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A scalarization method for fuzzy set optimization problems

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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.

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  1. Faculty of Science and Technology, Hirosaki University, Hirosaki, 036-8561, Japan

    Masamichi Kon

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  1. Masamichi Kon
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Kon, M. A scalarization method for fuzzy set optimization problems. Fuzzy Optim Decis Making 19, 135–152 (2020). https://doi.org/10.1007/s10700-020-09313-0

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  • DOI: https://doi.org/10.1007/s10700-020-09313-0

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