Approximations in hyperquasigroups

  • Jianming Zhan
  • Zhisong Tan


In this paper, we introduce the concept of fuzzy rough subhyperquasigroups of rough hyperquasigroups and obtain some interesting results. Moreover, we consider the relation β* defined on a hyperquasigroupG and interpret the lower and upper approximations as subsets of the quasigroupG/β*, and give some results in this connection.

AMS Mathematics Subject Classification

20N20 20N05 94D05 

Key words and phrases

(Regular) hyperquasigroups fundamental relation approximations 


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  1. 1.
    V. D. Belousov,Foudations of the theory of quasigroups and loops, (Russian), Nauka, Moscow, 1967.Google Scholar
  2. 2.
    R. Biswas and S. Nanda,Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math.42 (1994), 251–254.MATHMathSciNetGoogle Scholar
  3. 3.
    Z. Bonikowaski,Algebraic structures of rough sets, in W.P. Ziaroko Editor, Rough sets, Fuzzy sets and Knowledge Discovery, Spring-Verlag, Berlin, (1995), 242–247.Google Scholar
  4. 4.
    S. D. Comer,On connection between information systems, rough sets and algebraic logic, Algebraic Methods in Logic and Computer Sciences28 (1993), 117–123.MathSciNetGoogle Scholar
  5. 5.
    P. Corsini,Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993.Google Scholar
  6. 6.
    B. Davvaz,Remarks on weak hypermodules, Bull. Korean Math. Soc.36 (1999), 699–608.MathSciNetGoogle Scholar
  7. 7.
    B. Davvaz,Rough sets in a fundamental rings, Bull. Iranian Math. Soc.24 (1998), 49–61.MATHMathSciNetGoogle Scholar
  8. 8.
    B. Davvaz,Fuzzy H v-submodules, Fuzzy Sets and Systems117 (2001), 477–484.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    B. Davvaz,Lower and upper approximations in H v-groups, Ratio Math.13 (1999), 71–86.MATHMathSciNetGoogle Scholar
  10. 10.
    B. Davvaz,T H and S H-interval valued fuzzy subhupergroups, Indian J. Pure and Appl. Math.35 (2004), 61–69.MATHMathSciNetGoogle Scholar
  11. 11.
    B. Davvaz,Fuzzy H v-groups, Fuzzy Sets and Systems101 (1999), 191–195.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    B. Davvaz,Product of fuzzy H v-subgroups, J. Fuzzy Math.8 (2000), 43–51.MATHMathSciNetGoogle Scholar
  13. 13.
    B. Davvaz,Interval-valued fuzzy subhypergroups, J. Appl. Math. & Computing(old:KJCAM)6 (1999), 197–202.MATHMathSciNetGoogle Scholar
  14. 14.
    B. Davvaz,On H v-subgroups and anti fuzzy H v-subgroups, J. Appl. Math. & Computing(old:KJCAM)5 (1998), 181–190.MATHMathSciNetGoogle Scholar
  15. 15.
    W. A. Dudek,Fuzzy subquasigroups, Quasigroups and Related Systems.5 (1998), 81–98.MATHMathSciNetGoogle Scholar
  16. 16.
    W. A. Dudek and Y. B. Jun,Fuzzy subquasigroups over a t-norm, Quasigroup and Related Systems,6 (1999), 87–98.MATHMathSciNetGoogle Scholar
  17. 17.
    W. A. Dudek, B. Davvaz and Y. B. Jun,On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups, Inform Sci. 170(2005), no.2–4, 251–262.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    D. Frei,Una nota sul curore di un ipergruppo e sulla chiusura transitive β* di β, Rivista Mat. Pura. Appl.8 (1991), 153–156.Google Scholar
  19. 19.
    D. Frei,A new characterization of the derived hypergroup via strongly regular equivalence, Comm in Algebra30 (2002), 3977–3989.CrossRefGoogle Scholar
  20. 20.
    T. Iwinski,Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math.35 (1987), 673–683.MATHMathSciNetGoogle Scholar
  21. 21.
    K. H. Kim, W. A. Dudek and Y. B. Jun,Intuitionistic fuzzy subquasigroups of quasigroups, Quasigroups and Related Systems7 (2000), 15–28.MATHMathSciNetGoogle Scholar
  22. 22.
    M. Koskas,Groupoids, demi-hypergroups of hypergroups, J. Math. Pure Appl.49 (1970), 155–192.MATHMathSciNetGoogle Scholar
  23. 23.
    N. Kuroki and P. P. Wang,The lower and upper approximation in a group, Inform Sci.90 (1996), 203–220.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    F. Marty,Sur une generalization de la notation de grouse 8th Congress, Math Scandianaves, Stockholm, (1934), 45–49.Google Scholar
  25. 25.
    J. Pakl and S. C. Chung,An algorithms to compute some H v-groups, J. Appl. Math. & Computing(old:KJCAM)7 (2000), 433–453.Google Scholar
  26. 26.
    Z. Pawlak,Rough sets, Int. J. Inf. Sci.11 (1982), 341–356.CrossRefMathSciNetGoogle Scholar
  27. 27.
    A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl.35 (1971), 512–517.MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    S. Spartalis and T. Vougiouklis,The relation on H v-rings, Rivista Math. Pura. Math.14 (1994), 7–20.MATHMathSciNetGoogle Scholar
  29. 29.
    T. Vougiouklis,The fundamental relation in hyperrings. The general hyperfield. Algebraic hyperstructures and applications (Xanthi, 1990), 203–211, World Sci. Publishing, Teaneck, NJ, 1991.Google Scholar
  30. 30.
    T. Vougiouklis,H v-vector spaces, Proc of the 5th Congress on Algebraic Hyperstructure and Appl. (AHA, 1993), Jasi Rumani, Hadronic Press, Inc, Florida (1994), 181–190.Google Scholar
  31. 31.
    T. Vougiouklis,The fundamental relations in Hyperstructures, Bull. Greek Math. Soc.42 (1999), 113–118.MATHMathSciNetGoogle Scholar
  32. 32.
    T. Vougiouklis,Hyperstructures and their representations, Hadronic Press Inc., Palm Harber, USA (1994).MATHGoogle Scholar
  33. 33.
    L. A. Zadeh,Fuzzy sets, Inform and Control8 (1965), 338–353.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  1. 1.Department of MathematicsHubei Institute for NationalitiesEnshi, Hubei ProvinceP. R. China

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