一种判断矩阵的修正方法和修正效果的两个判据

两两比较判断矩阵的构造, 是层次分析法(AHP)的一个关键技术。按照Saaty[1]的观点, 当一致性比例CR>0.1时, 则认为判断矩阵的一致性差。文献[2]对此做过研究。本文先给出一个定理, 再由此导出判断矩阵的修正方法, 从而使得逻辑性更强。最后, 本文将给出检验修正效果的两个判据。

An Approach to Modifying Pairwise Comparison Matrices and Two Criteria of Modificatory Effectivenees

Consistency ratio (CR) is an important indicator of judging if the consistency of pairwisecomparison matrix is acceptable. It difficult to structuresuch a matrix, especially of higher order , with satisfactory consistency becauseof the complexity of the compared elements and the limited ability ofhuman thinking. This paper presents a theorem, on which an approximation method of modifyingpairwise comparison matrices is offered. By this method any positive reciprocal matrix with a large CRcan be so corrected that the modified matrix can both tally with the consistency requirement and reservethe most information that the original matrix contains. Two criteria of evaluating modificatoryeffectiveness are also proposed.