Stability of solutions for fuzzy set optimization problems with applications

In this paper, we introduce a new parametric fuzzy set optimization problem based on the ordering relations of fuzzy sets, where a parametric function and an objective function both take values on fuzzy sets. We show the continuity of solution mappings for such a problem under some mild conditions....

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Bibliographic Details
Published inFuzzy sets and systems Vol. 466; p. 108470
Main Authors Zhang, Chuang-liang, Huang, Nan-jing, O'Regan, Donal
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.08.2023
Subjects
Continuous-time fuzzy optimization problem
Fuzzy function
Fuzzy set optimization problem
Stability
Continuous-time fuzzy optimization problem
Stability
Fuzzy set optimization problem
Fuzzy function
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ISSN0165-0114
1872-6801
DOI10.1016/j.fss.2023.01.005

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Summary:In this paper, we introduce a new parametric fuzzy set optimization problem based on the ordering relations of fuzzy sets, where a parametric function and an objective function both take values on fuzzy sets. We show the continuity of solution mappings for such a problem under some mild conditions. Moreover, we give the Painlevé-Kuratowski upper convergence and lower convergence of solution sets for fuzzy set optimization problems. As applications, the stability results are applied to obtain the continuity of a minimal solution mapping and the Painlevé-Kuratowski convergence of minimal solution sets for continuous-time fuzzy set optimization problems.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.01.005