Top

Hint

Swipe to navigate through the articles of this issue

Published in:

09-03-2020 | Original Paper

Near approximations in rings

Authors: Bijan Davvaz, Soleha, Dian Winda Setyawati, Imam Mukhlash, Rinurwati

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2021

Abstract

This paper is a continuation of ideas presented by Bagirmaz (Appl Algebra Eng Commun Comput 30(4):285–297, 2019). Indeed, we introduce the notion of near approximations in a ring, which is an extended notion of a rough approximations in a ring. Then we define lower and upper near subrings based on ideals in a ring and give some properties of such subrings. Furthermore, we obtain a comparison between these types of approximations and the approximations introduced by Davvaz (Inf Sci 176:2417–2437, 2006).

previous article On the security of the modified Dual-ouroboros PKE using Gabidulin codes

next article On the error-detecting capability of the linear quasigroup code

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 69.000 Bücher
über 500 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Testen Sie jetzt 15 Tage kostenlos.

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Testen Sie jetzt 15 Tage kostenlos.

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Testen Sie jetzt 15 Tage kostenlos.

inform now

Bağirmaz, N.: Near approximations in groups. Appl. Algebra Eng. Commun. Comput. 30(4), 285–297 (2019) MathSciNetCrossRef

Bağirmaz, N.: Near ideals in near semigroups. Eur. J. Pure Appl. Math. 11, 505–516 (2018) MathSciNetCrossRef

Biswas, R., Nanda, S.: Rough groups and rough subgroups. Bull. Polish Acad. Sci. Math. 42, 251–254 (1994) MathSciNetMATH

Davvaz, B.: Roughness in rings. Inf. Sci. 164, 147–163 (2004) MathSciNetCrossRef

Davvaz, B.: Roughness based on fuzzy ideals. Inf. Sci. 176, 2417–2437 (2006) MathSciNetCrossRef

Davvaz, B.: Approximations in n-ary algebraic systems. Soft Comput. 12, 409–418 (2008) CrossRef

Davvaz, B.: Rough Algebraic Structures Corresponding to Ring Theory, Algebraic Methods in General Rough Sets. Trends in Mathematics, pp. 657–695. Birkhuser, Cham (2018) CrossRef

Davvaz, B.: A short note on approximations in a ring by using a neighborhood system as a generalization of Pawlak’s approximations. UPB Sci. Bull. Ser. A Appl. Math. Phys. 76(4), 77–84 (2014) MathSciNetMATH

Davvaz, B., Mahdavipour, M.: Roughness in modules. Inf. Sci. 176, 3658–3674 (2006) MathSciNetCrossRef

10.

Davvaz, B., Mahdavipour, M.: Rough approximations in a general approximation space and their fundamental properties. Int. J. Gen. Syst. 37(3), 373–386 (2008) MathSciNetCrossRef

11.

Davvaz, B., Malekzadeh, A.: Roughness in modules by using the notion of reference points. Iran. J. Fuzzy Syst. 10(6), 109–124 (2013) MathSciNetMATH

12.

Efremovic̆, V.: Geometry of proximities 1. Mat. Sb. 31(73), 189–200 (1952). (in Russian)

13.

Gagrat, M., Naimpally, S.: Proximity approach to semi-metric and developable spaces. Pac. J. Math. 44(1), 93–105 (1973) MathSciNetCrossRef

14.

İnan, E., Öztürk, M.A.: Near semigroups on nearness approximation spaces. Ann. Fuzzy Math. Inf. 10(2), 287–297 (2015) MathSciNetMATH

15.

İnan, E., Öztürk, M.A.: Near groups on nearness approximation spaces. Hacet. J. Math. Stat. 41(4), 545–558 (2012) MathSciNetMATH

16.

Kazanci, O., Davvaz, B.: On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings. Inf. Sci. 178(5), 1343–1354 (2008) MathSciNetCrossRef

17.

Kazanci, O., Yamak, S., Davvaz, B.: The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf. Sci. 178(10), 2349–2359 (2008) MathSciNetCrossRef

18.

Kuroki, N.: Rough ideals in semigroups. Inf. Sci. 100, 139–163 (1997) MathSciNetCrossRef

19.

Kuroki, N., Mordeson, J.N.: Structure of rough sets and rough groups. J. Fuzzy Math. 5(1), 183–191 (1997) MathSciNetMATH

20.

Kuroki, N., Wang, P.P.: The lower and upper approximations in a fuzzy group. Inf. Sci. 90, 203–220 (1996) MathSciNetCrossRef

21.

Pawlak, Z.: Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991) CrossRef

22.

Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982) CrossRef

23.

Peters, J.F.: Near sets, general theory about nearness of objects. Appl. Math. Sci. 1(53), 2609–2629 (2007) MathSciNetMATH

24.

Peters, J., Skowron, A., Stepaniuk, J.: Nearness in approximation spaces. In: Proceedings of the Concurrency, Specification and Programming. Humboldt Universitt (2006)

25.

Peters, J.F., Wasilewski, P.: Foundations of near sets. Inf. Sci. 179, 3091–3109 (2009) MathSciNetCrossRef

26.

Wang, C., Chen, D.: A short note on some properties of rough groups. Comput. Math. Appl. 59, 431–436 (2010) MathSciNetCrossRef

27.

Yamak, S., Kazancı, O., Davvaz, B.: Generalized lower and upper approximations in a ring. Inf. Sci. 180, 1759–1768 (2010) MathSciNetCrossRef

28.

Zhan, J., Davvaz, B.: Notes on “roughness in rings”. Inf. Sci. 346–347, 488–490 (2016) MathSciNetCrossRef

Title: Near approximations in rings
Authors: Bijan Davvaz
Soleha
Dian Winda Setyawati
Imam Mukhlash
Rinurwati
Publication date: 09-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 6/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00421-3

Springer Professional

Hint

Swipe to navigate through the articles of this issue

Abstract

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 6/2021

On the error-detecting capability of the linear quasigroup code

EA-inequivalence of bent functions

Numerical semigroups closed under addition of their divisors

On the security of the modified Dual-ouroboros PKE using Gabidulin codes

Premium Partner