一种基于加权马氏距离的TOPSIS改进评价法及其应用  

An Improved TOPSIS Evaluation Method Based on Mahalanohis Distance and Its Application

作　　者：王韦霞[1] WANG Wei-xia(Department of Basic knowledge Teaching, Anhui Technical College of Mechanical and Electrical Engineering, Anhui Wuhu 241003,Chin)

机构地区：[1]安徽机电职业技术学院基础教学部,安徽芜湖241003

出　　处：《重庆工商大学学报（自然科学版）》2018年第1期40-44,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：安徽省教育厅自然科学基金资助项目(KJ2015A418)

摘　　要：传统TOPSIS评价法构造的正、负理想解容易产生逆序现象,而且使用的欧氏距离无法考虑到决策指标之间的相关性;针对此类问题,提出了一种基于加权马氏距离的TOPSIS改进法:一是用极差变换法对评价指标进行无纲化处理,消除逆序现象;二是对评价方案做正交变换,利用变换后的评价方案到正、负理想解的马氏距离代替传统欧式距离,经案例证明,改进后的TOPSIS优于传统的方法。Positive and negative ideal solution created by traditional TOPSIS evaluation method is easy to cause reversal problem and the used Euclidean distance can not consider the correlation between decision-making indicators. For such problems,this paper proposes an improved TOPSIS method based on weighted Mahalanohis distance. The first is using the maximum difference dormalization method to eliminate the reversal problem in the traditional TOPSIS method,and the second is using the orthogonal transformation method by using the evaluation scheme after the transformation to calculate Mahalanohis distance to positive and negative ideal solution to replace the traditional Euclidean distance. The case analysis proves that the improved TOPSIS method is superior to the traditional method.

关 键 词：逆序 加权马氏距离 协方差阵 TOPSIS 

分 类 号：O223[理学—运筹学与控制论]