The eigenvalue method, suggested by the developer of the extensively used Analytic Hierarchy Process methodology, exhibits right-left asymmetry: the priorities derived from the right eigenvector do not necessarily coincide with the priorities derived from the reciprocal left eigenvector. This paper offers a comprehensive numerical experiment to compare the two eigenvector-based weighting procedures and their reasonable alternative of the row geometric mean with respect to four measures. The underlying pairwise comparison matrices are constructed randomly with different dimensions and levels of inconsistency. The disagreement between the two eigenvectors turns out to be not always a monotonic function of these important characteristics of the matrix. The ranking contradictions can affect alternatives with relatively distant priorities. The row geometric mean is found to be almost at the midpoint between the right and inverse left eigenvectors, making it a straightforward compromise between them.
翻译:广泛使用的分析性分层进程方法的开发者建议的二次数值方法显示右偏偏偏不对称:右向分层产生的优先顺序不一定与对等左向分层产生的优先顺序相吻合。本文提供了一个全面的数值实验,以比较两种基于二次基因的加权程序及其在四个计量方面对行数几何平均值的合理替代物。基础对齐比较矩阵是随机构造的,其尺寸和程度不一。两个分层的对比矩阵之间的分歧发现并非总是矩阵这些重要特征的单一函数。排位上的矛盾可能会影响相对遥远的优先顺序的替代物。发现行的几何平均值几乎处于右向和左偏向的中间点,使得它们之间的折中点成为直接的折中点。