Minimax programming problems subject to addition-Łukasiewicz fuzzy relational inequalities and their optimal solutions - Wang, Xue-ping; Li, Meng; Shu, Qian-yu (Fuzzy sets and systems, 2024)
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.