余等价关系下的粗糙集

摘要

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.%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。