Random-term-absent addition-min fuzzy relation inequalities and their lexicographic minimum solutions

• Published in: Fuzzy sets and systems Vol. 440; pp. 42 - 61
• Main Author: Yang, Xiao-Peng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 30.07.2022
• Subjects: Addition-min composition; Fuzzy relation equation; Fuzzy relation inequality; Lexicographic minimum solution; Peer-to-peer network system; Random-term-absent; Fuzzy relation equation; Lexicographic minimum solution; Random-term-absent; Fuzzy relation inequality; Addition-min composition; Peer-to-peer network system
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2021.08.007

Addition-min fuzzy relation inequalities are a recently proposed model for describing the transmission mechanism in a peer-to-peer (P2P) network system. Considering the random line faults that take place between two terminals in a P2P network system, we propose a new kind of model, namely, random-term-absent (RTA) addition-min fuzzy relation inequalities. Some of their relevant properties are investigated in this paper. In addition, to decrease the network congestion under a fixed priority grade of the terminals, we introduce the lexicographic minimum solutions of RTA addition-min fuzzy relation inequalities. An efficient algorithm is developed to find the unique lexicographic minimum solution with an illustrative example.