摘要
郭亚军等写的“一类决策问题的新算法”一文对通常的层次分析方法提出了简化方案，使得运算量大为减少．但当因素稍多时，成对比较阵一般不再是一致性矩阵，从而严重影响了方法的精度．本文从层次分析法传统标度和一致性矩阵的结构出发，考查了一类建立在序关系上的群，得到了该群的一些重要性质并由此找出问题的症结，对郭亚军等的文章作了若干改进。
In paper the popular algorithm of AHP is simplified and the amount of calculations is greatly reduced. However, the matrix of paired comparisons will not be consistent when there are a few more factors considered, which may reduce accuracy of the method proposed in . We obtain a kind of group by analysing the algebraic structure of consistent matrix and scaling system used in , and find a much simpler algorithm than usual to guarantee the consistency of paired comparison matrix. It is pointed out that an example in is recomputed by this algorithm in paper , which shows that the algorithm is much simpler and more accurate than that in .
关键词
群
同构
层次分析法
标度系统
代数结构
group isomorphism totally ordered set analytic hierarchy process matrix consistency quick sort
