Near Approximations in Modules-Reference-Cited by-同舟云学术

Near Approximations in Modules

Published:2021-12-01 Issue:4 Volume:46 Page:319-337
ISSN:2300-3405
Container-title:Foundations of Computing and Decision Sciences
language:en
Short-container-title:

Author:

Davvaz Bijan¹,Setyawati Dian Winda²,Soleha ²,Mukhlash Imam²,Subiono ²

Affiliation:

1. Department of Mathematics , Yazd University , Yazd , Iran

2. Department of Mathematics , Institut Teknologi Sepuluh Nopember , Kampus ITS, Sukolilo-Surabaya 60111 , Indonesia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/fcds-2021-0020

Reference13 articles.

1. [1] Bağirmaz N., Near approximations in groups, Appl. Algebra Engrg. Comm. Comput., 30, 4, 2019, 285–297.10.1007/s00200-018-0373-z

2. [2] Bağirmaz N., Near ideals in near semigroups, Eur. J. Pure Appl. Math., 11, 2018, 505–516.10.29020/nybg.ejpam.v11i2.2674

3. [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

4. [4] Davvaz B., Roughness in rings, Information Sciences, 164, 2004, 147–163.10.1016/j.ins.2003.10.001

5. [5] Davvaz B., Mahdavipour M., Roughness in modules, Information Sciences, 176, 2006, 3658–3674.10.1016/j.ins.2006.02.014

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