AHP中群组决策的综合判断

本文从理论上对群体决策过程程的判断矩阵几何平均综合法进行了分析。结论表明, 几何平均综合矩阵的一致性指标要小于各决策矩阵一致性指标的算术平均数。如果判断矩阵的干扰因子是随机的, 文章证明了几何平均综合矩阵将依概率收敛于一个一致性的正互反矩阵, 其排序向量刚好是各判断矩阵的几何平均综合排序向量。无疑这对于在群组决策时几何平均综合判断矩阵法的使用是重要的。

Synthesis of the Judgments For Making Group Decisions in AHP

In this paper the method of synthesis using geometric mean of the judgments(CMJ)for making group decisions in AHP was discussed theoretically.The conclusion indicated that the consistency of GMJ was less than the mean of the consistencies of judgments.If the pertubation factors in judgments are stochastic,it was proved in this paper that the matrix of GMJ will converge in probability at a consistent positive reciprocal matrix whose vector of priorities is just the geometric mean of the vectors of priorities for each judgments.That should be and important coclusions when GMJ is used to sythesize judgments for making group decision in AHP.