基于区间值毕达哥拉斯模糊数的多属性决策方法

Multi-attribute Decision Making Method Based on Interval Value Pythagoras Fuzzy Number

针对决策信息为区间值毕达哥拉斯模糊数(IVPFN)的多属性决策问题,提出了一种基于区间值毕达哥拉斯模糊交叉熵的多属性决策方法。首先,将交叉熵的概念引入到区间值毕达哥拉斯模糊集(IVPFS)中,定义了一种新的区间值毕达哥拉斯模糊集(IVPFS)交叉熵测度,并以此来刻画两个区间值毕达哥拉斯模糊集之间的差异程度;其次根据每个区间值毕达哥拉斯模糊数(IVPFN)的得分函数,确定区间值毕达哥拉斯环境下的正、负理想解;再次在TOPSIS原理基础上,根据每个方案与正、负理想解之间的相对贴近度来获取最佳方案;最后通过一个实例对文中所提出的方法进行验证,表明了该方法的可行性与合理性。

In order to solve the problem of multi-attribute decision making with interval value Pythagoras fuzzy number(IVPFN),a multi-attribute decision making method based on interval value Pythagoras fuzzy cross entropy is proposed.Firstly,the concept of cross entropy is introduced into the interval-valued Pythagoras fuzzy sets(IVPFS),and a new measure of cross entropy of the interval-valued Pythagoras fuzzy sets(IVPFS)is defined,which is used to describe the difference degree between the two interval-value Pythagoras fuzzy sets.Secondly,according to the score function of each interval value Pythagoras fuzzy number(IVPFN),the positive and negative ideal solutions of the interval value Pythagoras are determined.On the basis of TOPSIS principle,the optimal scheme is obtained according to the relative closeness between each scheme and the positive and negative ideal solution.Finally,an example is given to verify the proposed method,which shows its feasibility and rationality.