Weighted-minimax programming subject to the RTA max-product fuzzy relation inequality system and its optimal strong solution

Abstract

Recently the max-product fuzzy relation inequalities have been applied to describe the wireless communication basic-station system. In this paper we further define the so-called random-term-absent (RTA) max-product fuzzy relation inequalities, which enable the system to bear a random communication line fault. Moreover, in order to make all basic-stations take part in the communication activity and avoid waste of resources, we investigate the strong solution to the RTA system. In general case, the strong solution set is composed by a unique maximum strong solution and a finite number of minimal strong solutions. Based on the practical application consideration, we propose the corresponding weighted minimax optimization problem. Detailed algorithm is designed for obtaining the optimal strong solution of such an optimization problem, with an illustrative example.