Near Approximations in Modules

Bijan Davvaz; Dian Winda Setyawati; Soleha; Imam Mukhlash; Subiono

doi:10.2478/fcds-2021-0020

.blurhash-client-img { display: none !important; }

Near Approximations in Modules

Foundations of Computing and Decision Sciences

Volume 46 (2021): Issue 4 (December 2021)

By: Bijan Davvaz, Dian Winda Setyawati, Soleha, Imam Mukhlash and Subiono

Open Access

|Dec 2021

Abstract

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.

References

[1] Bağirmaz N., Near approximations in groups, Appl. Algebra Engrg. Comm. Comput., 30, 4, 2019, 285–297.10.1007/s00200-018-0373-z
Search in Google Scholar Back to article
[2] Bağirmaz N., Near ideals in near semigroups, Eur. J. Pure Appl. Math., 11, 2018, 505–516.10.29020/nybg.ejpam.v11i2.2674
Search in Google Scholar Back to article
[3] Davvaz B., Soleha, Setyawati D.W., Mukhlash I., Rinurwati, Near approximations in rings, Appl. Algebra Engrg. Comm. Comput., 2020, https://doi.org/10.1007/s00200-020-00421-3].10.1007/s00200-020-00421-3
Search in Google Scholar Back to article
[4] Davvaz B., Roughness in rings, Information Sciences, 164, 2004, 147–163.10.1016/j.ins.2003.10.001
Search in Google Scholar Back to article
[5] Davvaz B., Mahdavipour M., Roughness in modules, Information Sciences, 176, 2006, 3658–3674.10.1016/j.ins.2006.02.014
Search in Google Scholar Back to article
[6] Efremovič V., Geometry of proximities 1, Mat. Sb., 31, 73, 1952, 189–200 (in Russian).
Search in Google Scholar Back to article
[7] Gagrat M., Naimpally S., Proximity approach to semi-metric and developable spaces, Pacific J. Math., 44, 1, 1973, 93–105.10.2140/pjm.1973.44.93
Search in Google Scholar Back to article
[8] İnan E., Öztürk M.A., Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform., 10, 2, 2015, 287–297.
Search in Google Scholar Back to article
[9] İnan E., Öztürk M.A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat., 41, 4, 2012, 545–558.
Search in Google Scholar Back to article
[10] Pawlak Z., Rough sets, Int. J. Comput. Inform. Sci., 11, 1982, 341–356.10.1007/BF01001956
Search in Google Scholar Back to article
[11] Peters J.F., Near sets, general theory about nearness of objects, Appl. Math. Sci., 1, 53, 2007, 2609–2629.
Search in Google Scholar Back to article
[12] Peters J., Skowron A., Stepaniuk J., Nearness in approximation spaces, Proceedings of the Concurrency, Specification & Programming, Humboldt Universitat, 2006.
Search in Google Scholar Back to article
[13] Peters J.F., Wasilewski P., Foundations of near sets, Information Sciences, 179, 2009, 3091–3109.10.1016/j.ins.2009.04.018
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/fcds-2021-0020 | Journal eISSN: 2300-3405 | Journal ISSN: 0867-6356

Journal RSS Feed

Language: English

Page range: 319 - 337

Submitted on: Jan 11, 2021

Accepted on: Jul 2, 2021

Published on: Dec 17, 2021

Published by: Poznan University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Near set,

lower and upper approximations,

rough set,

module,

submodule

Related subjects:

Computer sciences,

Artificial intelligence,

Software development

© 2021 Bijan Davvaz, Dian Winda Setyawati, Soleha, Imam Mukhlash, Subiono, published by Poznan University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 46 (2021): Issue 4 (December 2021)