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

• Main Authors: Wang, Xue-Ping, Li, Meng, Shu, Qian-Yu
• Format: Journal Article
• Language: English
• Published: 06.06.2023
• Subjects: Mathematics - General Mathematics
• DOI: 10.48550/arxiv.2306.04651

Fuzzy Sets and Systems 492 (2024) 109067 This article focuses on minimax programming problems subject to addition-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.