论文标题
一些关于特征值法和几何方法得出的优先矢量相似性的注释
Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method
论文作者
论文摘要
本文研究了使用特征值法和几何均值方法从成对比较矩阵获得的顺序排名的差异。首先，我们介绍了关于矩阵大小的两种排名的（DIS）相似性及其不一致索引表达的几个命题。此外，我们研究了排名的差异与肯德尔等级相关系数$τ$与Spearman等级系数$ρ$之间的关系。除了理论上的结果外，还提供了直观的数值示例和蒙特卡洛模拟。
This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient $τ$ and Spearman's rank coefficient $ρ$. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided.
