基于主成分的改进马氏距离TOPSIS方法  

Method to Improved Mahalanobis Distance of TOPSIS Based on Principal Component

作　　者：张峰[1] 谢振华[1] 程江涛[1] 崔高仑 李林[1] 

机构地区：[1]海军航空工程学院青岛校区,山东青岛266041

出　　处：《火力与指挥控制》2015年第3期92-95,共4页Fire Control & Command Control

摘　　要：针对指标变量线性相关,导致变量协方差矩阵行列式(广义样本方差)为零无法应用马氏距离的情况,采用主成分分析法对指标变量进行线性组合,在不减少信息量的同时,得到少数几个不相关的主成分,由主成分构成的协方差矩阵行列式不再为零。依据降维后的主成分变量,采用基于马氏距离的逼近理想解法对五种预警机探测引导能力进行了排序,经检验其结果与实际情况相符。Aim at the thing that indexes are linear correlative ,which lead to the emergence of the thing that determinants of covariance matrix of variables （generaLized sample-variance） is zero. In this condition,mahalanobis distance calculation can＇t go along . Principal component analysis is adopted to combine indexes linearly. At the same time , a few irrelevant principal components are attained, and the indexes information isn＇t decreased; accordingly,determinants of covariance matrix of principal components isn＇t zero. The method to Mahalanobis distance of TOPSIS based on principal component is adopted to calculate performance guidance of five kinds of early-warning aircraft, and list in order of size. The results are verified by the fact.

关 键 词：逼近理想解法(TOPSIS) 主成分 马氏距离 广义样本方差 

分 类 号：O212.4[理学—概率论与数理统计] E92[理学—数学]