Advertisement

The largest family of generalized fuzzy subhypergroups

  • Morteza NorouziEmail author
  • Hesam Safa
  • Azam Adineh Zadeh
Article
  • 25 Downloads

Abstract

In this paper, we introduce the largest family of generalized fuzzy subhypergroups based on concepts of belongingness and quasi-coincidence of a fuzzy point to a fuzzy subset. In this regards, \((\in ,\in \vee q^{\delta })\)-fuzzy subhypergroups and \((\in ,\in \vee q^{\delta }_{k})\)-fuzzy subhypergroups of hypergroups are defined as a generalization of fuzzy subhypergroups, \((\in , \in \vee q)\)-fuzzy subhypergroups and \((\in , \in \vee q_{k})\)-fuzzy subhypergroups of hypergroups. Some properties of them are investigated and their differences with other types are studied.

Keywords

Hypergroup Fuzzy subhypergroup (\(\in , \in \vee q^{\delta }_{k}\))-fuzzy subhypergroup 

Mathematics Subject Classification

16Y99 20N20 

Notes

Acknowledgements

This research was in part supported by a grant from University of Bojnord (no. 97/367/19047).

Compliance with ethical standards

Conflict of interest

We declare that there are no conflicts of interest regarding the publication of this paper.

References

  1. Bhakat SK, Das P (1996) \((\in, \in \vee q)\)-fuzzy subgroup. Fuzzy Sets Syst 80:359–368CrossRefGoogle Scholar
  2. Corsini P (1993) Prolegomena of Hypergroup Theory. Aviani Editore, TricesimozbMATHGoogle Scholar
  3. Davvaz B (1999a) Fuzzy \(H_v\)-groups. Fuzzy Sets Syst 101:191–195Google Scholar
  4. Davvaz B (1999b) Interval-values fuzzy subhypergroups. Korean J Comput Appl Math 6:197–202MathSciNetCrossRefGoogle Scholar
  5. Davvaz B (2000) On fuzzy relations and fuzzy subhypergroups. Pure Math Appl 11(1):51–58MathSciNetzbMATHGoogle Scholar
  6. Davvaz B, Corsini P (2006) Generalized fuzzy sub-hyperquasigroups of hyperquasigroups. Soft Comput 10(3):1109–1114CrossRefGoogle Scholar
  7. Davvaz B, Cristea I (2015) Fuzzy algebraic hyperstructures: an introduction, stud. Fuzziness soft computing. Springer, BerlinCrossRefGoogle Scholar
  8. Jun YB, Ozturk MA, Muhiuddin G (2016) A generalization of \((\in, \in \vee q)\)-fuzzy subgroups. Int J Algebra Stat 5(1):7–18CrossRefGoogle Scholar
  9. Kazanci O, Davvaz B, Yamak S (2009) Fuzzy \(n\)-ary polygroups related to fuzzy points. Comput Math Appl 58:1466–1474MathSciNetCrossRefGoogle Scholar
  10. Kazanci O, Davvaz B, Yamak S (2010) Fuzzy \(n\)-ary hypergroups related to fuzzy points. Neural Comput Appl 19:649–655CrossRefGoogle Scholar
  11. Khan FM, Yufeng N, Khan HU, Khan BM (2018) Ordered semigroups based on \((\in, \in \vee q^{\delta }_{k})\)-fuzzy ideals. Adv Fuzzy Syst 2018:5304514zbMATHGoogle Scholar
  12. Mahmood T, Ali MI, Hussain A (2018) Generalized roughness in fuzzy filters and fuzzy ideals with thresholds in ordered semigroups. Comput Appl Math 37(4):5013–5033MathSciNetCrossRefGoogle Scholar
  13. Marty F (1934) Sur une generalization de la notion de groupe, \(8^{iem}\) congres des Mathematiciens Scandinaves Stockholm, 45–49Google Scholar
  14. Rosenfeld A (1971) Fuzzy groups. J Math Anal 35:512–517MathSciNetCrossRefGoogle Scholar
  15. Shabir M, Mahmood T (2011) Characterizations of hemirings by \((\in, \in \vee q_{k})\)-fuzzy ideals. Comput Math Appl 61:1059–1078MathSciNetCrossRefGoogle Scholar
  16. Shabir M, Mahmood T (2012) Spectrum of \((\in, \in \vee q)\)-fuzzy prime h-ideals of a hemiring. World Appl Sci J 17(12):1815–1820Google Scholar
  17. Shabir M, Mahmood T (2013) Semihypergroups characterized by \((\in, \in \vee q_{k})\)-fuzzy hyperideals. Inf Sci Lett 2(2):101–121Google Scholar
  18. Shabir M, Mahmood T (2015) Semihypergroups characterized by \((\in _{\gamma }, \in _{\gamma }\vee q_{\delta })\)-fuzzy hyperideals. J Intell Fuzzy Syst 28:2667–2678CrossRefGoogle Scholar
  19. Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press Inc., Palm HarborzbMATHGoogle Scholar
  20. Yin Y, Zhan J, Huang X (2012a) Generalized fuzzy \(n\)-ary subhypergroups of a commutative \(n\)-ary hypergroup. Math Slovaca 62(2):201–230MathSciNetCrossRefGoogle Scholar
  21. Yin Y, Zhan J, Davvaz B (2012b) New types of fuzzy \(n\)-ary subhypergroups of an \(n\)-ary hypergroup. Iran J Fuzzy Syst 9(5):105–124MathSciNetzbMATHGoogle Scholar
  22. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesUniversity of BojnordBojnordIran

Personalised recommendations