Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb for the acceptable level of inconsistency, proposed by Saaty, to incomplete pairwise comparison matrices. The extension is based on choosing the missing elements such that the maximal eigenvalue of the incomplete matrix is minimised. Consequently, the well-established values of the random index cannot be adopted: the inconsistency of random matrices is found to be the function of matrix size and the number of missing elements, with a nearly linear dependence in the case of the latter variable. Our results can be directly built into decision-making software and used by practitioners as a statistical criterion for accepting or rejecting an incomplete pairwise comparison matrix.

翻译：在缺少一些配对的环境下,越来越多地使用Pairwise比较矩阵;然而,类似的不完整数据集的不一致指数很少,没有合理的衡量标准,因此没有相关的阈值;本文概括了Saaty提出的可接受的不一致程度的著名拇指规则,将之归纳为不完全对等比较矩阵;扩展的根据是选择缺失的元素,以尽可能减少不完整矩阵的最大值;因此,不可能采用随机指数的既定值:随机矩阵的不一致性被认为是矩阵大小和缺失元素数量的功能,在后一种变量中几乎是线性依赖性;我们的结果可以直接纳入决策软件,供从业人员用作接受或拒绝不完整对等对比矩阵的统计标准。