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.

在这项研究中，类似于 BitTorrent 的点对点 (BT-P2P) 文件共享系统被简化为具有加法最小组成的模糊关系不等式 (FRI) 系统。为了研究数据传输和网络拥塞的稳定性，提出了一个受加法-最小FRI约束的最小-最大规划问题。从节约成本的角度来看，min-max 规划问题的最优解可能不是最小最优解。此外，虽然“最优”解决方案提供了更好的性价比，但“最小”解决方案提供了文件共享系统的最少拥塞。在本文中，我们建议采用基于某些新理论特性的绑定变量方法来寻找最小-最大规划问题的最小最优解。正是针对这些新特性，通过绑定变量方法获得的最小最优解将最小化最大传输水平；此外，最佳解决方案中的数据下载量将尽可能平衡。在每个新属性之后都提供了一些数值示例，以说明我们方法的优点。