Minimax programming problems subject to addition-{\L}ukasiewicz fuzzy relational inequalities and their optimal solutions

Xue-Ping Wang; Meng Li; Qian-Yu Shu

doi:10.1016/j.fss.2024.109067

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arXiv · 2306.04651

Minimax programming problems subject to addition-{\L}ukasiewicz fuzzy relational inequalities and their optimal solutions

Xue-Ping Wang·Meng Li·Qian-Yu Shu

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Abstract

This article focuses on minimax programming problems subject to addition-{\L}ukasiewicz fuzzy relational inequalities. We first establish two necessary and sufficient conditions that a solution of the fuzzy relational inequalities is a minimal one and explore the existence condition of the unique minimal solution. We also supply an algorithm to search for minimal solutions of the fuzzy relational inequalities starting from a given solution. We then apply minimal solutions of the fuzzy relational inequalities to the minimax programming problems for searching optimal solutions. We provide two algorithms to solve a kind of single variable optimization problems, and obtain the greatest optimal solution. The algorithm for finding minimal solutions of a given solution are also used for searching minimal optimal solutions.

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BibTeX RIS

Xue-Ping Wang, Meng Li, Qian-Yu Shu. 2023-06-06. Minimax programming problems subject to addition-{\L}ukasiewicz fuzzy relational inequalities and their optimal solutions. https://doi.org/10.1016/j.fss.2024.109067

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