毕达哥拉斯犹豫模糊集的相关测度

Correlation measures of Pythagorean hesitant fuzzy set

毕达哥拉斯犹豫模糊集,既能描述隶属度与非隶属度之和超过1、而平方和不超过1的模糊现象,又能表达决策者在隶属度和非隶属度上的犹豫不决,因此它是表达不确定现象的一个强有力工具.考虑到相关测度在统计学和管理科学中发挥着重要的作用,在模糊集、直觉模糊集以及毕达哥拉斯模糊集等相关测度基础上,研究毕达哥拉斯犹豫模糊集的相关测度.为此,定义毕达哥拉斯犹豫模糊集的信息能量、相关指标以及相关系数,证明相关系数的性质.由于决策中经常要考虑到属性权重,定义毕达哥拉斯犹豫模糊集的加权相关系数,并讨论其性质.最后,通过求出每个方案与正理想方案之间的加权相关系数,实现方案的排序择优,并通过算例表明其可行性与有效性.

Pythagorean hesitant fuzzy set,which can not only describe the fuzzy phenomenon that the sum of membership degree and nonmembership degree may be bigger than 1 but their square sum is equal to or less than 1,but also express hesitations in membership degree and nonmembership degree,can be considered as a powerful tool for expressing uncertain information in the process of decision making.Considering that correlation measures play important role in statistics and management science,in this paper,correlation measures of the Pythagorean hesitant fuzzy set is studied.On the basis of the definition of the informational energy of the Pythagorean hesitant fuzzy set,the correlation coefficients between Pythagorean hesitant fuzzy sets are defined,and their natures are discussed.Then,the weights of attributes are often taken into account,and the concept of the weighted correlation coefficient between Pythagorean hesitant fuzzy sets is also introduced,and the natures are studied.Finally,through the weighted correlation coefficients between each alternative and the positive ideal alternative,the ranking order of all alternatives can be determined and the best alternative can be identified.An example is given to illustrate the feasibility and applicability of the proposed method.