粗糙集的矩阵刻画  

The Matrix Depict Approaches of Rough Sets

作　　者：刘文军 郭庆[2] LIU Wen-jun;GUO Qing(Department of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410076,China;School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410076 [2]合肥工业大学数学学院,安徽合肥230009

出　　处：《模糊系统与数学》2019年第3期169-174,共6页Fuzzy Systems and Mathematics

基　　金：2015年湖南省创新平台与人才计划项目(2015RS4049)

摘　　要：本文首先从一个二元关系矩阵出发,给出经典粗糙集、模糊粗糙集、粗糙模糊集的上下近似的矩阵描述,然后研究了它们的性质,最后将粗糙集、模糊粗糙集、粗糙模糊集的上下近似的定义用矩阵的方法统一起来,给研究带来了方便。矩阵的方法不仅提供了上下近似的简单的计算方法,也提供了一种新的推理的方法。In this paper,the author studies the rough sets used matrix.First,the upper and lower approximation operators of Pawlak rough sets,fuzzy-rough sets,rough-fuzzy sets are redefined using the matrix representation;then the properties of these upper and lower approximation operators are discussed;at last,the definitions of the upper and lower approximation operators of Pawlak rough sets,fuzzy-rough sets,rough-fuzzy sets are unified through the compound operator of matrix.The matrix approach afford not only a simply computing method of the upper and lower approximation operators of rough sets,but also a new inference method.

关 键 词：粗糙集 模糊粗糙集 粗糙模糊集 关系矩阵 上下近似 

分 类 号：O159[理学—数学]