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.

在本文中，我们研究了一种称为模糊关系不等式的新型模糊关系系统，该系统具有加最小乘积组合操作，以对点对点 (P2P) 文件共享系统进行建模。研究了这种加减乘积系统的一些特性。然后我们描述了解决方案集的结构。此外，为了减少网络拥塞并提高数据传输的稳定性，建立并研究了一个具有加法-最小-乘积模糊关系不等式约束的最小-最大规划问题。我们将这个最小-最大规划问题划分为几个具有单个方程约束的子问题。基于这些子问题的最优解，我们可以解决原始的模糊关系最小-最大规划问题。两种算法，具有多项式计算复杂度，开发是为了寻找我们研究问题的最佳解决方案。通过一个数值例子来检验算法的有效性。