Linear optimization of bipolar fuzzy relational equations with max-Łukasiewicz composition

According to the literature, a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max-Łukasiewicz composition can be translated into a 0-1 integer linear programming problem and solved using integer optimization techniques. However, the technique of integer optimization may involve hight computation complexity. To improve computational efficiency for solving such an optimization problem, this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component's lower bound or upper bound value. Because of this characteristic, a simple value matrix with some simplified rules can be proposed to reduce the problem size first. A simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0-1 integer linear programming problem. Two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm.