语言犹豫模糊集的相关系数及其在决策中的应用  

Correlation coefficient of linguistic hesitant fuzzy set and its application in decision making

作　　者：黄先玖[1] 彭伟姝 HUANG Xian-jiu;PENG Wei-shu(School of Sciences,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学理学院,南昌330031

出　　处：《控制与决策》2020年第5期1211-1216,共6页Control and Decision

基　　金：国家自然科学基金项目(11961045,11661053);江西省自然科学基金项目(20161BAB201009);江西省杰出青年人才计划项目(20171BCB23004)。

摘　　要：语言犹豫模糊集是指决策者可以用一些有隶属度的语言术语项表示他/她对一件事情的偏好.这种类型的集合很好地反映了决策者定性和定量的认知以及它的不确定性,因此受到越来越多学者的关注.首先,提出语言犹豫模糊集的相关系数概念,并给出语言犹豫模糊集的相关系数和加权相关系数的计算法则和性质;然后,指出引入的相关系数的显着特征是它位于区间[-1,1]内,这与统计中的经典相关系数一致,而其他文献中提出的语言犹豫模糊集的相关系数都位于区间[0,1]内;最后,将所提出的方法应用于医疗诊断中,并将该方法得到的计算结果与已有的语言犹豫模糊集的相关系数进行比较,比较结果表明,新的语言犹豫模糊集的相关系数的分布更好,能更准确地反映出病人的身体状况与各疾病的关系,从而迅速高效地作出诊断.Linguistic hesitant fuzzy sets(LHFSs)permits the decision maker to apply several linguistic terms with membership degrees to denote his/her preference for one thing.Because this type of fuzzy sets can well reflect the qualitative and quantitative cognition of decision maker and it’s uncertainty,it attracts more and more scholars’attention.Firstly,we put forward the concept of the correlation coefficient of LHFSs,and give the calculation rules and properties of the correlation coefficient and weighted correlation coefficient of LHFSs.The significant characteristic of the introduced correlation coefficient in this paper is that it lies in the interval[-1,1],which is in accordance with the classic correlation coefficient in statistic.However,all the correlation coefficients of LHFSs in other related literature are in the interval[0,1].Finally,we apply the method proposed in this paper to medical diagnosis,and we compare the results in this paper with the previous research results of the correlation coefficient of LHFSs.As a result,it is found that the distribution of new correlation coefficient of the linguistic hesitant fuzzy sets is better,which can more accurately reflect the relationship between the patients’physical condition and various diseases,so that the diagnosis can be made quickly and efficiently.

关 键 词：语言犹豫模糊集 相关系数 加权相关系数 医疗诊断 

分 类 号：O177.91[理学—数学] O211.3[理学—基础数学]