基于马氏距离的TOPSIS决策方法及其应用

针对决策指标之间的相关性问题,将马氏距离引入传统TOPSIS方法,提出了基于马氏距离的TOPSIS方法.在此基础上,分析了基于马氏距离改进后贴近度的性质,并以投资决策方案选择为例加以说明.结果表明,基于马氏距离改进的TOPSIS方法对决策数据的非奇异线性变换具有不变性.协方差矩阵体现了决策指标之间的相关性,因而可以有效避免指标的相关性对决策效果的影响.

Mahalanobis Distance-based TOPSIS Decision Making Method and Its Application

In order to solve the issues of correlations between the decision making indicators,after introducing Mahalanobis distance into the traditional TOPSIS method,this paper proposed an improved TOPSIS method based on Mahalanobis distance.On this basis,the properties of the improved closeness were analyzed,and an actual example was given to illustrate the effectiveness of the new method.The results show that non-singular linear transformations do not change the decision making results of the improved method.Covariance matrix reflects the correlation between the indicators.Thus,the improved method can avoid the effect of decision-making indexes correlations.