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

• Published in: IEEE transactions on fuzzy systems Vol. 31; no. 12; pp. 4361 - 4373
• Main Authors: Shu, Qianyu, Yang, Xiaopeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Addition-min composition; Algorithms; bilevel programming; Flow control; fuzzy relation inequality; Inequalities; linear objective function; Linear programming; Minimax techniques; min–max objective function; Network systems; Optimization; Peer-to-peer computing; Programming
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2023.3284392

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 article, combining these two objectives, we establish a corresponding bilevel fuzzy relation programming subject to the addition-min inequalities. For solving the bilevel 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 bilevel 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.