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:由广泛使用的层次分析过程方法的开发者所提出的特征值方法具有左右不对称性:从右特征向量导出的优先级不一定与从倒数左特征向量导出的优先级相符。本文提供了一项全面的数值实验,比较了这两种基于特征向量的加权过程及其合理的替代方法——行几何平均——与四个度量标准的关系。采用不同维度和不同程度的不一致性随机构建成对比矩阵。两个特征向量之间的差异不总是这些矩阵的重要特征的单调函数。排名矛盾可能影响优先级相对较远的替代方案。行几何平均被发现几乎位于右特征向量和逆向左特征向量之间,使其成为它们之间一个直接的折衷方案。