CAJ | 학술논문

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。
위료해결혼합형다속성결책문제，장불동속성치전환위구간수형식。재기우마씨거리적핍근이상해배서법（TOPSIS）중，지표간선성강상관도치협방차구진위기이구진，불능계산마씨거리。인차，정의료구간수적협방차구진，채용기이치분해방법계산협방차구진적엄의（M-P）역구진。개진적산법극복료전통TOPSIS존재적지표신식중복、주관부권불합리、대속도난이학정，이급가능출현여이상해구식거리근적방안여부이상해적구식거리야근적불족。최후，급출료해방법적일개산례，결과표명해결책방법시실용화가행적。
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 , covariance 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. In the end, a numerical example illustrated the validity and applicability of the proposed method.