Interval neutrosophic covering rough sets based on neighborhoods
Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021224?viewType=HTML |
| _version_ | 1819315413421391872 |
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| author | Dongsheng Xu Huaxiang Xian Xiewen Lu |
| author_facet | Dongsheng Xu Huaxiang Xian Xiewen Lu |
| author_sort | Dongsheng Xu |
| collection | DOAJ |
| description | Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets. |
| first_indexed | 2024-12-24T09:59:43Z |
| format | Article |
| id | doaj.art-73d6432045924b6992b2a07b5ca10709 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-24T09:59:43Z |
| publishDate | 2021-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-73d6432045924b6992b2a07b5ca107092022-12-21T17:01:08ZengAIMS PressAIMS Mathematics2473-69882021-02-01643772378710.3934/math.2021224Interval neutrosophic covering rough sets based on neighborhoodsDongsheng Xu0Huaxiang Xian1 Xiewen Lu2School of Science, Southwest Petroleum University, Chengdu 610500, ChinaSchool of Science, Southwest Petroleum University, Chengdu 610500, ChinaSchool of Science, Southwest Petroleum University, Chengdu 610500, ChinaCovering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets.http://www.aimspress.com/article/doi/10.3934/math.2021224?viewType=HTMLneutrosophic setsinterval neutrosophic setsrough setscovering rough setsneighborhood |
| spellingShingle | Dongsheng Xu Huaxiang Xian Xiewen Lu Interval neutrosophic covering rough sets based on neighborhoods AIMS Mathematics neutrosophic sets interval neutrosophic sets rough sets covering rough sets neighborhood |
| title | Interval neutrosophic covering rough sets based on neighborhoods |
| title_full | Interval neutrosophic covering rough sets based on neighborhoods |
| title_fullStr | Interval neutrosophic covering rough sets based on neighborhoods |
| title_full_unstemmed | Interval neutrosophic covering rough sets based on neighborhoods |
| title_short | Interval neutrosophic covering rough sets based on neighborhoods |
| title_sort | interval neutrosophic covering rough sets based on neighborhoods |
| topic | neutrosophic sets interval neutrosophic sets rough sets covering rough sets neighborhood |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021224?viewType=HTML |
| work_keys_str_mv | AT dongshengxu intervalneutrosophiccoveringroughsetsbasedonneighborhoods AT huaxiangxian intervalneutrosophiccoveringroughsetsbasedonneighborhoods AT xiewenlu intervalneutrosophiccoveringroughsetsbasedonneighborhoods |