Fixed-Index-Set Based Approach for Solving a Bilevel Fuzzy Relation Programming With Addition-Min Composition

Abstract

In recent years, the addition-min fuzzy relation inequalities have been adopted to describe the flow constraint in a P2P network system. Each solution of the inequalities represents a feasible flow control scheme. Motivated by some different managerial objectives, several optimization problems subject to the addition-min inequalities have been recently studied. For example, considering the total efficiency for decreasing the network congestion, the linear objective function was adopted. While considering the fairness among the terminals, the min-max objective function was employed. In this work, combining these two objectives, we establish a corresponding bi-level fuzzy relation programming subject to the addition-min inequalities. For solving the bi-level programming, we first investigate some properties of the first-level programming, using the concept of fixed index set. Based on the properties of the first-level programming, our studied bi-level programming could be equivalently converted into a single-level programming and then solved by the existing linear programming approach. Our resolution approach is carried out by the fixed-index-set based algorithm and illustrated by some numerical examples.