广义犹豫模糊软集的不确定性度量及其应用  

The Uncertainty Measures of the Generalized Hesitant Fuzzy Soft Sets and Its Application

作　　者：黄鹤[1] 王艳平[1] 王金英[1] HUANG He;WANG Yan-ping;WANG Jin-ying(Science College,Liaoning University of Technology,Jinzhou 121001 ,China)

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001

出　　处：《模糊系统与数学》2018年第2期83-91,共9页Fuzzy Systems and Mathematics

摘　　要：本文在广义模糊软集和犹豫模糊软集的基础上给出广义犹豫模糊软集的概念,并研究广义犹豫模糊软集的不确定性度量。首先在犹豫模糊集包含度的公理化定义基础上,建立犹豫模糊集合的三种包含度公式;然后给出广义犹豫模糊软集包含度的公理化定义,并利用犹豫模糊集合的包含度公式构造广义犹豫模糊软集间的包含度公式,这些公式可以计算参数集不同时两个广义犹豫模糊软集间的包含度。接下来给出广义犹豫模糊软集不确定性度量的公理化定义,并从其包含度出发来构造广义犹豫模糊软集的不确定性度量公式,这种不确定性度量的计算方法同样适用于参数集不同的广义犹豫模糊软集,最后利用广义犹豫模糊软集不确定性度量方法应用到聚类分析实例中,通过实例验证了所提出方法的可行性和有效性。The concept of generalized hesitant fuzzy soft set is proposed based on the generalized fuzzy soft set and hesitant fuzzy soft set in this paper, and the uncertainty measure of the generalized hesitant fuzzy soft sets is discussed. At first, three hesitant fuzzy set contains degrees formula has been established based on the axiomatic definition of hesitant fuzzy set contains degrees. And then, the axiomatic definition of the generalized hesitate fuzzy soft set contains degrees is given, the inclu- sion degrees formula of generalized hesitate fuzzy soft set has been structured by the hesitant fuzzy set inclusion degree formula. These formulas can calculate the inclusion degree between two generalized hesitant fuzzy soft set when the parameter set is not equal. At next, the axiomatic definition of the generalized hesitant fuzzy soft uncertainty measures has been given. This generalized hesitant fuzzy soft uncertainty measures formula has been structured based on the inclusion degree. The calculation method of uncertainty measures is also suitable for generalized hesitant fuzzy soft which has different parameter sets. Finally, the new uncertainty measures method has been applied in clustering analysis instances. The feasibility of the proposed method is illustrated by examples.

关 键 词：广义模糊软集 犹豫模糊软集 广义犹豫模糊软集 不确定性度量 包含度 聚类分析 

分 类 号：O159[理学—数学]