Fuzzy relational equations and the covering problem

Abstract

The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved that maximal solutions of the system correspond to irredundant coverings of the characteristic matrix. At last, the necessary and sufficient conditions that the system has a unique(maximal) solution are given.