TY - JOUR
T1 - Near Approximations in Modules
AU - Davvaz, Bijan
AU - Setyawati, DIan Winda
AU - Soleha,
AU - Mukhlash, Imam
AU - Subiono,
N1 - Publisher Copyright:
© 2021 Bijan Davvaz et al., published by Sciendo.
PY - 2021/12/1
Y1 - 2021/12/1
N2 - 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.
AB - 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.
KW - Near set
KW - lower and upper approximations
KW - module
KW - rough set
KW - submodule
UR - http://www.scopus.com/inward/record.url?scp=85122892974&partnerID=8YFLogxK
U2 - 10.2478/fcds-2021-0020
DO - 10.2478/fcds-2021-0020
M3 - Article
AN - SCOPUS:85122892974
SN - 0867-6356
VL - 46
SP - 319
EP - 337
JO - Foundations of Computing and Decision Sciences
JF - Foundations of Computing and Decision Sciences
IS - 4
ER -