广义直觉模糊粗糙集的粒结构  

Granular Structure of Generalized Intuitionistic Fuzzy Rough Sets

作　　者：宋鑫瑶 刘晓娟[1,2] 米据生 SONG Xin-yao;LIU Xiao-juan;MI Ju-sheng(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei International Joint Research Center for Mathematics and Interdisciplinary Science,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄河北050024 [2]河北省数学与交叉科学国际联合研究中心,河北石家庄050024

出　　处：《模糊系统与数学》2021年第6期101-110,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61502144,62076088);河北省自然科学基金资助项目(F2018205196,F2019205295);河北省高等学校自然科学基金资助项目(BJ2019014);河北省博士后择优资助科研项目(B2016003013);河北省三三三人才杠程培养经费(A2017002112)。

摘　　要：模糊集可以表示为一些模糊粒的并集,粗糙集也可表示成相应模糊粒的并集。本文主要探讨直觉模糊粗糙集的粒结构,直觉模糊粗糙集是在直觉模糊关系下结合了粗糙集和直觉模糊集构造出来的。本文首先在直觉模糊等价关系下定义了两种模糊粒,利用它们构造直觉模糊集的上下近似算子并给出例子。然后首次在相似关系下构造直觉模糊粗糙集的粒结构并探讨其性质,给出相应隶属函数的表达式,证明了利用模糊粒定义的近似算子等价于利用隶属函数定义的近似算子,进一步拓展了直觉模糊粗糙集在粒计算中的应用。A fuzzy set can be represented as the union of some fuzzy granules,and the rough set can also be represented as the union of corresponding fuzzy sets.This paper mainly discusses the particle structure of intuitionistic fuzzy rough sets.The intuitionistic fuzzy rough sets are constructed by combining the rough sets and intuitionistic fuzzy sets under the intuitionistic fuzzy relation.In this paper,fuzzy information granules based on the intuitionistic fuzzy equivalence relations are defined and used to characterize the structures of the lower and upper approximations of intuitionistic fuzzy sets.Then,for the first time,we extend them to construct the particle structure of intuitionistic fuzzy rough sets under the intuitionistic fuzzy similarity relation and study their properties.It is proved that the proposed definition of approximation operators defined by fuzzy granules are equivalent to those defined by the membership functions.The application of intuitionistic fuzzy rough set in particle computation is further expanded.

关 键 词：直觉模糊粗糙集 直觉模糊关系 模糊粒 三角模 

分 类 号：O159[理学—数学]