Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities - Wu, Yan-Kuen; Wen, Ching-Feng; Hsu, Yuan-Teng; Wang, Ming-Xian (Fuzzy optimization and decision making, 2022)
In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmission and network congestion, a min-max programming problem subject to addition-min FRI is proposed. From a cost-saving perspective, the optimal solution to the min-max programming problem may not be the minimal optimal solution. Furthermore, while the “optimal” solution provides better cost performance, the “minimal” solution provides for the least congestion of the file-sharing system. In this paper, we propose adopting a binding variable approach based on certain new theoretical properties to find a minimal optimal solution for the min-max programming problem. It is for these new properties that the minimal optimal solution obtained via the binding variable approach would minimize the maximum transmission level; further, the amounts of data download in the optimal solution would be as balanced as possible. Some numerical examples are provided after each of the new properties to illustrate the advantages of our approach.