程度粗糙集  

Graded Rough Sets

作　　者：张贤勇[1] 谢寿才[1] 莫智文[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2010年第1期12-16,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671030);四川省青年科技基金(07ZQ026114)资助项目;四川师范大学科学研究基金(08KYL06)

摘　　要：从广义程度粗糙集出发,定义了程度粗糙集,深入讨论了其内部构造,得出了程度粗糙集简化运算的重要方法.对比经典粗糙集性质,研究了程度粗糙集3个方面的性质:集合与其程度近似集的关系、程度近似算子的幂作用、程度边界算子对粗糙集性质的修正.得出了若干具有理论和应用价值的结果,并从算子论和集合论的角度丰富了粗糙集理论.In this paper,based on generalized graded rough sets,graded rough sets are defined.The internal constructions of them are discussed,and the simplified method of graded rough sets is achieved.In contrast to the properties of classical rough sets,three properties of graded rough sets are studied,which are the connection between sets and their graded approximations,the power action of graded approximation operators,the improvement of boundary operators of graded approximations on the properties of rough sets.Some important conclusions in theory and application are achieved,and the rough set theory has been enriched from the operator-oriented and set-oriented views.

关 键 词：粗糙集 程度粗糙集 评价函数 程度近似算子 边界算子 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]