基于证据理论的群组层次分析法判断矩阵集结方法

An Aggregation Method for Group AHP Judgment Matrices Based on the Evidence Theory

针对现有群组集结方法关注于专家权重和集结元素之间相似性,缺少对层次分析法(AHP)判断矩阵元素一致性考虑的不足,提出一种基于证据理论的群组AHP判断矩阵集结方法。该方法以群组AHP判断矩阵元素的相似性和一致性为证据源,采用DS证据理论计算上三角元素的合理性指标值;并以该指标值为边权计算最大生成树和相对应的完全一致矩阵;该方法在完全一致矩阵和PG算子集结矩阵的约束下,结合残缺元素的修复策略,计算满足最优相似一致度的群组集结结果。通过算例分析,说明该方法的可行性与有效性。

The existing group aggregation methods pay more attentions on the weights of experts and the similarity between entries being fused,but has not synthetically considered the satisfactory consistency of entries located in the same matrix. Therefore,an aggregation method for the group matrices is proposed. With the evidential sources associated with the similarity and consistency for the entries in group matrices,the method uses DS evidence theory to calculate the rationality of upper triangle entries,which can be used to calculate the maximum spanning tree and the corresponding consistent matrix. Under the constraints of the consistent matrix and the collective matrix obtained by the PG operator,the method can calculate the optimum similarity-consistency result with the estimation of missed entries in an incomplete matrix. Finally,the numerical examples show that the method is feasible and effective.