一种基于可能满意度与加权几何平均的一致性改进方法

对层次分析法中判断矩阵的一致性改进方法进行了研究。针对现有调整方法多重视收敛速度而忽略相对原始判断信息偏离的不足,将可能满意度的概念引入改进过程。利用判断矩阵的最大特征值及其F roben ius范数,给出判断矩阵可能度和满意度的定义与计算公式,分别考察一致性改进程度和相对原始判断矩阵的偏离程度,并将两者合并为一个衡量一致性改善效果的综合指标:判断矩阵的可能满意度。利用该指标,并结合常用的加权几何平均改进算法,可以有效地控制不一致判断矩阵的调整力度,在对决策者原始判断信息偏离最小条件下,逐步达到可接受的一致性。最后通过算例对比说明了新算法的有效性。

A Consistency Improving Method Based on Possibility-Satisfiability Degree and Weighted Geometric Mean

The methods of consistency improvement of the judgment matrix in AHP are studied.The concept of "possibility-satisfiability degree" are introduced into the improvement process to overcome the deficiencies of existing methods which often prefer convergence rate to deviations from original judgment. Using the maximum eigenvalue and Frobenius norm of the matrix,the definiens and formulas of the possibility and satisfyiability degree of the comparison matrix are given which can examine respectively the improvement extent and the deviation degree of the adjusted matrix from the original one.Then by combining the two measurements into a synthetical index: the possibility-satisfiability degree of the comparison matrix,the general effect of the improvement can be embodied.Accompanied with the traditional weighted geometric mean method,the improvement extent of the inconsistent matrix can be controlled effectively with this index,and acceptable consistency can be achieved gradually with minimum deviation from the(original) preference.Finally,through comparison with other methods for a numerical example,the efficiency of the new approach is demonstrated.