AHP中判断矩阵的区间权重及其一致性检验

AHP中由判断矩阵导出排序权重时,传统的方法只能得到"点"权重向量。为使结果更具柔性,考虑求解判断矩阵的区间权重向量。本文通过建立线性规划模型实现了这一点。与此同时,模型的最优值反映了判断矩阵的不一致性,故可借此进行一致性检验。通过模拟计算,对该检验方法和传统的通过计算CR值的方法间的相关性进行了统计分析。结果表明,二者具有显著的相关性。最后给出算例分析。

Interval Weights and Consistency Check of Judgment Matrix in the Analytic Hierarchy Process

Traditional methods can only educe strict weights from a judgment matrix in the analytic hierarchy process. To make the solution be more flexible, an interval weight vector is obtained, which is achieved through linear programming method in this paper. Meanwhile, the optimal objective value of the LP model implies consistency of the judgment matrix. Consequently, it can be used to process consistency check. By simulation computing, statistical analysis on the correlation between this check method and traditional method by CR value is made. The result indicates that the correlation between the two methods is significant. Finally an example is given.