Monomial geometric programming with fuzzy relation equation constraints

In this paper, an optimization model with an objective function as monomial subject to a system of the fuzzy relation equations with max-bounded difference (maxBD) composition operator is presented. We firstly determine its feasible solution set. Then some special characteristics of its feasible domain and the optimal solutions are studied. Some procedures for reducing and decomposing the problem into several subproblems with smaller dimensions are proposed. Finally, an algorithm is designed to optimize the objective function of each sub-problem.