模糊信息系统的代数结构及其约简  

Algebraic structure and reduction of fuzzy information systems

作　　者：陈德刚[1] 刘民[1] 吴澄[1] 李法朝[1] 

机构地区：[1]清华大学自动化系,北京100084

出　　处：《清华大学学报（自然科学版）》2003年第9期1233-1235,1264,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(60004010)

摘　　要：模糊粗糙集理论是一种处理不确定性信息的重要的数据挖掘方法。为了建立模糊信息系统的约简建立理论基础,该文首先利用三角范数及其余范数给出了模糊集合近似算子的一般形式,进而定义了上、下可定义模糊集合,证明了它们分别构成完全分配格,并对其结构进行了刻画。在此基础上定义了模糊信息系统及其约简,讨论了它与经典的信息系统的约简的关系,为进一步研究模糊信息系统及其约简理论奠定了基础,同时也丰富了模糊集理论。Fuzzy rough set theory is an important method for data mining of uncertain data. This paper presents a theoretical foundation for the reduction of fuzzy information system. A general formula is given for the approximation operators of fuzzy sets using the triangular norm and its conorm. Then the upper definable sets and lower definable sets are defined and shown to form a complete distributive lattice. These relationships were used to define a fuzzy information system and its reduction and to study its relation with a crisp information system and its reduction, as a theoretical foundation for the reduction of fuzzy information systems. The results well facilitate the analysis of fuzzy sets and rough sets for improving data mining. 

关 键 词：模糊粗糙集理论 模糊信息系统 代数结构 数据挖掘 三角范数 余范数 模糊集合 约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O159[自动化与计算机技术—控制科学与工程]