Abstract: Composition Rule of Influence（CRI） is one of the most important methods in fuzzy reasoning.However，the time and space complexity of common CRI method are O(mn).Composed to Fuzzy set，the information expressed by Vague set is more abundant and closer to reality.So，in the first this paper generalizes CRI method and max-min operator which on Fuzzy set to Vague set，and gets a expand CRI method based on Vague set.In order to reduce the time complexity of CRI method，the properties are analyzed related to max-min operator and a quick CRI method is gottern，whose time and space complexity are cut down to O(m+n).At last，an example is used to illustrate the efficiency of the method.

摘要： CRI方法是模糊推理的重要方法之一，然而常用的CRI方法的时间和空间复杂度均为O(mn)。相对于Fuzzy集而言，Vague集所能表达的信息更加丰富，更接近实际。故首先把Fuzzy集上的CRI方法和max-min算子扩充到Vague集上，得到基于Vague集的CRI方法。为了降低CRI方法的时间复杂度，深入分析了max-min算子相关性质，最后得到一个快速的CRI方法，其时间复杂度和空间复杂度降为O(m+n)。最后用实例来说明该方法的高效性。