On the transitivity and consistency approximated thresholds of some consistency indices for pairwise comparison matrices
On the transitivity and consistency approximated thresholds of some consistency indices for pairwise comparison matrices
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DOI：
10.1016/j.ins.2019.08.042
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发表时间：
2020-01-01
影响因子：
8.1
通讯作者：
Marcarelli, Gabriella
中科院分区：
文献类型：
--
作者：
Amenta, Pietro;Lucadamo, Antonio;Marcarelli, Gabriella
在文献中已经提出了几种措施来验证的合理性和一致性的判断表示成对比较的手段。然而，其中一些指数缺乏有意义的解释，因为没有与之相关的阈值。在本文中，我们首先引入的一致性近似阈值的Salo-Hamalainen指数推导出一个不一致的容忍度，这是类似于提出的一致性比率Saaty，几何一致性指数阿瓜隆-莫雷诺希门尼斯，和一致性措施Koczkodaj。然后，通过模拟，我们提出了n x n矩阵的传递性阈值，它可以提供有关错误分类程度和偏好可靠性的有意义的信息，同时避免修改判断的需要。在不同的n，我们得到的传递性阈值Salo-Hamalainen和文献中提出的其他一致性指标。(C)2019爱思唯尔公司All rights reserved.
Several measures have been proposed in the literature to verify the rationality and consistency of judgements expressed by means of pairwise comparisons. However, some of these indices lack a meaningful interpretation because of the absence of thresholds associated with them. In this paper, we first introduce the consistency approximated thresholds for the Salo-Hamalainen index by deriving an inconsistency tolerance level, which is analogous to that proposed for the Consistency Ratio by Saaty, for the Geometric Consistency Index by Aguaron-Moreno Jimenez, and for the Consistency Measure by Koczkodaj. Then, via a simulation, we propose a transitivity threshold, for n x n matrices, which may give meaningful information about the degree of misclassification and the reliability of preferences while avoiding the need to revise the judgements. On varying n, we derive the transitivity thresholds for Salo-Hamalainen and for the other consistency indices proposed in literature. (C) 2019 Elsevier Inc. All rights reserved.