A New Characterisation of the Minimal Solution Set to Max-min Fuzzy Relation Inequalities

Abstract

In this paper, max-min fuzzy relation inequalities are applied to describe a BitTorrent-like Peer-to-Peer file sharing system. In order to decrease the network congestion under some fixed priority grade of the terminals, we define concept of lexicographic solution in such system. It is found that each minimal solution of max-min fuzzy relation inequalities happen to be a lexicographic solution. Moreover, the lexicographic solution set is exactly the minimal solution set. Numerical example is given to illustrate our results. At last, for the addition-min fuzzy relation inequalities, we provide a guess, trying to describe the relation between its lexicographic solution set and minimal solution set.

Keywords

• Fuzzy relation inequality
• Fuzzy relation equation
• Lexicographic solution
• Minimal solution
• Max-min composition
• Peer-to-Peer network system