A Linear Programming Approach for Minimizing a Linear Function Subject to Fuzzy Relational Inequalities With Addition–Min Composition

• Published in: IEEE transactions on fuzzy systems Vol. 25; no. 4; pp. 985 - 992
• Main Authors: Guu, Sy-Ming, Wu, Yan-Kuen
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Addition–min composition; Bandwidth; Continuity (mathematics); Data communication; Data transmission; fuzzy relational inequalities; Indexes; Inequalities; Linear programming; linear programming approach; Mathematical model; network congestion; Optimization; Peer to peer computing; Social networks
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2016.2593496

In this paper, we study an optimization problem of minimizing a linear function subject to fuzzy relational inequalities with the addition-min composition. This optimization setting has recently been proposed to model the network cogestion issue when a BitTorrent-like peer-to-peer file-sharing system is used for data transmission. In a 2014 paper, a pseudominimal index (PMI)-based approach was proposed to search for an optimal solution. It turns out that the PMI-based approach may require to solve several to many linear programming problems in order to get an optimal solution. In this paper, we point out that the feasible domain is indeed convex. And we only need to solve a single linear programming problem to generate an optimal solution for the original optimization problem. Furthermore, our approach could be extended to the case with a nonlinear continuous objective function.