This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples.

中文翻译：

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Max-Archimedean双极模糊关系方程解的覆盖问题

本文讨论了max-Archimedean双极模糊关系方程的求解。在文献中，已经提出了许多基于 0-1 整数规划问题或简化方法的双极模糊关系方程优化方法。本文引入了一种基于覆盖思想和先导、非先导变量概念的新概念，用于求解最大-阿基米德双极模糊关系方程。结果表明，求最大-阿基米德双极模糊关系方程组的完全解集的问题等价于求解一个覆盖问题，该方程组的解对应于覆盖问题的冗余覆盖。所提出的方法用一些例子来说明。