Weighted minimax programming subject to the max-min fuzzy relation inequalities

• Published in: AIMS mathematics Vol. 9; no. 6; pp. 13624 - 13641
• Main Authors: Chen, Miaoxia, Shibghatullah, Abdul Samad, Subramaniam, Kasthuri, Yang, Xiaopeng
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: fuzzy relation inequality; mathematical model; max-min composition; p2p network system; weighted minimax programming
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2024665

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.