The characterizations of upper approximation operators based on special coverings
In this paper, we discuss the approximation operators apr¯NS${\overline {apr} _{NS}}$ and apr¯S${\overline {apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary cond...
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De Gruyter
2017-03-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2017-0015 |
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doaj-ce0d8ff01b2040959475d3e12ca5ccc42021-09-06T19:20:08ZengDe GruyterOpen Mathematics2391-54552017-03-0115119320210.1515/math-2017-0015math-2017-0015The characterizations of upper approximation operators based on special coveringsWang Pei0Li Qingguo1College of Mathematics and Econometrics, Hunan University, Hunan, 410012, ChinaCollege of Mathematics and Econometrics, Hunan University, Hunan, 410012, ChinaIn this paper, we discuss the approximation operators apr¯NS${\overline {apr} _{NS}}$ and apr¯S${\overline {apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.https://doi.org/10.1515/math-2017-0015upper approximation operatorclosure operatorbasetopology54-0054a1054a99 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wang Pei Li Qingguo |
| spellingShingle |
Wang Pei Li Qingguo The characterizations of upper approximation operators based on special coverings Open Mathematics upper approximation operator closure operator base topology 54-00 54a10 54a99 |
| author_facet |
Wang Pei Li Qingguo |
| author_sort |
Wang Pei |
| title |
The characterizations of upper approximation operators based on special coverings |
| title_short |
The characterizations of upper approximation operators based on special coverings |
| title_full |
The characterizations of upper approximation operators based on special coverings |
| title_fullStr |
The characterizations of upper approximation operators based on special coverings |
| title_full_unstemmed |
The characterizations of upper approximation operators based on special coverings |
| title_sort |
characterizations of upper approximation operators based on special coverings |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2017-03-01 |
| description |
In this paper, we discuss the approximation operators apr¯NS${\overline {apr} _{NS}}$ and apr¯S${\overline {apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators. |
| topic |
upper approximation operator closure operator base topology 54-00 54a10 54a99 |
| url |
https://doi.org/10.1515/math-2017-0015 |
| work_keys_str_mv |
AT wangpei thecharacterizationsofupperapproximationoperatorsbasedonspecialcoverings AT liqingguo thecharacterizationsofupperapproximationoperatorsbasedonspecialcoverings AT wangpei characterizationsofupperapproximationoperatorsbasedonspecialcoverings AT liqingguo characterizationsofupperapproximationoperatorsbasedonspecialcoverings |
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1717777233715658752 |