摘要
目的研究层次分析法（ＡＨＰ）中，关于正互反矩阵元素扰动的灵敏性分析问题．方法提出正互反矩阵元素的相邻扰动概念，利用正互反矩阵元素相邻扰动对排序权向量的影响进行层次分析法灵敏性分析研究，在严格证明了理论结果的基础上，对更一般的情况进行了统计模拟．结果与结论正互反矩阵元素的相邻扰动与排序权向量的相应元素的变化有一致的关系，对层次分析法的科学运用有重要意义．
Aim To study the sensitivity problem of the pairwise comparison alternative matrix's, element perturbation in analytic hierarchy process (AHP).Methods The concept on the consecutive perturbation of the pairwise comparison alternative matrix was given, and based on the effect of the consecutive perturbation of the pairwise comparison alternative matrix on the sequencing weight vector, the sensitivity of analytic hierarchy process was discussed. The theoretical result was strictly proved and statistical simulation was done in general case. Results and Conclusion The consecutive perturbation of the pairwise comparison alternative matrix and the perturbation of the corresponding elements in the sequencing weight vector are conformable, it has an important influence on using AHP.
出处
《北京理工大学学报》
EI
CAS
CSCD
1999年第3期275-279,共5页
Transactions of Beijing Institute of Technology
关键词
层次分析法
相邻扰动
正互反矩阵
排序权向量
analytic hierarchy process(AHP)
consecutive perturbation
pairwise comparison alternative matrix
sequencing weight vector
