优化理论在层次分析法中的应用

Application of Optimization Theory in Analytical Hierarchy Process

层次分析法是美国运筹学家、匹兹堡大学A.L。Saaty在70年代初提出的。它是通过明确问题、建立层次结构、构造判定矩阵、层次单排序、层次总排序、一致性检验六个步骤来进行整个系统层次分析的。但是传统的层次分析法在进行层次单排序时,一般是通过求特征值和特征向量的方法(称幂法)来确定层次单排序结果的,不但求解复杂、计算量大,而且求得的权重也不是最优的;

This paper applies the optimization theory to AHP and proposes a new priority method which makes priority more accurately. When the comparison matrix dissatisfies consistency, a new revision method is given which solves the consistency problem very effectively. In the end, the paper give an example for the applicatio of this method and compares the results of the new and the old methods.