Minimax programming problems subject to addition-Łukasiewicz fuzzy relational inequalities and their optimal solutions

This article focuses on minimax programming problems subject to addition-Łukasiewicz fuzzy relational inequalities. We first establish two necessary and sufficient conditions for a solution of the fuzzy relational inequalities being a minimal one and explore the existence condition of the unique min...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 492; p. 109067
Main Authors Wang, Xue-ping, Li, Meng, Shu, Qian-yu
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.09.2024
Subjects
Addition-Łukasiewicz composition
Fuzzy relational inequality
Minimal solution
Minimax programming problem
Optimal solution
Minimax programming problem
Fuzzy relational inequality
Minimal solution
Addition-Łukasiewicz composition
Optimal solution
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ISSN0165-0114
1872-6801
DOI10.1016/j.fss.2024.109067

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Summary:This article focuses on minimax programming problems subject to addition-Łukasiewicz fuzzy relational inequalities. We first establish two necessary and sufficient conditions for a solution of the fuzzy relational inequalities being a minimal one and explore the existence condition of the unique minimal solution. We then supply an algorithm for obtaining some minimal solutions starting from a given one and apply minimal solutions to the minimax programming problems for searching optimal solutions. We also provide two algorithms for solving a kind of single variable optimization problems and get the greatest optimal solution. The algorithm for finding some minimal solutions of a given one is also used for searching some minimal optimal solutions.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2024.109067