Abstract Addition-min fuzzy relation inequalities were introduced for describing the quantitative relationship in the peer-to-peer (P2P) file sharing system. In order to reduce the network congress, the system manager has to minimize the variables in the addition-min fuzzy relation inequalities. The corresponding min-max programming has been established in the existing works. However in such model, all the variables are viewed equally. In this paper, considering the different important degrees of the variables, we propose and investigate the weighted min–max programming subject to the addition-min fuzzy relation inequalities. Due to the different objective function, the existing methods are no longer effective for our proposed problem. Dichotomy algorithm has been developed in this paper for searching the approximate optimal solution of the weighted min-max programming. The feasibility and effectiveness of the dichotomy algorithm is illustrated by numerical example.

中文翻译：

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求解具有加法-最小模糊关系不等式约束的加权最小-最大规划问题的二分法算法

摘要 引入加最小模糊关系不等式来描述对等（P2P）文件共享系统中的定量关系。为了减少网络会议，系统管理员必须最小化加-最小模糊关系不等式中的变量。现有的工作中已经建立了相应的最小-最大规划。然而，在这样的模型中，所有变量都被平等地看待。在本文中，考虑到变量的不同重要程度，我们提出并研究了受加最小模糊关系不等式约束的加权最小-最大规划。由于目标函数不同，现有方法对我们提出的问题不再有效。本文开发了二分算法，用于搜索加权最小-最大规划的近似最优解。数值例子说明了二分法算法的可行性和有效性。