两种修正判断矩阵一致性方法的比较分析

对层次分析中判断矩阵一致性的修正方法进行了研究，证明了修正判断矩阵一致性的加权算术平均法的收敛性，并同时加权几何平均法进行了详细的比较。理论分析表明：虽然这2种方法都具有收敛性，且均可对一致性较差的判断矩阵进行修正，但加权几乎平均法比加权算术平均法简洁，且前者无需通过转换，直接保持了修正后的判断矩阵的互反性。数值结果也显示：加权几何平均法所需的迭代次数比加权算术平均法所需迭代次数少。

Analysis and comparison of two methods for improving consistency of judgement matrix

The methods for improving consistency of judgement matrix in the analytic hierarchy process are studied. The convergence of the weighted arithmetic mean method for improving consistency of judgement matrix is proven, and the comparison between the weighted arithmetic mean method and the weighted geometric mean method is also given in detail. Theoretical analysis shows that both methods are of convergence and can be used to improve the judgement matrix with unacceptable consistency. However, the weighted geometric mean method is simpler than the weighted arithmetic mean method, and the former can keep the reciprocity of the improved judgement matrix without transformation. The numerical results also indicate that the weighted geometric mean method needs less number of iteration than the weighted arithmetic mean method.