Optimal Strong Solution of the Minimax Problem With Two-Sided Fuzzy Relation Inequality Constraints

Abstract

To avoid unoccupied base stations, we introduce the concept of a strong solution to max-product fuzzy relation inequalities in this paper. Such a strong solution enables all base stations take part in wireless communication activities. The structure of the set of all strong solutions is discussed. The strong solution set is composed of a finite number of closed intervals. To decrease the damage caused by electromagnetic radiation, one always aims to find an optimal strong solution, in which each component reaches its minimum value. However, this is generally impossible. Hence, finding an optimal strong solution with a specific objective function is more feasible. In this work, we investigate the optimization, minimizing the largest component of a strong solution. A detailed algorithm is developed to find an optimal strong solution. The experimental results show that our proposed algorithm is efficient. In addition, we further discuss the structure of the complete optimal strong solution set.

Keywords

• Fuzzy relation inequality
• max-product composition
• minimax optimization
• nonconvex optimization
• strong solution