判断矩阵一致性的一个充要条件

来源期刊：中南大学学报(自然科学版)1997年第3期

论文作者：李学全 李松仁

文章页码：286 - 289

关键词：判断矩阵； 一致性； 排序权向量

Key words：judgement matrix； identity； weight vector

摘    要：层次分析法在许多领域已广泛应用，然而，其判断矩阵的一致性检验尽管有许多方法，如最小二乘法、特征根法等，但都没有一个客观标准，本文证明了判断矩阵的一致性的一个充要条件，并在此充要条件的基础上，提出了一种直接进行排序权向量计算的方法，并得到了实例检验．

Abstract: The analytic hierarchy process has been extensively applied to various fields. However, it has not yet any objective standard, even though there are many verification methods of the identity of its judgement matrix such as least square method and characteristic value method, etc. In this paper a necessary and sufficient condition for the identity of the judgement matrix is proved. Based on the condition, the direct calculation method of weight vector in sequencing decisive factors is put forward. The calculation method synthesizes the information in the judgement matrix, and it is also proved by the given example that the method in this paper is very useful.