一种基于最优可能满意度的群AHP判断矩阵集结方法

An aggregation method for the AHP judgment matrices based on optimum possibility-satisfiability degree

针对层次分析法(AHP)判断矩阵群决策问题,提出一种新方法:定义可能度和满意度指标,分别衡量属性排序约束下合成矩阵的一致性程度和合成矩阵与群组判断矩阵的差异程度;利用模糊互补判断矩阵的线性和连续性,计算与群组判断矩阵差异最小的最优可能度矩阵和无约束的最优满意度矩阵;采用两个最优矩阵上三角元素的几何平均,获取满足最优可能满意度的群决策合成矩阵.最后通过算例表明了所提出方法的有效性和实用性.

A new aggregation method for the analytic hierarchy process（AHP） judgment matrices in group decision-making is proposed. Firstly, the possibility degree which measures consistency under the condition of attributes ordering and the satisfiability degree which measures the difference between group judgment matrices and synthetic matrix are defined. Then, the optimum possibility degree matrix and the optimum satisfiability degree matrix are computed based on the linearly and continuity of fuzzy complementary judgment matrices. Finally, with the geometrical average between upper triangular elements of two optimum matrices, the optimum possibility-satisfiability degree synthetic matrix is acquired. Numerical examples show the effectiveness and practicability of the method proposed.