模糊多属性群决策问题的一种新TOPSIS方法

基于梯形模糊数的期望值算子,给出了一种新的TOPSIS方法来处理模糊决策矩阵、属性权重和决策者权重都已知,且均以梯形模糊数给出的模糊多属性群决策问题.先采用加权算术平均(Weighted Arithmetic Averaged)算子把所有规范化模糊决策矩阵集结为综合加权规范化模糊决策矩阵.然后以梯形模糊数的期望值排序方法和距离公式,求得模糊理想解和模糊负理想解及备选方案到模糊理想解和模糊负理想解的距离,从而确定各备选方案对模糊理想解的相对贴进度,并以其大小判断方案的优劣次序.最后通过一个实例说明该群决策方法的有效性.

A new TOPSIS method for fuzzy multiple attribute group decision making problem

Based on the expected value operator of trapezoidal fuzzy number, a new TOPSIS method is presented to deal with fuzzy multiple attribute group decision making problem when the fuzzy decision matrixes and the weights of the decision attributes and decision makers are all given by trapezoidal fuzzy number. First, all normalized fuzzy decision matrixes are aggregated to the integrated weighted normalized fuzzy decision matrix by weighted arithmetic average operator. Then, according to the expected ranking method and distance formula of trapezoidal fuzzy number, the fuzzy positive-ideal solution, fuzzy negative-ideal solution and the relative distance of each alternative from fuzzy positive-ideal solution and fuzzy negative-ideal solution are obtained. The relative closeness of every alternative to fuzzy positive-ideal solution is thus determined. The ranking of all alternative is judged by the relative closeness. Finally, an example is presented to show the effectiveness of the proposed group decision making method.