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oai:gredos.usal.es:10366/1608472025-04-30T20:51:26Zcom_10366_149732com_10366_4576com_10366_3823col_10366_149733

Zhan, Jianming Alcantud, José Carlos R. Rough set Convex geometries Convexity Definable subset Approximation operator [EN] This paper addresses a foundational aspect of imprecision in information and knowledge. It makes a convincing case that convexity can take part in the progress of rough set theory in finite settings. To this purpose we resort to convex geometries, which constitute a special type of coverings that abstract many combinatorial features of convexity. We define convex geometry (cg) approximation spaces on a grand set, and we produce novel cgupper and cg-lower approximation operators. Their basic properties are presented. Then we show that the model that arises has connections with well-established models in the rough set literature, both from relation and covering-based approaches. We identificate three types of subsets of the grand set that have different behaviors with respect to their cg-approximations, and we refine this classification in some benchmark cases. Finally, we produce a canonical convex geometry approximation space from any covering on a set. Examples illustrate our constructions and main results. 2024-11-29 2024-11-29 2022 info:eu-repo/semantics/article Alcantud, J. C. R., & Zhan, J. (2022). Convex rough sets on finite domains. Information Sciences, 611, 81-94. 0020-0255 1872-6291 http://hdl.handle.net/10366/160847 10.1016/j.ins.2022.08.013 eng https://doi.org/10.1016/j.ins.2022.08.013 http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier