用特征向量估计方案权与方案下标序的关系

The Relation Between the Estimation of Criterion Weights Using Eigenvectors and the Index Orders of the Criteria

本文讨论了层次分析法中用特征向量估计方案权与方案下标序的关系。指出特征向量法的解相对于方案下标序来说是不变的,而梯度特征向量法的解依赖于方案的下标序。同时,证明了当方案个数为3时,梯度特征向量法的解的几何平均就等于特征向量法的解。

This paper discusses the relation between the estimation of criterion weights using eigenveetors and the index orders of the criteria in AHP. It points out that the solution of eigenvalue method (EM) is invariant with respect to the index order of the criteria, and that the solution of graded eigenveetor method (GEM) is dependent on the index order of the criteria. It also proves that the solution of EM is identical to the geometric means of the solution of GEM corresponding to all permutation of the index orders when the number of criteria is three.