Near Approximations in Modules

• Autorzy: Davvaz Bijan , Setyawati Dian Winda , Soleha , Mukhlash Imam , Subiono

Identyfikatory

DOI

10.2478/fcds-2021-0020

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

near set; lower and upper approximations; rough set; module; prime submodule

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2021
• Tom: Vol. 46, No. 4
• Strony: 319--337
• Opis fizyczny: Bibliogr. 13 poz., tab.

Twórcy

autor

Davvaz Bijan

• Department of Mathematics, Yazd University, Yazd, Iran

autor

Setyawati Dian Winda

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

autor

Soleha

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

autor

Mukhlash Imam

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

autor

Subiono

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

Bibliografia

• [1] Bağirmaz N., Near approximations in groups, Appl. Algebra Engrg. Comm. Comput., 30, 4, 2019, 285-297.
• [2] Bağirmaz N., Near ideals in near semigroups, Eur. J. Pure Appl. Math., 11, 2018, 505-516.
• [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].
• [4] Davvaz B., Roughness in rings, Information Sciences, 164, 2004, 147-163.
• [5] Davvaz B., Mahdavipour M., Roughness in modules, Information Sciences, 176, 2006, 3658-3674.
• [6] Efremovič V., Geometry of proximities 1, Mat. Sb., 31, 73, 1952, 189-200 (in Russian).
• [7] Gagrat M., Naimpally S., Proximity approach to semi-metric and developable spaces, Pacific J. Math., 44, 1, 1973, 93-105.
• [8] İnan E., Öztürk M.A., Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform., 10, 2, 2015, 287-297.
• [9] İnan E., Öztürk M.A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat., 41, 4, 2012, 545-558.
• [10] Pawlak Z., Rough sets, Int. J. Comput. Inform. Sci., 11, 1982, 341-356.
• [11] Peters J.F., Near sets, general theory about nearness of objects, Appl. Math. Sci., 1, 53, 2007, 2609-2629.
• [12] Peters J., Skowron A., Stepaniuk J., Nearness in approximation spaces, Proceedings of the Concurrency, Specification & Programming, Humboldt Universitat, 2006.
• [13] Peters J.F., Wasilewski P., Foundations of near sets, Information Sciences, 179, 2009, 3091-3109.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).