Inconsistency of special cases of pairwise comparisons matrices
Inconsistency of special cases of pairwise comparisons matrices
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DOI：
10.1016/j.ijar.2018.01.004
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发表时间：
2018-04-01
影响因子：
3.9
通讯作者：
Szybowski, J.
中科院分区：
文献类型：
--
作者：
Cernanova, V.;Koczkodaj, W. W.;Szybowski, J.
这项研究提出了不一致的成对比较PC矩阵的特殊情况。对选定的不一致性指标进行了分析。比较的不一致之一是流行的基于特征值的一致性指数（CI），它不遵循公理化最近发表的杂志。另一种不一致性是基于指数可逆测度（也称为Koczkodaj不一致性指标或Kii），它遵循公理化。所有研究的PC矩阵的特殊情况都是Toeplitz矩阵，只有三个不同的元素1，x和1/x。循环矩阵已被用于成对比较，以分析不一致性。虽然这类PC矩阵可能被认为是受限制的，但它足够普遍，可以覆盖从最低到最高的基于特征值的不一致性指数的所有值。精确的数学表达式和估计，其中精确的表达式是不可能找到的，提供。(C)2018爱思唯尔公司All rights reserved.
This study presents special cases of inconsistent pairwise comparisons PC matrices. The analysis of the selected inconsistency indicators is provided. One of the compared inconsistencies is the popular eigenvalue-based consistency index (CI) which fails to follow axiomatization recently published by this journal. The other inconsistency, based on the exponentially invertible measure (also known as Koczkodaj's inconsistency indicator or Kii) follows the axiomatization.All studied special cases of PC matrices are Toeplitz matrices with only three different entries 1, x, and 1/x. A circulant matrix has been used for pairwise comparisons to analyze inconsistency. Although this class of PC matrices may be perceived as restricted, it is general enough to cover all values of the eigenvalue-based inconsistency index from the lowest to the highest. Both exact mathematical expressions and estimations, where the exact expression was impossible to find, are provided. (C) 2018 Elsevier Inc. All rights reserved.