Minimizing a linear objective function subject to fuzzy relation equations constraints with max-Hamacher product composition

In this paper, an optimization model with a linear objective function subject to a system of fuzzy relation equations, using max-Hamacher product composition operator, is presented. Since its nonempty feasible solution set is in general a nonconvex set, conventional linear programming methods are not suitable to solve such a problem, so an efficient solution procedure for such problems is necessary. In this paper, the feasible solution set of this problem is studied at first. Then, one efficient algorithm (i.e. tabular method algorithm) is proposed in order to solve the problem. Some procedures are also presented to reduce the original problem. Then, the reduced problem is decomposed (if possible) into several sub-problems with smaller dimensions, so solving them becomes much easier by the algorithm. By combining the algorithm and these procedures, another more efficient algorithm is suggested in order to obtain the optimal solution of the original problem. Some numerical examples are also given to illustrate the algorithms.