粗糙近似算子在无限论域上的特征刻划

用构造性方法定义了无限集上的近似算子和粗糙集，讨论了无限集上的近似算子的一些性质，并得出各种类型的二元关系与粗糙近似算子之间的关系。用公理形式定义了粗糙近似算子，各种类型的粗糙集代数可以被各种不同的公理集所刻划阐明了近似算子的公理集可以保证找到相应的二元关系，使得由关系通过构造性方法定义的粗糙近似算子恰好就是用公理化定义的近似算子。

On Characterization of Rough Approximation Operators in Infinite Universes

The theory of rough sets can be developed in at least two aspects: constructive and axiomatic approaches. They are complementary to each other. The constructive approach is more suitable for practical applications of rough sets, while the axiomatic approach is appropriate for studying the structures of rough set algebras. In this paper, the constructive and axiomatic approaches in the study of rough fuzzy set in infinite universes are presented. In the constructive approach, one starts from a binary relation and defines a pair of lower and upper rough approximation operators. Different classes of rough set algebras are obtained from different types of binary crisp relations. In the axiomatic approach, one defines a pair of dual rough approximation operators and states that axioms must be satisfied by the operators. Various classes of rough algebras are characterized by different sets of axioms. Axioms of rough approximation operators guarantee the existence of certain types of binary crisp relations producing the same rough approximation operators.