<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately, different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.</p></abstract>

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately, different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.

Rough sets based on Galois connections

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Rough sets based on Galois connections"}

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an...

Rough sets based on Galois connections

Publié en ligne: 04 juil. 2020

Pages: 299 - 313

Reçu: 09 juin 2019

Accepté: 13 févr. 2020

DOI: https://doi.org/10.34768/amcs-2020-0023

Mots clés
rough sets, Galois connections, approximation operators

© 2020 Nicolás Madrid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Rough sets based on Galois connections

Publié en ligne: 04 juil. 2020

Pages: 299 - 313

Reçu: 09 juin 2019

Accepté: 13 févr. 2020

DOI: https://doi.org/10.34768/amcs-2020-0023

Mots clésrough sets, Galois connections, approximation operators

© 2020 Nicolás Madrid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
rough sets, Galois connections, approximation operators