Convex rough sets on finite domains
[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 th...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/160847 |
| Acceso en línea: | http://hdl.handle.net/10366/160847 |
| Access Level: | acceso abierto |
| Palabra clave: | Rough set Convex geometries Convexity Definable subset Approximation operator 1202.01 Álgebra de Operadores 1204 Geometría |
| Sumario: | [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. |
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