基于灰色理想解法的模糊多属性决策方法研究

Study on the Approach of Fuzzy Multi-Attribute Decision Making Based on Degree of Grey Incidence and TOPSIS

针对方案评估中属性信息的模糊性,提出了一种基于熵权和灰色理想解法的决策方法.该方法先将属性的模糊信息转化为三角模糊数,再利用三角模糊数的性质和信息熵的思想,求出属性的熵权.然后,用灰色理论对传统理想解法进行拓展,将灰色关联度和欧氏距离有机结合构造出一种相似接近度对方案进行评价.相似接近度同时反映了方案与正负理想方案之间的位置和数据曲线的相似性差异,这种方法使其物理意义更加明确.通过算例说明了方法的可行性和有效性.

Aimed at the fuzziness of scheme evaluation, a new decision making method based on entropy weight and gray TOPSIS is presented. The fuzzy information of the attribute is firstly transformed to the triangular fuzzy numbers. According to the characters of triangular fuzzy numbers and the entropy, each attribute weight is worked out. Then, the traditional TOPSIS is improved by grey theory, a new kind of similar approach degree is established by combining the Euclidean distance with grey correlation degree to appraise the scheme. The similar approach degree reflects the distance and the difference of data curves among a selected scheme, the ideal solution and negative ideal solution. This method has clear physical implication. Finally, the feasibility and effectivity of the method is proved by an example.