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arXiv · 2205.09672

A Note on Categories about Rough Sets

Y. R. Syau·E. B. Lin·C. J. Liau
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Abstract

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.

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Y. R. Syau, E. B. Lin, C. J. Liau. 2022-05-19. A Note on Categories about Rough Sets. https://arxiv.org/abs/2205.09672

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