New Topological Approaches to Rough Sets via Subset Neighborhoods
This paper aims to obtain new types of approximations by using topological concepts. Firstly, different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then, j-subset approximations based on these topologies are introduced and their basic propert...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3942708 |
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| _version_ | 1850166579996655616 |
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| author | Esra Dalan Yildirim |
| author_facet | Esra Dalan Yildirim |
| author_sort | Esra Dalan Yildirim |
| collection | DOAJ |
| description | This paper aims to obtain new types of approximations by using topological concepts. Firstly, different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then, j-subset approximations based on these topologies are introduced and their basic properties are examined. In addition to this, Sj-near open and θβSj-open sets are defined and the connections among them are given. Later, new approximations are presented with the help of the aforementioned sets, and their main properties are investigated. Furthermore, the proposed approximations are compared both with themselves and with the previous one. From this, it is shown that the approximations based on θβSj-open sets are more accurate than those based on Sj-open and Sj-near open sets under arbitrary binary relation and than those based on j-open sets under similarity relation. Finally, a real-life problem related to COVID-19 is addressed to highlight the importance of applying the proposed approximations. |
| format | Article |
| id | doaj-art-e3d7e0156abb463d95fedb57f19a8222 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e3d7e0156abb463d95fedb57f19a82222025-08-20T02:21:24ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3942708New Topological Approaches to Rough Sets via Subset NeighborhoodsEsra Dalan Yildirim0Department of MathematicsThis paper aims to obtain new types of approximations by using topological concepts. Firstly, different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then, j-subset approximations based on these topologies are introduced and their basic properties are examined. In addition to this, Sj-near open and θβSj-open sets are defined and the connections among them are given. Later, new approximations are presented with the help of the aforementioned sets, and their main properties are investigated. Furthermore, the proposed approximations are compared both with themselves and with the previous one. From this, it is shown that the approximations based on θβSj-open sets are more accurate than those based on Sj-open and Sj-near open sets under arbitrary binary relation and than those based on j-open sets under similarity relation. Finally, a real-life problem related to COVID-19 is addressed to highlight the importance of applying the proposed approximations.http://dx.doi.org/10.1155/2022/3942708 |
| spellingShingle | Esra Dalan Yildirim New Topological Approaches to Rough Sets via Subset Neighborhoods Journal of Mathematics |
| title | New Topological Approaches to Rough Sets via Subset Neighborhoods |
| title_full | New Topological Approaches to Rough Sets via Subset Neighborhoods |
| title_fullStr | New Topological Approaches to Rough Sets via Subset Neighborhoods |
| title_full_unstemmed | New Topological Approaches to Rough Sets via Subset Neighborhoods |
| title_short | New Topological Approaches to Rough Sets via Subset Neighborhoods |
| title_sort | new topological approaches to rough sets via subset neighborhoods |
| url | http://dx.doi.org/10.1155/2022/3942708 |
| work_keys_str_mv | AT esradalanyildirim newtopologicalapproachestoroughsetsviasubsetneighborhoods |