A note on deriving weights from pairwise comparison ratio matrices
A note on deriving weights from pairwise comparison ratio matrices
复制标题
关于从成对比较比率矩阵导出权重的说明
DOI：
10.1016/0377-2217(94)90153-8
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发表时间：
1994
影响因子：
6.4
通讯作者：
A. Hashimoto
中科院分区：
文献类型：
--
作者：
A. Hashimoto
本文讨论了库克和克雷斯的方法，关于使用数学规划来获得权重的成对比较比矩阵。我们注意到，库克和克雷斯制定的缺点，可能会出现替代的最优解，这将导致一个无限的可能的权重。本文提出了解决这个问题，制定了第二阶段的优化程序来解决使用二次规划。该数学公式基于在统计上最有可能导致相关联的成对比较矩阵的权重向量的确定。它的结论是，库克和克雷斯的方法伴随着拟议的第二阶段的方法总是可以得到一个独特的一组权重从成对的比较矩阵。
This paper addresses the Cook and Kress method regarding the use of mathematical programming to derive weights from pairwise comparison ratio matrices. We note that the Cook and Kress formulation has the shortcoming that alternative optimal solutions may occur, which would lead to an infinite set of possible weights. This paper proposes to resolve the problem by formulating a Phase II optimization procedure to be solved using quadratic programming. This mathematical formulation is based on the determination of a weight vector that is statistically most likely to cause the associated pairwise comparison matrix. It is concluded that the Cook and Kress method accompanied with the proposed Phase II approach can always derive a unique set of weights from a pairwise comparison matrix.