Bilevel Optimization Problem With Random-Term-Absent Max-Product Fuzzy Relation Inequalities Constraint

The max-product fuzzy relation inequalities have been applied to describe the quantitative relation in a wireless communication base-station system in the existing work. However, the potential line fault between a base station and a signal testing point has not been considered. In this article, we define the so-called random-term-absent max-product fuzzy relation inequalities for describing the wireless communication base-station system with a random line fault. Based on the practical application consideration, we further construct a bilevel optimization problem subject to random-term-absent max-product fuzzy relation inequalities. For solving such bilevel optimization problem, properties of the random-term-absent system, as well as the common single-level fuzzy relation programming, are investigated. At last, a detailed algorithm is developed to find the optimal solution of our proposed bilevel optimization problem.