Addition-min fuzzy relation inequalities are introduced to characterize the Peer-to-Peer (P2P) network system. In order to decrease the network congestion, considering both efficiency and fairness, we define the leximax minimum solution for system of addition-min fuzzy relation inequalities. The leximax-optimality refines both Pareto-optimality and max-optimality. For solving the leximax minimum solution, concepts of minimum zero point and minimax value are defined, with corresponding resolution algorithms, i.e. Algorithms I and II. Based on these two algorithms, Algorithm III is further developed to find the unique leximax minimum solution. Numerical examples illustrate the validity of our proposed algorithms.

引入了加法最小模糊关系不等式来表征对等（P2P）网络系统。为了减少网络拥塞，同时考虑了效率和公平性，我们定义了最小加法关系模糊不等式系统的leximax最小解。leximax-optimality改进了帕累托最优和max-optimality。为了求解leximax最小值解，定义了最小零点和minimax值的概念，以及相应的分辨率算法，即算法I和II。基于这两种算法，进一步开发了算法III，以找到唯一的leximax最小解。数值例子说明了我们提出的算法的有效性。