Cardinality rough neighborhoods with applications DOI Creative Commons
Tareq M. Al-shami, Rodyna A. Hosny, Abdelwaheb Mhemdi

et al.

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(11), P. 31366 - 31392

Published: Jan. 1, 2024

<p>Rough set theory serves as an effective method for managing complicated real-world data. Through rough approximation operators, it discerns both confirmed and possible data attainable through subsets. Earlier studies have presented several models, drawing inspiration from neighborhood systems aimed at enhancing accuracy degree satisfying the axioms of traditional spaces (TAS) that were initiated by Pawlak. This article proposes easy to deal with information in most cases, wherein introduces a new forming generalized spaces, namely, cardinality neighborhoods. It is defined depending on cardinal number $ \mathcal{N}_\sigma $-neighborhoods elements are established under arbitrary relation. Their main features investigated connections between them, well their relationships preceding kinds systems, uncovered aid some examples. Then, novel paradigms induced neighborhoods displayed satisfy properties Pawlak's paradigm. Next, topological study these provided, this produces operators similar given six cases proved. Additionally, practical example concerning books authors who authored them or participated authorship applied. To illuminate need current concepts, we elaborate advantages different views. Finally, summary obtained results suggestions forthcoming work offered.</p>

Language: Английский

Overlapping containment rough neighborhoods and their generalized approximation spaces with applications DOI
Tareq M. Al-shami, Abdelwaheb Mhemdi

Journal of Applied Mathematics and Computing, Journal Year: 2024, Volume and Issue: unknown

Published: Oct. 12, 2024

Language: Английский

Citations

3
Cardinality rough neighborhoods with applications DOI Creative Commons
Tareq M. Al-shami, Rodyna A. Hosny, Abdelwaheb Mhemdi

et al.

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(11), P. 31366 - 31392

Published: Jan. 1, 2024

<p>Rough set theory serves as an effective method for managing complicated real-world data. Through rough approximation operators, it discerns both confirmed and possible data attainable through subsets. Earlier studies have presented several models, drawing inspiration from neighborhood systems aimed at enhancing accuracy degree satisfying the axioms of traditional spaces (TAS) that were initiated by Pawlak. This article proposes easy to deal with information in most cases, wherein introduces a new forming generalized spaces, namely, cardinality neighborhoods. It is defined depending on cardinal number $ \mathcal{N}_\sigma $-neighborhoods elements are established under arbitrary relation. Their main features investigated connections between them, well their relationships preceding kinds systems, uncovered aid some examples. Then, novel paradigms induced neighborhoods displayed satisfy properties Pawlak's paradigm. Next, topological study these provided, this produces operators similar given six cases proved. Additionally, practical example concerning books authors who authored them or participated authorship applied. To illuminate need current concepts, we elaborate advantages different views. Finally, summary obtained results suggestions forthcoming work offered.</p>

Language: Английский

Citations

1