programming method is introduced. In the interactive method, after determining the fuzzy goals of the DMs at both levels, a satisfactory solution is derived efficiently by updating the minimal satisfactory level of the upper level DM with considerations of overall satisfactory balance between both levels. Furthermore, the proposed method is extended to deal with two-level linear programming problems with fuzzy parameters.

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Authors and Affiliations

  1. Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, 739-8527, Japan

    Masatoshi Sakawa

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  1. Masatoshi Sakawa
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  1. University of Auckland, New Zealand

    Matthias Ehrgott

  2. Université de Valenciennes, France

    Xavier Gandibleux

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Sakawa, M. (2003). Fuzzy Multiobjective and Multilevel Optimization. In: Ehrgott, M., Gandibleux, X. (eds) Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. International Series in Operations Research & Management Science, vol 52. Springer, Boston, MA. https://doi.org/10.1007/0-306-48107-3_4

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