New Types of μ-Proximity Spaces and Their Applications
Near set theory supplies a major basis for the perception, differentiation, and classification of elements in classes that depend on their closeness, either spatially or descriptively. This study aims to introduce a lot of concepts; one of them is μ-clusters as the useful notion in the study of μ-pr...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1657993 |
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| author | Rodyna A. Hosny Tareq M. Al-shami Abdelwaheb Mhemdi |
| author_facet | Rodyna A. Hosny Tareq M. Al-shami Abdelwaheb Mhemdi |
| author_sort | Rodyna A. Hosny |
| collection | DOAJ |
| description | Near set theory supplies a major basis for the perception, differentiation, and classification of elements in classes that depend on their closeness, either spatially or descriptively. This study aims to introduce a lot of concepts; one of them is μ-clusters as the useful notion in the study of μ-proximity (or μ-nearness) spaces which recognize some of its features. Also, other types of μ-proximity, termed Rμ-proximity and Oμ-proximity, on X are defined. In a μ-proximity space X,δμ, for any subset K of X, one can find out nonempty collections δμK=G⊆X∣Kδ¯μG, which are hereditary classes on X. Currently, descriptive near sets were presented as a tool of solving classification and pattern recognition problems emerging from disjoint sets; hence, a new approach to basic μ-proximity structures, which depend on the realization of the structures in the theory of hereditary classes, is introduced. Also, regarding to specific options of hereditary class operators, various kinds of μ-proximities can be distinguished. |
| format | Article |
| id | doaj-art-cac4c9cfd6134af0b2d92fedb930c212 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cac4c9cfd6134af0b2d92fedb930c2122025-02-03T01:08:57ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1657993New Types of μ-Proximity Spaces and Their ApplicationsRodyna A. Hosny0Tareq M. Al-shami1Abdelwaheb Mhemdi2Department of MathematicsDepartment of MathematicsDepartment of MathematicsNear set theory supplies a major basis for the perception, differentiation, and classification of elements in classes that depend on their closeness, either spatially or descriptively. This study aims to introduce a lot of concepts; one of them is μ-clusters as the useful notion in the study of μ-proximity (or μ-nearness) spaces which recognize some of its features. Also, other types of μ-proximity, termed Rμ-proximity and Oμ-proximity, on X are defined. In a μ-proximity space X,δμ, for any subset K of X, one can find out nonempty collections δμK=G⊆X∣Kδ¯μG, which are hereditary classes on X. Currently, descriptive near sets were presented as a tool of solving classification and pattern recognition problems emerging from disjoint sets; hence, a new approach to basic μ-proximity structures, which depend on the realization of the structures in the theory of hereditary classes, is introduced. Also, regarding to specific options of hereditary class operators, various kinds of μ-proximities can be distinguished.http://dx.doi.org/10.1155/2022/1657993 |
| spellingShingle | Rodyna A. Hosny Tareq M. Al-shami Abdelwaheb Mhemdi New Types of μ-Proximity Spaces and Their Applications Journal of Mathematics |
| title | New Types of μ-Proximity Spaces and Their Applications |
| title_full | New Types of μ-Proximity Spaces and Their Applications |
| title_fullStr | New Types of μ-Proximity Spaces and Their Applications |
| title_full_unstemmed | New Types of μ-Proximity Spaces and Their Applications |
| title_short | New Types of μ-Proximity Spaces and Their Applications |
| title_sort | new types of μ proximity spaces and their applications |
| url | http://dx.doi.org/10.1155/2022/1657993 |
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