一种新的用于群组排序的最小平方逼近法

A NEW LEAST-SQUARE METHOD OF PRIORITY FOR GROUP AHP

本文将文献[1,2]所给的最小平方逼近法推广应用于层次分析法中的群决策排序。文中对由多个判断决策者给出的多个不同的判断矩阵,提出通过求解群组判断矩阵最小平方偏差的方法得出判断矩阵的最佳排序和理想综合判断矩阵;通过对群组判断矩阵进行一致性讨论,据此又给出了一种用于群组判断矩阵排序的最小加权平方逼近法。理论分析和应用实例表明,应用最小平方逼近法和最小加权平方逼近法对群组判断矩阵进行排序是可行的和有效的。

The Least-square method presented in [1,2] is extended and applied to the group AHP. By solving the least-square deviation of group comparison matrixes given by decision-makers, the optimal priority and an ideal synthetic comparison matrix are obtained. After discussion on the consistency of group AHP, a new weighted least-square method is proposed. As shown in theoretical analyses and practical applications, the methods introduced in the paper are feasible and effective in dealing with the group AHP.