Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities

• Published in: Fuzzy optimization and decision making Vol. 21; no. 2; pp. 291 - 317
• Main Authors: Qiu, Jianjun, Yang, Xiaopeng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Calculus of Variations and Optimal Control; Optimization; Data transmission; Inequalities; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Polynomials; Probability Theory and Stochastic Processes; Programming; Min–max programming problem; Fuzzy relation equation; Addition-min-product composition; Peer-to-Peer file sharing system; Fuzzy relation inequality
• ISSN: 1568-4539; 1573-2908
• DOI: 10.1007/s10700-021-09368-7

In this paper, we study a new type of fuzzy relation system called fuzzy relational inequalities with addition-min-product composition operations to model a peer-to-peer (P2P) file sharing system. Some properties of this addition-min-product system are investigated. We then characterize the structure of the solution set. Furthermore, to reduce the network congestion and improve the stability of data transmission, a min–max programming problem with constraints of addition-min-product fuzzy relation inequalities is established and investigated. We divide this min–max programming problem into several subproblems with the constraint of a single equation. Based on the optimal solutions to these subproblems, we can solve the original fuzzy relation min–max programming problem. Two algorithms, with polynomial computational complexity, are developed to search for an optimal solution to our studied problem. The validity of the algorithms is examined through a numerical example.