Is It Reasonable for Saaty's Consistency Test in the Pairwise Comparison Method?

Wei-jun Xu, Yucheng Dong, Weilin Xiao
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引用次数: 17

Abstract

In the pairwise comparison method, Saaty's consistency test is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons. Saaty suggested that the consistency ratio (CR) should be less than or equal to 0.1. Some researchers argued that the cut-off rule should be a function of the matrix size. In this paper, by simulation analysis, we find that, as the matrix size increases, the percent of the matrices with acceptable consistency (CR les 0.1) decreases dramatically, however, on the other hand, there will be more and more contradictory judgements in these sufficiently consistent matrices. This paradox shows that it is impossible to find some proper critical values of CR for different matrix sizes. Thus we argue that Saaty's consistency test could be unreasonable.
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两两比较法中Saaty一致性检验是否合理?
在两两比较方法中,为了保证决策者的两两比较既不是随机的,也不是不合逻辑的,需要进行Saaty的一致性检验。Saaty建议一致性比(CR)应小于或等于0.1。一些研究者认为截止规则应该是矩阵大小的函数。本文通过仿真分析发现,随着矩阵大小的增大,具有可接受一致性(CR < 0.1)的矩阵所占比例急剧下降,但另一方面,在这些充分一致的矩阵中,会出现越来越多的相互矛盾的判断。这一悖论表明,对于不同的矩阵大小,不可能找到合适的CR临界值。因此我们认为Saaty的一致性检验可能是不合理的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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