论文标题
特征向量法的右左不对称：一项模拟研究
Right-left asymmetry of the eigenvector method: A simulation study
论文作者
论文摘要
由广泛使用的分析层次结构过程方法的开发人员提出的特征值法表现出右左不对称：源自右特征向量的优先级不一定与从互惠左左特征向量获得的优先级相吻合。本文提供了一项全面的数值实验，以比较两个基于特征向量的加权程序及其相对于四个措施的行几何平均值的合理替代方法。基础成对比较矩阵是随机构建的，具有不同的维度和不一致的水平。事实证明，两个特征向量之间的分歧并不总是矩阵这些重要特征的单调函数。排名矛盾会影响具有相对较远优先级的替代方案。发现行几何平均值几乎位于右侧和左侧特征向量之间的中点，这使其在它们之间是直接的妥协。
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.
