Variable-Absent Fuzzy Relation Inequality With Max-Min Composition

Fuzzy relation system with max-min composition could be applied to describe the three-tier multimedia streaming architecture. In such an architecture, the regional servers supply their local multimedia streaming services to the clients. Random fault has not been considered in the relevant existing researches. However, the random fault of a regional server is possible to occur, or even unavoidable, due to some unpredictable reasons. In this article, we consider a random fault occurring at either one of the regional servers. With such a consideration, the corresponding architecture is characterized by the so-called variable-absent fuzzy relation inequalities system with max-min composition. Some properties of our proposed variable-absent fuzzy relation inequalities system are investigated. Based on such properties, we further propose a 2-D path approach for obtaining the complete solution of the variable-absent system. In addition, we also study a corresponding weighted minimax optimization problem motivated by the practical management objective. An effective algorithm is developed for searching the optimal solution, with an illustrative example.