Linear objective function optimization with fuzzy relation equation constraints regarding max–av composition

In this paper, an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max–av composition is presented. The solution set of such a fuzzy relation equations is a non-convex set. In this paper, firstly we discuss the feasible solution set with two schemes and, secondly, study relationship between maximum and minimum points, and also, the feasible points as well. Furthermore, an algorithm and few concrete examples are presented in order to optimize linear objective function.