Finding minimal solutions to the system of addition-min fuzzy relational inequalities

• Published in: Fuzzy optimization and decision making Vol. 21; no. 4; pp. 581 - 603
• Main Authors: Wu, Yan-Kuen, Wen, Ching-Feng, Hsu, Yuan-Teng, Wang, Ming-Xian
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Calculus of Variations and Optimal Control; Optimization; File sharing; Inequalities; Iterative algorithms; Iterative methods; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Peer to peer computing; Probability Theory and Stochastic Processes; Variables; Iterative algorithm; Minimal solution; Fuzzy relational inequality; Addition-min composition
• ISSN: 1568-4539; 1573-2908
• DOI: 10.1007/s10700-021-09377-6

In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables.