从距离矩阵看层次分析法

从距离矩阵的角度出发，通过对比较矩阵各元素取对数，构成只与方案之间得分差有关，而与方案得分无关的决策距离矩阵，变ＡＨＰ在实数平面上的相对比较为准则平面上的绝对比较。从而使得计算ＡＨＰ问题不存在保序性问题。并以此距离矩阵为基点，分析ＡＨＰ存在的问题，指出ＡＨＰ的问题是因准则权重概念的模糊而引起的，其“保序性”问题实际上是一种不可比较的现象。

Analysis of Analytic Hierarchy Process from Distance Matrix

From the concept of distance matrix, by taking the logarithm of elements in AHP's comparing matrix, we get a decision distance matrix which is only related to the score difference between alternatives, while not related to the pair comparison parameter, thus changing AHP' relative comparison to an absolute comparison, and getting evaluation results without "rank preservation" problem.Based on the matrix, we also analyze AHP's defect, and point out that the problem is induced by its vague concept of criterion weight, and its "rank preservation" problem is actually an incomparable case.