Near Approximations in Modules
Rough set theory is a mathematical approach to imperfect knowledge. The near set approach leads to partitions of ensembles of sample objects with measurable information content and an approach to feature selection. In this paper, we apply the previous results of Bagirmaz [Appl. Algebra Engrg. Comm....
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2021-12-01
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| Series: | Foundations of Computing and Decision Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/fcds-2021-0020 |
| _version_ | 1798039782295601152 |
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| author | Davvaz Bijan Setyawati Dian Winda Soleha Mukhlash Imam Subiono |
| author_facet | Davvaz Bijan Setyawati Dian Winda Soleha Mukhlash Imam Subiono |
| author_sort | Davvaz Bijan |
| collection | DOAJ |
| description | Rough set theory is a mathematical approach to imperfect knowledge. The near set approach leads to partitions of ensembles of sample objects with measurable information content and an approach to feature selection. In this paper, we apply the previous results of Bagirmaz [Appl. Algebra Engrg. Comm. Comput., 30(4) (2019) 285-29] and [Davvaz et al., Near approximations in rings. AAECC (2020). https://doi.org/10.1007/s00200-020-00421-3] to module theory. We introduce the notion of near approximations in a module over a ring, which is an extended notion of a rough approximations in a module presented in [B. Davvaz and M. Mahdavipour, Roughness in modules, Information Sciences, 176 (2006) 3658-3674]. Then we define the lower and upper near submodules and investigate their properties. |
| first_indexed | 2024-04-11T21:58:27Z |
| format | Article |
| id | doaj.art-3f60322c9fa444c1ac11299a7a5eb55f |
| institution | Directory Open Access Journal |
| issn | 2300-3405 |
| language | English |
| last_indexed | 2024-04-11T21:58:27Z |
| publishDate | 2021-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Foundations of Computing and Decision Sciences |
| spelling | doaj.art-3f60322c9fa444c1ac11299a7a5eb55f2022-12-22T04:01:02ZengSciendoFoundations of Computing and Decision Sciences2300-34052021-12-0146431933710.2478/fcds-2021-0020Near Approximations in ModulesDavvaz Bijan0Setyawati Dian Winda1Soleha2Mukhlash Imam3Subiono4Department of Mathematics, Yazd University, Yazd, IranDepartment of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS, Sukolilo-Surabaya 60111, IndonesiaDepartment of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS, Sukolilo-Surabaya 60111, IndonesiaDepartment of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS, Sukolilo-Surabaya 60111, IndonesiaDepartment of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS, Sukolilo-Surabaya 60111, IndonesiaRough set theory is a mathematical approach to imperfect knowledge. The near set approach leads to partitions of ensembles of sample objects with measurable information content and an approach to feature selection. In this paper, we apply the previous results of Bagirmaz [Appl. Algebra Engrg. Comm. Comput., 30(4) (2019) 285-29] and [Davvaz et al., Near approximations in rings. AAECC (2020). https://doi.org/10.1007/s00200-020-00421-3] to module theory. We introduce the notion of near approximations in a module over a ring, which is an extended notion of a rough approximations in a module presented in [B. Davvaz and M. Mahdavipour, Roughness in modules, Information Sciences, 176 (2006) 3658-3674]. Then we define the lower and upper near submodules and investigate their properties.https://doi.org/10.2478/fcds-2021-0020near setlower and upper approximationsrough setmodulesubmodule |
| spellingShingle | Davvaz Bijan Setyawati Dian Winda Soleha Mukhlash Imam Subiono Near Approximations in Modules Foundations of Computing and Decision Sciences near set lower and upper approximations rough set module submodule |
| title | Near Approximations in Modules |
| title_full | Near Approximations in Modules |
| title_fullStr | Near Approximations in Modules |
| title_full_unstemmed | Near Approximations in Modules |
| title_short | Near Approximations in Modules |
| title_sort | near approximations in modules |
| topic | near set lower and upper approximations rough set module submodule |
| url | https://doi.org/10.2478/fcds-2021-0020 |
| work_keys_str_mv | AT davvazbijan nearapproximationsinmodules AT setyawatidianwinda nearapproximationsinmodules AT soleha nearapproximationsinmodules AT mukhlashimam nearapproximationsinmodules AT subiono nearapproximationsinmodules |