A New Single-Valued Neutrosophic Rough Sets and Related Topology
(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationshi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5522021 |
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| _version_ | 1832546037953200128 |
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| author | Qiu Jin Kai Hu Chunxin Bo Lingqiang Li |
| author_facet | Qiu Jin Kai Hu Chunxin Bo Lingqiang Li |
| author_sort | Qiu Jin |
| collection | DOAJ |
| description | (Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U,R, a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces. |
| format | Article |
| id | doaj-art-0ebb31a6a39f4a72958e0b370945270d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0ebb31a6a39f4a72958e0b370945270d2025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55220215522021A New Single-Valued Neutrosophic Rough Sets and Related TopologyQiu Jin0Kai Hu1Chunxin Bo2Lingqiang Li3School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U,R, a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.http://dx.doi.org/10.1155/2021/5522021 |
| spellingShingle | Qiu Jin Kai Hu Chunxin Bo Lingqiang Li A New Single-Valued Neutrosophic Rough Sets and Related Topology Journal of Mathematics |
| title | A New Single-Valued Neutrosophic Rough Sets and Related Topology |
| title_full | A New Single-Valued Neutrosophic Rough Sets and Related Topology |
| title_fullStr | A New Single-Valued Neutrosophic Rough Sets and Related Topology |
| title_full_unstemmed | A New Single-Valued Neutrosophic Rough Sets and Related Topology |
| title_short | A New Single-Valued Neutrosophic Rough Sets and Related Topology |
| title_sort | new single valued neutrosophic rough sets and related topology |
| url | http://dx.doi.org/10.1155/2021/5522021 |
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