Addition-min fuzzy relation inequalities with application in BitTorrent-like Peer-to-Peer file sharing system

• Published in: Fuzzy sets and systems Vol. 343; pp. 126 - 140
• Main Authors: Yang, Xiao-Peng, Lin, Hai-Tao, Zhou, Xue-Gang, Cao, Bing-Yuan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.07.2018
• Subjects: Addition-min composition; BitTorrent-like P2P file sharing systems; Convex set; Fuzzy relation equation; Fuzzy relation inequalities; Minimal solution; Minimal solution; BitTorrent-like P2P file sharing systems; Fuzzy relation equation; Convex set; Addition-min composition; Fuzzy relation inequalities
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2017.04.002

The data transmission mechanism in BitTorrent-like Peer-to-Peer (P2P) file sharing systems may be reduced to some addition-min fuzzy relation inequalities. The solution set of addition-min fuzzy relation inequalities plays an important role in the corresponding optimization problem. In this paper, we study some properties of the solutions to such system. Convexity of the solution set and number of minimal solutions are discussed, with comparison to those of the classical max-T fuzzy relation equations or inequalities. Besides, vertex solution and variable-ordering minimal solution are also investigated, with application in BitTorrent-like P2P file sharing system. Two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable-ordering solution.