摘要
二元关系作为一类特殊的集合,可考虑它的余集.文中首先从等价关系的集合属性出发,给出余等价关系的定义及其内部关系刻画,构造基于余等价关系的广义粗糙集,论证其公理化基础.其次研究经典粗糙集和余等价关系下的广义粗糙集之间的相互联系,并在特定条件下借助余等价关系下的广义粗糙集,简化相应经典近似算子的相关运算,刻画基本精确集等重要知识.
A binary relation can be regarded as a set, and thus its complementary set is taken into account. Based on the set attribute of the equivalence relations, the definition of the complementary equivalence relation is given firstly, and its characterization of the relationship among the internal elements is probed. Firstly, the rough set based on the complementary equivalence relation is constructed, and the basis of its axiomatization is discussed as well. Secondly, the mutual relation between the rough set based on the complementary equivalence relation and the classical rough set is studied. And by the proposed rough set, the corresponding calculations of the classical approximation operators is predigested, and the key knowledge like basic accurate set is also fixed.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2014年第10期873-878,共6页
Pattern Recognition and Artificial Intelligence
基金
国家自然科学基金项目(No.61379021
61303131
61300121
61170107)
河北省自然科学基金项目(No.A2013208175
QN20131159)
福建省自然科学基金项目(No.2013J01028
2013J01029
2013J01265
2012D141)
福建省属高校科研项目(No.JK2011031
JK2013027)
福建省软科学研究科技项目(No.2012R0090)
福建省教育厅科技项目(No.JA12223)资助
关键词
粗糙集
等价关系
余等价关系
精确集
Rough Set, Equivalence Relation, Complementary Equivalence Relation, Accurate Set
