层次分析法中整体一致性判别及校正

Judgment and Correction of Global Consistency in AHP

针对层次分析法(AHP)中下层存在不满足满意一致性条件判断矩阵的整体一致性判别问题,提出了具有满意一致性的充要条件.对判断矩阵,提出一种不需求最大特征值即可计算出一致性指标的新方法,用此方法可非常方便地求出判断矩阵的最大特征值.给出了判断矩阵一致性的统计检验方法的使用条件,提出了不满足满意一致性的判断矩阵的校正新方法,所给出的方法用计算机实现非常方便,对于低阶矩阵,手工计算也非常简便.

For global consistency judgment problem in AHP, a necessary and sufficient condition that the satisfy global consistency is true was provided. A new method was presented to compute consistency index without maximum eigenvalue, by which one also can find maximum eigenvalue conveniently. Furthermore, Statistical testing method and consistent correction of judgment matrix were also discussed in detail. The methods is easy to do by computer, even by hand.