A new solution methodology for fuzzy relation equations

Abstract

In this paper a general methodology for studying and solving fuzzy relation equations based on sup-t composition, where t is any continuous triangular norm, is proposed. To this end the concept of the “solution matrices” is introduced, as a way of representing the process information required for the resolution. Using this concept, the solution existence of a fuzzy relation equation is first examined. When the relation equation has no solution, the reasons for this lack of solvability are found. Otherwise, the solution set is determined.