<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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). <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1007/s00200-020-00421-3">https://doi.org/10.1007/s00200-020-00421-3</ext-link>] 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.</p>
</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.

Near Approximations in Modules

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"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...

Near Approximations in Modules

Published Online: Dec 17, 2021

Page range: 319 - 337

Received: Jan 11, 2021

Accepted: Jul 02, 2021

DOI: https://doi.org/10.2478/fcds-2021-0020

Keywords
Near set, lower and upper approximations, rough set, module, submodule

© 2021 Bijan Davvaz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Near Approximations in Modules

Published Online: Dec 17, 2021

Page range: 319 - 337

Received: Jan 11, 2021

Accepted: Jul 02, 2021

DOI: https://doi.org/10.2478/fcds-2021-0020

KeywordsNear set, lower and upper approximations, rough set, module, submodule

© 2021 Bijan Davvaz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Near set, lower and upper approximations, rough set, module, submodule