A chi-square-based inconsistency index for pairwise comparison matrices
提出一种新的卡方指数来评估两两比较矩阵的不一致性，无需优化计算，与Saaty一致性指数密切相关且对方案数量更稳定。
In this paper, we introduce a new method for evaluating the inconsistency level of a pairwise comparison matrix. The classical Chi-square index suggests an interesting formal similarity for a consistent pairwise comparison matrix and, as a consequence, a method for measuring the relative deviation of the elicited preferences from a set of consistent preferences defined on the basis of the similarity mentioned above. Contrary to some previously introduced Chi-square-based approaches, no optimisation problems are involved. We verify that the new index satisfies some recently introduced characterising properties of inconsistency indices. Then, by means of numerical simulations, we compare our index with some other well-known inconsistency indices and we focus, in particular, on the comparison with Saaty’s consistency index. We discuss some numerical results showing that the new index is closely related with Saaty’s one but it is more stable with respect to the number of alternatives.