不完全两两比较矩阵的不一致阈值
Inconsistency thresholds for incomplete pairwise comparison matrices
摘要：
成对比较矩阵越来越多地用于缺少某些对的设置。然而，存在一些类似的不完整的数据集的不一致性指标，并没有合理的措施有一个相关的阈值。本文概括了著名的经验法则的可接受程度的不一致性，提出了Saaty，不完整的两两比较矩阵。扩展是基于选择丢失的元素，使得不完整矩阵的最大特征值最小化。因此，建立良好的随机指数的值不能被采用：随机矩阵的不一致性被发现是矩阵的大小和缺失元素的数量的函数，在后一个变量的情况下，几乎线性相关。我们的研究结果可以直接内置到决策软件中，并由从业者作为接受或拒绝不完整的成对比较矩阵的统计标准。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
