A Note on Categories about Rough Sets

Abstract

Using the concepts of category and functor, we provide some insights and prove an intrinsic property of the category $\mathbf{AprS}$ of approximation spaces and relation-preserving functions, the category $\mathbf{RCls}$ of rough closure spaces and continuous functions, and the category $\mathbf{RInt}$ of rough interior spaces and continuous functions. Furthermore, we define the category $\mathbf{IS}$ of information systems and O-A-D homomorphisms, and establish the relationship between the category $\mathbf{IS}$ and the category $\mathbf{AprS}$ by considering a subcategory $\mathbf{NeIS}$ of $\mathbf{IS}$ whose objects are information systems and whose arrows are non-expensive O-A-D homomorphisms with surjective attribute mappings.

15 pages