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 Making Based on Generalized Mahalanobis Distance

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。

Abstract:

In order to solve the hybrid multiple-attribute decision making problem, different attribute values were unifiedinto interval number. In the TOPSIS based on Mahalanobis distance, because of the strong linear correlation indexes, thecovariance matrix was singular, and calculating the Mahalanobis distance didn’t work . Therefore , covariance matrix of in.terval number was defined and singular value decomposition method was adopted to calculate generalized inverse matrix ofcovariance 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 themembership function and possibility of the scheme closed to ideal solution and negative-ideal solution concurrently. In theend, a numerical example illustrated the validity and applicability of the proposed method.