基于马田系统与TOPSIS的区间数多属性决策方法

Multiple attribute decision making method with intervals based on Mahalanobis-Taguchi system and TOPSIS method

针对区间数多属性决策问题,提出了一种利用马田系统处理区间数决策向量信息、利用TOPSIS法对区间数决策向量进行排序的方法.该方法将决策方案的区间数决策向量看作是多维属性空间中的超长方体,利用2水平正交表在该超长方体上均匀、分散地进行布点,并组成布点集来代表该决策方案;利用马氏距离测度决策方案布点集中的布点到正负理想方案布点集的距离;利用信噪比定义决策方案与正理想方案的贴近度.给出了详细的决策步骤.最后通过实例同其他方法进行了对比分析,结果表明本方法可行、有效.

For the problem of interval numbers multiple attribute decision, this paper proposes a ranking method for interval numbers decision vectors. This method processes the information of interval numbers decision vectors using Mahalanobis-Taguchi system and ranks interval numbers decision vectors using TOPSIS method. In this method, an m-dimensional interval numbers decision vector is regarded as super cuboids in m-dimensional attributes space; some points are uniformly and dispersedly selected by two-level orthogonal arrays. Those points compose of distribution points set to stand for decision making project. The distance of points in distribution points set of decision making project and distribution points set of positive ideal project is calculated with Mahalanobis distance; the closeness degree from decision making project to positive ideal project is defined by signal to noise ratio. The detailed decision making steps are given. Finally, an application example is analyzed. At the same time, the method proposed and others are compared, which shows the effectiveness and feasibility of the method.