灰色层次分析中确定方案偏序的方法

摘要

Since elements in a grey-judgment matrix are interval numbers, the weight-vector derived from them is also constituted by interval numbers. In most cases some of the interval numbers will intersect. Then the projects' order will no longer be certain nor clear, and the decision-making will also become difficult. Based on the relation between the order and the judgment-elements, this paper gives some convicted theorem, and a way on how to determine the orders by whitening methods. Finally, an example is given to demonstrate the feasibility of the method.%灰色判断矩阵的判断元素是区间数形式的,因而得到的权重向量也是区间数形式,其分量多数情况下会出现相交部分,这时方案的偏序关系也不再明朗甚至无法确定,也影响了决策的最终产生.本文主要通过对方案偏序与判断矩阵元素取值之间关系的研究给出几个判定定理,并利用白化的方法来辅助给出方案的最终排序,最后通过算例说明方法是可行的.