AHP判断矩阵一致性改进的若干问题研究

Research on Consistency Modification Problem of Comparison Matrix in the Analytical Hierarchy Process

研究层次分析法中判断矩阵次序一致性检验及改进方法.指出判断矩阵次序一致性和基本一致性之间无相关性的特点,提出对判断矩阵应首先进行次序一致性检验,并把判断矩阵转化成0-1矩阵,利用图论理论得到如下结论:0-1矩阵对应的有向图中,若含有边长大于3的循环链,则一定能构造出边长为3的循环链.基于此结论,设计检验判断矩阵是否具有次序一致性的算法.对不具有次序一致性的判断矩阵,提出两条修改原则.

The test and modification approach on the ordinal consistency in the analytical hierarchy process （AHP） is studied. The irrelevant relationship between the ordinal consistency and the basis consistency of the Comparison matrix is put forward. Then, the conclusion that the comparison matrix must be checked firstly on the ordinal consistency is concluded. To find the ordinal consistency test approach, the comparison matrix is transformed into a particular matrix that is comprised of zero or one. Following that, a test algorithm and two ordinal modification rules are developed based on the conclusion that a three-side circuit can be constructed if there exists a more than three-side circuit in the directed graph from the particular matrix.