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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.
Aiming at the AHP judgment matrix group decision-making problem, a new method is proposed: defining the probability and satisfaction index, respectively measuring the degree of consistency of the composite matrix and the degree of difference between the composite matrix and the group judgment matrix ; Using the linearity and continuity of the fuzzy complementary judgment matrix to calculate the optimal probability matrix with the smallest difference with the group judgment matrix and the unconstrained optimal satisfaction matrix; using the geometric mean of the triangular elements of the two optimal matrices, The group decision matrices satisfying the optimal possible satisfaction are given.Finally, an example is given to show the effectiveness and practicability of the proposed method.