属性权重未知picture模糊多属性决策方法及其应用

针对属性权重未知的picture模糊多属性决策问题,提出一种基于picture模糊熵和picture模糊加权对称交叉熵的多属性决策方法.首先,基于余弦函数提出一类新的picture模糊熵,并验证该熵值满足picture模糊熵的公理化定义;其次,针对标准化处理后的picture模糊决策矩阵,以picture模糊熵确定各属性权重,同时确定正、负理想方案;再次,分别计算各方案与正、负理想方案的picture模糊加权对称交叉熵,考虑决策者的主观评价倾向以模糊折中值得到各备选方案的排序结果;最后,将所提多属性决策方法应用于河南自贸试验区郑州片区创新型项目遴选,并通过对比分析验证该决策方法的有效性与合理性.

Picture fuzzy multi-attribute decision making method with unknown attribute weight and its application

In order to solve the picture fuzzy multi-attribute decision making problem with unknown attribute weights, this paper proposed a new picture fuzzy entropy and picture fuzzy weighted symmetric cross entropy for multi-attribute decision making method. Firstly, based on the cosine function, this paper proposed a new picture fuzzy entropy and verified that the entropy value meeted the axiomatic definition of picture fuzzy entropy. Secondly, according to the picture fuzzy decision matrix after standardization, this paper used the picture fuzzy entropy to determine the weight of each attribute, based on this, determined the positive and negative ideal alternatives at the same time. Thirdly, it calculated the picture fuzzy weighted symmetric cross entropy of each alternative with positive and negative ideal alternatives respectively. According to the decision maker''s subjective evaluation tendency, the ranking results of each alternative could be obtained by fuzzy compromise ratio. Finally, the selection of innovative projects in Zhengzhou area of Henan Pilot Free Trade Zone could illustrate the proposed method, and by using comparative analysis to verify effectiveness and rationality of the decision-making method.