Reducing the feasible region of fuzzy relational equation systems regarding two different compositions

In this paper, systems of fuzzy relational equations (FRE) regarding the max-average and the max-Archimedean triangular norm compositions are considered. For this purpose, some theorems and results are presented and proved to thoroughly identify and reduce the feasible sets of the FRE systems. Possibility of each result is confirmed by a numerical example. Finally, the proposed methods to simplify the systems are effectively tested by two randomly generated consistent test problems.