Deriving weights from general pairwise comparison matrices
Deriving weights from general pairwise comparison matrices
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DOI：
10.1016/j.mathsocsci.2007.07.006
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发表时间：
2008-03-01
影响因子：
0.6
通讯作者：
Sokolov, Mikhail V.
中科院分区：
文献类型：
--
作者：
Hovanov, Nikolai V.;Kolari, James W.;Sokolov, Mikhail V.
从成对比较矩阵导出权重的问题已在文献中得到广泛讨论。大多数结果都适用于所考虑的矩阵互对称的情况（即，对于每个 i 和 j，矩阵的第 i, j 个元素与其 j, 第 i 个元素互为倒数）。然而，当底层矩阵不互对称时，该框架有一些应用。在本文中，我们采用统计和公理论证来从此类矩阵中导出权重。这两种方法都会产生几何平均型近似。还提供了所获得的几何平均型解与 Saaty 特征向量方法的数值比较。 (c) 2007 Elsevier B.V. 保留所有权利。
The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matrices are not reciprocally symmetric. In this paper we employ both statistical and axiomatic arguments to derive weights from such matrices. Both of these approaches lead to geometric mean-type approximations. Numerical comparison of the obtained geometric mean-type solutions with Saaty's eigenvector method is provided also. (c) 2007 Elsevier B.V. All rights reserved.