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A scalarization method for fuzzy set optimization problems

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  • Masamichi Kon

    (Hirosaki University)

Abstract

In the present paper, we consider fuzzy optimization problems which involve fuzzy sets only in the objective mappings, and give two concepts of optimal solutions which are non-dominated solutions and weak non-dominated solutions based on orderings of fuzzy sets. First, by using level sets of fuzzy sets, the fuzzy optimization problems treated in this paper are reduced to set optimization problems, and relationships between (weak) non-dominated solutions of the fuzzy optimization problems and the reduced set optimization problems are derived. Next, the set optimization problems are reduced to scalar optimization problems which can be regarded as scalarization of the fuzzy optimization problems. Then, relationships between non-dominated solutions of the fuzzy optimization problems and optimal solutions of the reduced scalar optimization problems are derived.

Suggested Citation

  • Masamichi Kon, 2020. "A scalarization method for fuzzy set optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 135-152, June.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:2:d:10.1007_s10700-020-09313-0
    DOI: 10.1007/s10700-020-09313-0
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
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    3. Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
    4. Takashi Maeda, 2012. "On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 263-279, May.
    5. Masahiro Inuiguchi, 2005. "Multiple Objective Linear Programming with Fuzzy Coefficients," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 723-757, Springer.
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