Skip to main content
Erschienen in: Applicable Algebra in Engineering, Communication and Computing 4/2019

08.11.2018 | Original Paper

Near approximations in groups

verfasst von: Nurettin Bağırmaz

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 4/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we firstly introduce the notion of a near approximations in a group, which is an extended notion of a rough approximations in a group. Then we define lower and upper near subgroups based on normal subgroups in a group and give some properties of such subgroups. Furthermore, we obtain a comparison between these types of approximations and the approximation introduced by Kuroki and Wang (Inf Sci 90:203–220, 1996).

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 102.000 Bücher
  • über 537 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

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

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




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

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




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Abd El-Monsef, M.E., Abu-Donia, H.M., Marei, E.A.: Special Approach to Near Set Theory. Mathematical Problems in Engineering, vol. 2011 (2011) Abd El-Monsef, M.E., Abu-Donia, H.M., Marei, E.A.: Special Approach to Near Set Theory. Mathematical Problems in Engineering, vol. 2011 (2011)
2.
Zurück zum Zitat Bağırmaz, N., Özcan, A.F.: Rough semigroups on approximation spaces. Int. J. Algebra 9, 339–350 (2015)CrossRef Bağırmaz, N., Özcan, A.F.: Rough semigroups on approximation spaces. Int. J. Algebra 9, 339–350 (2015)CrossRef
4.
Zurück zum Zitat Biswas, R., Nanda, N.: Rough groups and rough subgroups. Bull. Polish Acad. Sci. Math. 42, 251–254 (1994)MathSciNetMATH Biswas, R., Nanda, N.: Rough groups and rough subgroups. Bull. Polish Acad. Sci. Math. 42, 251–254 (1994)MathSciNetMATH
5.
Zurück zum Zitat Bonikowaski, Z.: Algebraic structures of rough sets. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 242–247. Springer, Berlin (1995) Bonikowaski, Z.: Algebraic structures of rough sets. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 242–247. Springer, Berlin (1995)
6.
Zurück zum Zitat Cheng, W., Mo, Z., Wang, J.: Notes on “the lower and upper approximations in a fuzzy group” and “rough ideals in semigroups”. Inf. Sci. 177, 5134–5140 (2007)CrossRefMATH Cheng, W., Mo, Z., Wang, J.: Notes on “the lower and upper approximations in a fuzzy group” and “rough ideals in semigroups”. Inf. Sci. 177, 5134–5140 (2007)CrossRefMATH
8.
Zurück zum Zitat Iwinski, T.: Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math. 35, 673–683 (1987)MathSciNetMATH Iwinski, T.: Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math. 35, 673–683 (1987)MathSciNetMATH
9.
Zurück zum Zitat İnan, E., Öztürk, M.: Near groups on nearness approximation spaces. Hacettepe J. Math. Stat. 4, 545–558 (2012)MathSciNetMATH İnan, E., Öztürk, M.: Near groups on nearness approximation spaces. Hacettepe J. Math. Stat. 4, 545–558 (2012)MathSciNetMATH
10.
Zurück zum Zitat İnan, E., Öztürk, M.: Near semigroups on nearness approximation spaces. Ann. Fuzzy Math. Inform. 10(2), 287–297 (2015)MathSciNetMATH İnan, E., Öztürk, M.: Near semigroups on nearness approximation spaces. Ann. Fuzzy Math. Inform. 10(2), 287–297 (2015)MathSciNetMATH
13.
Zurück zum Zitat Li, F., Zhang, Z.: The Homomorphisms and operations of rough groups. Sci. World J. 2014, Article ID 507972 (2014) Li, F., Zhang, Z.: The Homomorphisms and operations of rough groups. Sci. World J. 2014, Article ID 507972 (2014)
14.
Zurück zum Zitat Miao, D., Han, S., Li, D., Sun, L.: Rough group, rough subgroup and their properties. In: Ślkezak, D., et al. (eds.) RSFDGrC 2005, LNAI 3641, pp. 104–113. Springer Berlin Heidelberg, Berlin (2005) Miao, D., Han, S., Li, D., Sun, L.: Rough group, rough subgroup and their properties. In: Ślkezak, D., et al. (eds.) RSFDGrC 2005, LNAI 3641, pp. 104–113. Springer Berlin Heidelberg, Berlin (2005)
15.
Zurück zum Zitat Özcan, A.F., Bağırmaz, N.: Comparison of near sets by means of a chain of features. Hacettepe J. Math. Stat. 45(1), 69–76 (2016)MathSciNet Özcan, A.F., Bağırmaz, N.: Comparison of near sets by means of a chain of features. Hacettepe J. Math. Stat. 45(1), 69–76 (2016)MathSciNet
20.
Zurück zum Zitat Pawlak, Z.: Classification of Objects by means of Attributes, Institute for Computer Science, Polish Academy of Sciences, Report 429 (1981) Pawlak, Z.: Classification of Objects by means of Attributes, Institute for Computer Science, Polish Academy of Sciences, Report 429 (1981)
21.
Zurück zum Zitat Peters, J.F.: Near sets, general theory about nearness of objects. Appl. Math. Sci. 1(53), 2609–2629 (2007)MathSciNetMATH Peters, J.F.: Near sets, general theory about nearness of objects. Appl. Math. Sci. 1(53), 2609–2629 (2007)MathSciNetMATH
23.
Zurück zum Zitat Peters, J.F.: Classification of perceptual objects by means of features. Int. J. Inf. Technol. Intell. Comput. 3(2), 1–35 (2008) Peters, J.F.: Classification of perceptual objects by means of features. Int. J. Inf. Technol. Intell. Comput. 3(2), 1–35 (2008)
24.
Zurück zum Zitat Peters, J.F.: Fuzzy sets, near sets, and rough sets for your computational intelligence toolbox. Found. Comput. Intell. 2, 3–25 (2009) Peters, J.F.: Fuzzy sets, near sets, and rough sets for your computational intelligence toolbox. Found. Comput. Intell. 2, 3–25 (2009)
25.
Zurück zum Zitat Peters, J.F., Ramanna, R.: Feature selection: a near set approach. In: ECML & PKDD Workshop on Mining Complex Data, Warsaw, pp. 1–12 (2007) Peters, J.F., Ramanna, R.: Feature selection: a near set approach. In: ECML & PKDD Workshop on Mining Complex Data, Warsaw, pp. 1–12 (2007)
26.
Zurück zum Zitat Peters, J.F., Naimpally, S.: Applications of near sets. Not. Am. Math. Soc. 59(4), 536–542 (2012)MathSciNetMATH Peters, J.F., Naimpally, S.: Applications of near sets. Not. Am. Math. Soc. 59(4), 536–542 (2012)MathSciNetMATH
27.
Zurück zum Zitat Peters, J.F., Pal, S.K.: Cantor, fuzzy, near, and rough sets in image analysis. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Image Analysis: Foundations and Methodologies, pp. 1.1–1.16. CRC Pres, Taylor and Francis Group, Boca Raton (2010) Peters, J.F., Pal, S.K.: Cantor, fuzzy, near, and rough sets in image analysis. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Image Analysis: Foundations and Methodologies, pp. 1.1–1.16. CRC Pres, Taylor and Francis Group, Boca Raton (2010)
29.
Zurück zum Zitat Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approx. Reason. 15(4), 333–365 (1997)MathSciNetCrossRefMATH Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approx. Reason. 15(4), 333–365 (1997)MathSciNetCrossRefMATH
30.
Zurück zum Zitat Pomykala, J., Pomykala, J.A.: The stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36, 495–508 (1998)MathSciNetMATH Pomykala, J., Pomykala, J.A.: The stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36, 495–508 (1998)MathSciNetMATH
31.
Zurück zum Zitat Taşbozan, H., İçen, İ., Bağırmaz, N., Özcan, A.F.: Soft sets and soft topology on nearness approximation spaces. Filomat 31(13), 4117–4125 (2017)MathSciNetCrossRef Taşbozan, H., İçen, İ., Bağırmaz, N., Özcan, A.F.: Soft sets and soft topology on nearness approximation spaces. Filomat 31(13), 4117–4125 (2017)MathSciNetCrossRef
32.
Zurück zum Zitat Wang, C., Chen, D., Hu, Q.: On rough approximations of groups. Int. J. Mach. Learn. Cyber. 4(5), 445–449 (2013)CrossRef Wang, C., Chen, D., Hu, Q.: On rough approximations of groups. Int. J. Mach. Learn. Cyber. 4(5), 445–449 (2013)CrossRef
34.
Zurück zum Zitat Wang, Z., Shu, L.: The lower and upper approximations in a group. Int. J. Math. Comput. Sci. 6, 158–162 (2012) Wang, Z., Shu, L.: The lower and upper approximations in a group. Int. J. Math. Comput. Sci. 6, 158–162 (2012)
35.
Zurück zum Zitat Wang, Q., Zhan, J., Borzooei, R.A.: A study on soft rough semigroups and corresponding decision making applications. Open Math. 15, 1400–1413 (2017)MathSciNetMATH Wang, Q., Zhan, J., Borzooei, R.A.: A study on soft rough semigroups and corresponding decision making applications. Open Math. 15, 1400–1413 (2017)MathSciNetMATH
36.
Zurück zum Zitat Wolski, W.: Perception and classification. A note on near sets and rough sets. Found. Inform. 101, 143–155 (2010)MathSciNetMATH Wolski, W.: Perception and classification. A note on near sets and rough sets. Found. Inform. 101, 143–155 (2010)MathSciNetMATH
Metadaten
Titel
Near approximations in groups
verfasst von
Nurettin Bağırmaz
Publikationsdatum
08.11.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing / Ausgabe 4/2019
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-018-0373-z

Weitere Artikel der Ausgabe 4/2019

Applicable Algebra in Engineering, Communication and Computing 4/2019 Zur Ausgabe