A Note on Categories about Rough Sets

05/19/2022

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by   Y. R. Syau, et al.

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