基于广义马氏距离的混合型多属性决策的TOPSIS方法  

TOPSIS Method for Hybrid Multiple-Attribute Decision MakingTOPSIS Making Based on Generalized Mahalanobis Distance

作　　者：张峰[1] 谢振华[1] 程江涛[1] 林健[2] 徐衡博[3] 

机构地区：[1]海军航空工程学院青岛校区 [2]91033部队 [3]91423部队

出　　处：《海军航空工程学院学报》2013年第6期674-678,共5页Journal of Naval Aeronautical and Astronautical University

摘　　要：为了解决混合型多属性决策问题,将不同属性值转换为区间数形式。在基于马氏距离的逼近理想解排序法(TOPSIS)中,指标间线性强相关导致协方差矩阵为奇异矩阵,不能计算马氏距离。因此,定义了区间数的协方差矩阵,采用奇异值分解方法计算协方差矩阵的广义(M-P)逆矩阵。改进的算法克服了传统TOPSIS存在的指标信息重复、主观赋权不合理、隶属度难以确定,以及可能出现与理想解欧式距离近的方案与负理想解的欧式距离也近的不足。最后,给出了该方法的一个算例,结果表明该决策方法是实用和可行的。In order to solve the hybrid multiple-attribute decision making problem, different attribute values were unified into interval number. In the TOPSIS based on Mahalanobis distance, because of the strong linear correlation indexes, the covariance matrix was singular, and calculating the Mahalanobis distance didn＇ t work. Therefore, covarianee matrix of in- terval number was defined and singular value decomposition method was adopted to calculate generalized inverse matrix of covariance matrix. The improved algorithm overcame the defects in the traditional TOPSIS model of river health assess- ment, such as correlations between indices, uncertainty in estimating the weights subjectively, difficulty in determining the membership function and possibility of the scheme closed to ideal solution and negative-ideal solution concurrently. Inthe end, a numerical example illustrated the validity and applicability of the proposed method.

关 键 词：混合型多属性决策 区间数 协方差矩阵 广义逆矩阵 逼近理想解排序法 

分 类 号：E91[军事] C934[经济管理—管理学]