犹豫模糊软集的相关系数及其在决策中的应用

The correlation coefficient of hesitant fuzzy soft set and its application in decision making

犹豫模糊软集结合了Torra(2010)的犹豫模糊集理论和Molodtsov(1999)的软集理论.鉴于相关系数是数据分析中应用最广泛的指标之一,提出一种犹豫模糊软集相关系数,同时给出犹豫模糊软集的平均值和方差的定义,基于这些概念给出犹豫模糊软集相关系数的计算公式.新的犹豫模糊软集相关系数的值在区间[-1, 1]上,而不是[0, 1]上,这与统计学中经典相关系数一致,因此克服了已有犹豫模糊软集相关系数中存在的缺陷.为了提升其应用的广泛性,提出犹豫模糊软集加权相关系数的概念.最后,通过医院评估的实例验证所提出的犹豫模糊软集相关系数的适用性和有效性.

A hesitant fuzzy soft set(HFSS) is a combination of the Torra’s(2010) hesitant fuzzy set(HFS) and the Molodtsov’s(1999) soft set theory. Considering that correlation coefficient is one of the most widely used indices in data analysis, a novel concept of correlation coefficient between HFSSs is proposed. At the same time, the mean and the variance of a HFSS are defined. Based on these concepts, a novel correlation coefficient formulation between two HFSSs is developed. The value of the introduced correlation coefficient between two HFSSs lies in the interval [-1, 1] rather than [0, 1], which is in accordance with the classical correlation coefficient in statistics, thus overcomes the weakness of existing correlation coefficient between HFSSs. The weighted correlation coefficient is also proposed to make it more applicable. Finally, an example of hospital assessment is given to illustrate the applicability and effectiveness of the proposed correlation between HFSSs.