Min-Max Programming Problem Subject to Addition-Min Fuzzy Relation Inequalities

• Published in: IEEE transactions on fuzzy systems Vol. 24; no. 1; pp. 111 - 119
• Main Authors: Yang, Xiao-Peng, Zhou, Xue-Gang, Cao, Bing-Yuan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: addition-min composition; BitTorrent-like P2P file sharing system; Data communication; fuzzy relation equation; Fuzzy relation inequalities; Linear programming; min-max programming; Minimization; Optimization; Peer-to-peer computing; Programming; fuzzy relation equation; bitTorrent-like P2P file-sharing system; fuzzy relation inequalities; min-max programming; Addition-min composition
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2015.2428716

A BitTorrent-like peer-to-peer file-sharing system can be reduced into a system of addition-min fuzzy relation inequalities. Addition-min is a new composition, and the solution set of addition-min fuzzy relation inequalities differs much from that of general max-t-norm fuzzy relation inequalities or equations. In order to avoid network congestion and improve the stability of data transmission, a min-max programming problem is proposed subject to addition-min fuzzy relation inequalities in this paper. Based on some relevant theorems on resolution, a novel algorithm is developed step by step to find an optimal solution of the proposed problem. Moreover, an application example is given to illustrate the feasibility and efficiency of the algorithm. Finally, some further discussions are made concerning the optimal solution of the proposed problem.