Solving linear optimization problems with max-star composition equation constraints

In this paper an optimization model with a linear objective function subject to a system of fuzzy relation composition equations is presented. Since the non-empty feasible solution set of the fuzzy relation equations is generally a non-convex set, the conventional linear programming method will not be suitable for solving such a problem. Therefore, an efficient solution procedure for such problems appears to be necessary. In this paper, firstly, we characterize the feasible solution set, and then introduce two efficient procedures for solving the problem. Finally, two concrete examples are included for more details.