A scalarization method for fuzzy set optimization problems

Masamichi Kon ()
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Masamichi Kon: Hirosaki University

Fuzzy Optimization and Decision Making, 2020, vol. 19, issue 2, No 1, 135-152

Abstract: 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.

Keywords: Fuzzy set optimization; Scalarization; Fuzzy max order; Order preserving property; Set optimization (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10700-020-09313-0

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