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Intuitionistic (S, T)-fuzzy hyperquasigroups

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Abstract

The concept of intuitionistic fuzzy subhyperquasigroups in a hyperquasigroup with respect to an s-norm and a t-norm on intuitionistic fuzzy sets is introduced and their properties of such hyperquasigroups are studied. Intuitionistic (S, T)-fuzzy relations on a hyperquasigroup G are discussed. In particular, we investigate connections hyperquasigroups with binary quasigroups.

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References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov KT (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61: 137–142

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets. Theory and applications. Studies in fuzziness and soft computing, vol 35. Physica-Verlag, Heidelberg

  • Corsini P (1993) Prolegomena of hypergroup theory. Aviani Editor

  • Corsini P, Leoreanu V (2003) Applications of hyperstructures theory. In: Adv in Math. Kluwer, Dordrecht

  • Davvaz B (1999) Fuzzy H v -groups. Fuzzy Sets Syst 101: 191–195

    Article  MATH  MathSciNet  Google Scholar 

  • Davvaz B (2000) Product of fuzzy H v -subgroups. J Fuzzy Math 8: 43–51

    MATH  MathSciNet  Google Scholar 

  • Davvaz B, Dudek WA, Jun YB (2006) Intuitionistic fuzzy H v -submodules. Inform Sci 176: 285–300

    Article  MATH  MathSciNet  Google Scholar 

  • De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117: 209–213

    Article  MATH  MathSciNet  Google Scholar 

  • Dengfeng L, Chunfian C (2002) New similarity measures of intuitionistic fuzzy sets and applications to pattern recognitions. Pattern Reconit Lett 23: 221–225

    Article  MATH  Google Scholar 

  • Dudek WA, Davvaz B, Jun YB (2005) On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups. Inform Sci 170: 251–262

    Article  MATH  MathSciNet  Google Scholar 

  • Frei D (1991) Una nota sul curore di un ipergruppo e sulla chiusura transitive β* di β. Rivista Mat Pura Appl 8: 153–156

    Google Scholar 

  • Frei D (2002) A new characterization of the derived hypergroup via strongly regular equivalence. Commun Algebra 30: 3977–3989

    Article  Google Scholar 

  • Gau WL, Buehre DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23: 610–614

    Article  MATH  Google Scholar 

  • Kim KH, Dudek WA, Jun YB (2000) Intuitionistic fuzzy subquasigroups of quasigroups. Quasigroups Relat Syst 7: 15–28

    MATH  MathSciNet  Google Scholar 

  • Koskas M (1970) Groupoids, demi-hypergroups of hypergroups. J Math Pure Appl 49: 155–192

    MATH  MathSciNet  Google Scholar 

  • Marty F (1934) Sur une generalization de la notation de grouse 8th Congress. Math Scandianaves, Stockholm, pp 45–49

  • Nurillo P, Bustince H (1996) Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 79: 403–405

    Article  Google Scholar 

  • Pflugfelder H (1990) Quasigroups and loops. Helderman-Verlag

  • Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35: 512–517

    Article  MATH  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118: 467–477

    Article  MATH  MathSciNet  Google Scholar 

  • Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press Inc., Palm Harber

    MATH  Google Scholar 

  • Yu Y, Mordeson JN, Cheng SC (1994) Elements of L-algebras. Lecture notes in fuzzy math. and computer sciences. Creighton Univ, Omaha

  • Zadeh LA (1965) Fuzzy sets. Inform Control 8: 338–353

    Article  MATH  MathSciNet  Google Scholar 

  • Zhan J (2006) On properties of fuzzy hyperideals in hypernear-rings with t-norms. J Appl Math Comput 20: 255–277

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Wiesław A. Dudek

  2. Department of Mathematics, Hubei Institute for Nationalities, 445000, Enshi, Hubei Province, People’s Republic of China

    Jianming Zhan

  3. Department of Mathematics, Yazd University, Yazd, Iran

    Bijan Davvaz

Authors
  1. Wiesław A. Dudek
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  2. Jianming Zhan
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  3. Bijan Davvaz
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Correspondence to Wiesław A. Dudek.

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Dudek, W.A., Zhan, J. & Davvaz, B. Intuitionistic (S, T)-fuzzy hyperquasigroups. Soft Comput 12, 1229–1238 (2008). https://doi.org/10.1007/s00500-008-0285-0

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  • DOI: https://doi.org/10.1007/s00500-008-0285-0

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