Generalized rough sets based on neighborhood systems and topological spaces
Rough sets theory is an important method for dealing with uncertainty, fuzziness and undefined objects. In this paper, we introduce a new approach for generalized rough sets based on the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approximation operators are...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X16300098 |
| _version_ | 1828388760667029504 |
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| author | R. Mareay |
| author_facet | R. Mareay |
| author_sort | R. Mareay |
| collection | DOAJ |
| description | Rough sets theory is an important method for dealing with uncertainty, fuzziness and undefined objects. In this paper, we introduce a new approach for generalized rough sets based on the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approximation operators are generated from the core of neighborhood systems. Relationship among different approximation operators are presented. We generate different topological spaces by using the core of these neighborhood systems. Relationship among different generated topologies are discussed. |
| first_indexed | 2024-12-10T06:18:07Z |
| format | Article |
| id | doaj.art-684959e975e54e39a5095c501647b9f6 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-10T06:18:07Z |
| publishDate | 2016-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-684959e975e54e39a5095c501647b9f62022-12-22T01:59:24ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-10-0124460360810.1016/j.joems.2016.02.002Generalized rough sets based on neighborhood systems and topological spacesR. MareayRough sets theory is an important method for dealing with uncertainty, fuzziness and undefined objects. In this paper, we introduce a new approach for generalized rough sets based on the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approximation operators are generated from the core of neighborhood systems. Relationship among different approximation operators are presented. We generate different topological spaces by using the core of these neighborhood systems. Relationship among different generated topologies are discussed.http://www.sciencedirect.com/science/article/pii/S1110256X16300098Rough setsNeighborhood systemsCoreTopology |
| spellingShingle | R. Mareay Generalized rough sets based on neighborhood systems and topological spaces Journal of the Egyptian Mathematical Society Rough sets Neighborhood systems Core Topology |
| title | Generalized rough sets based on neighborhood systems and topological spaces |
| title_full | Generalized rough sets based on neighborhood systems and topological spaces |
| title_fullStr | Generalized rough sets based on neighborhood systems and topological spaces |
| title_full_unstemmed | Generalized rough sets based on neighborhood systems and topological spaces |
| title_short | Generalized rough sets based on neighborhood systems and topological spaces |
| title_sort | generalized rough sets based on neighborhood systems and topological spaces |
| topic | Rough sets Neighborhood systems Core Topology |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X16300098 |
| work_keys_str_mv | AT rmareay generalizedroughsetsbasedonneighborhoodsystemsandtopologicalspaces |