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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| Vydané v: | Fuzzy sets and systems Ročník 492; s. 109067 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
15.09.2024
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| ISSN: | 0165-0114, 1872-6801 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 109067 |
| Author | Shu, Qian-yu Wang, Xue-ping Li, Meng |
| Author_xml | – sequence: 1 givenname: Xue-ping orcidid: 0000-0003-4376-9859 surname: Wang fullname: Wang, Xue-ping email: xpwang1@hotmail.com – sequence: 2 givenname: Meng surname: Li fullname: Li, Meng email: 1228205272@qq.com – sequence: 3 givenname: Qian-yu surname: Shu fullname: Shu, Qian-yu email: 34956229@qq.com |
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| Keywords | Minimax programming problem Fuzzy relational inequality Minimal solution Addition-Łukasiewicz composition Optimal solution |
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Fuzzy Syst. doi: 10.1109/TFUZZ.2015.2428716 – start-page: 452 year: 2012 ident: 10.1016/j.fss.2024.109067_br0090 article-title: Fuzzy relation inequalities about the data transmission mechanism in BitTorrent-like Peer-to-Peer file sharing systems – volume: 255 start-page: 41 year: 2014 ident: 10.1016/j.fss.2024.109067_br0230 article-title: An algorithm for minimizing a linear objective function subject to the fuzzy relation inequalities with addition-min composition publication-title: Fuzzy Sets Syst. doi: 10.1016/j.fss.2014.04.007 – volume: 447 start-page: 22 year: 2022 ident: 10.1016/j.fss.2024.109067_br0190 article-title: Generalized min-max programming problems subject to addition-min fuzzy relational inequalities publication-title: Fuzzy Sets Syst. doi: 10.1016/j.fss.2022.03.017 – volume: 25 start-page: 985 year: 2017 ident: 10.1016/j.fss.2024.109067_br0060 article-title: A linear programming approach for minimizing a linear function subject to fuzzy relational inequalities with addition-min composition publication-title: IEEE Trans. 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Fuzzy Syst. doi: 10.3233/IFS-151546 – volume: 12 start-page: 189 year: 1965 ident: 10.1016/j.fss.2024.109067_br0130 article-title: Representation of associative functions publication-title: Publ. Math. (Debr.) doi: 10.5486/PMD.1965.12.1-4.19 |
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