【摘要】 对在层次分析法(AHP法)中采用的加权几何平均法的一致性进行了研究,并证明了加权几何平均复合判断矩阵(WGMCJM)具有满意一致性;同时还证明了当判断矩阵An×n完全一致时,将A按列归一化处理后得到的矩阵Bn×1中的每一列向量本身就是A的最大特征值n所对应的归一化向量.研究结果为在群体决策环境下应用加权几何平均法提供了理论基础.更多还原

【Abstract】 Research was conducted on the consistency of WGMM (the weighted geometric mean method) in AHP (the Analytic Hierarchy Process) in group decisionmaking environment. It was proved that WGMCJM was of perfect consistency and if the judgement matrix An×n was of perfectly consistency, each column vector in the Matrix Bn×1 as the result of An×n being standardized according to A’s columns is the standardized vector corresponding to the A’s maximum eigenvalue n. Accordingly a theoretic basis has been developed for the application of AHP in group decisionmaking.更多还原