Fuzzy Closure Spaces vs. Fuzzy Rough Sets
This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2014-03-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865814000089 |
| _version_ | 1797716959532417024 |
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| author | S.P. Tiwari Shambhu Sharan Vijay K. Yadav |
| author_facet | S.P. Tiwari Shambhu Sharan Vijay K. Yadav |
| author_sort | S.P. Tiwari |
| collection | DOAJ |
| description | This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a certain extra condition. |
| first_indexed | 2024-03-12T08:29:14Z |
| format | Article |
| id | doaj.art-d93a6af014e34c52b67fe1bfcd8b5383 |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T08:29:14Z |
| publishDate | 2014-03-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-d93a6af014e34c52b67fe1bfcd8b53832023-09-02T17:56:42ZengTsinghua University PressFuzzy Information and Engineering1616-86582014-03-01619310010.1016/j.fiae.2014.06.007Fuzzy Closure Spaces vs. Fuzzy Rough SetsS.P. Tiwari0Shambhu Sharan1Vijay K. Yadav2Department of Applied Mathematics, Indian School of Mines, Dhanbad- 826004, IndiaDepartment of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar- 751024, IndiaDepartment of Applied Mathematics, Indian School of Mines, Dhanbad- 826004, IndiaThis paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a certain extra condition.http://www.sciencedirect.com/science/article/pii/S1616865814000089Fuzzy rough setFuzzy reflexive approximation spaceFuzzy tolerance approximation spaceFuzzy closure spaceFuzzy topology |
| spellingShingle | S.P. Tiwari Shambhu Sharan Vijay K. Yadav Fuzzy Closure Spaces vs. Fuzzy Rough Sets Fuzzy Information and Engineering Fuzzy rough set Fuzzy reflexive approximation space Fuzzy tolerance approximation space Fuzzy closure space Fuzzy topology |
| title | Fuzzy Closure Spaces vs. Fuzzy Rough Sets |
| title_full | Fuzzy Closure Spaces vs. Fuzzy Rough Sets |
| title_fullStr | Fuzzy Closure Spaces vs. Fuzzy Rough Sets |
| title_full_unstemmed | Fuzzy Closure Spaces vs. Fuzzy Rough Sets |
| title_short | Fuzzy Closure Spaces vs. Fuzzy Rough Sets |
| title_sort | fuzzy closure spaces vs fuzzy rough sets |
| topic | Fuzzy rough set Fuzzy reflexive approximation space Fuzzy tolerance approximation space Fuzzy closure space Fuzzy topology |
| url | http://www.sciencedirect.com/science/article/pii/S1616865814000089 |
| work_keys_str_mv | AT sptiwari fuzzyclosurespacesvsfuzzyroughsets AT shambhusharan fuzzyclosurespacesvsfuzzyroughsets AT vijaykyadav fuzzyclosurespacesvsfuzzyroughsets |