Resolution of bipolar fuzzy relation equations with max-Łukasiewicz composition

Abstract

The bipolar system of fuzzy relation equations with the max-Łukasiewicz composition is investigated in this work. A bipolar path approach is proposed for such a system. It is found that the complete solution set of the bipolar system is fully determined by its conservative bipolar paths, which are finite. Our proposed resolution approach is performed using the so-called path-based algorithm, step by step, and illustrated with numerical examples. Moreover, the global and local minimal (or maximal) solutions are discussed in this paper with a comparison to those of a classical unipolar system.