linear objective function optimization with the max-product fuzzy relation inequality constraints

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal solutions. some procedures are proposed to reduce and decompose the original problem into several sub-problems with smaller dimensions. combining the procedures, a new algorithm is proposed to solve the original problem. an example is also provided to show the efficiency of the algorithm.