Morphisms in Binary Rough Set Theory

摘要

Some scholars have proposed homomorphisms between information systems based on consistent functions. However, the binary relations in the codomain induced by consistent functions thoroughly depend on the binary relations induced by the original domain systems. This paper introduces the concept of core knowledge to analyze the intrinsical topology structures of binary approximation spaces, binary knowledge bases and binary information systems. Because of the three different categories, we use the term "morphism" from category theory to depict the communication into the three categories. A morphism can be regarded as the composition of a natural projection induced by core knowledge and an embedding, which are more general than homomorphisms. What's more, this paper proposes the notion of isomorphism and shows that the two isomorphic categories can be seen as one category based on the topological invariance. Considering that the reduction of knowledge and attributes should be based on the premise of maintaining the structure of core knowledge, isomorphisms will provide the theoretical basis of the reduction.