Paper ID: 2205.09672

A Note on Categories about Rough Sets

Y. R. Syau, E. B. Lin, C. J. Liau

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

Submitted: May 19, 2022