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Approximations in hyperquasigroups

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Abstract

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.

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References

  1. V. D. Belousov,Foudations of the theory of quasigroups and loops, (Russian), Nauka, Moscow, 1967.

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

    MATH  MathSciNet  Google Scholar 

  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. S. D. Comer,On connection between information systems, rough sets and algebraic logic, Algebraic Methods in Logic and Computer Sciences28 (1993), 117–123.

    MathSciNet  Google Scholar 

  5. P. Corsini,Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993.

  6. B. Davvaz,Remarks on weak hypermodules, Bull. Korean Math. Soc.36 (1999), 699–608.

    MathSciNet  Google Scholar 

  7. B. Davvaz,Rough sets in a fundamental rings, Bull. Iranian Math. Soc.24 (1998), 49–61.

    MATH  MathSciNet  Google Scholar 

  8. B. Davvaz,Fuzzy H v -submodules, Fuzzy Sets and Systems117 (2001), 477–484.

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Davvaz,Lower and upper approximations in H v -groups, Ratio Math.13 (1999), 71–86.

    MATH  MathSciNet  Google Scholar 

  10. B. Davvaz,T H and S H -interval valued fuzzy subhupergroups, Indian J. Pure and Appl. Math.35 (2004), 61–69.

    MATH  MathSciNet  Google Scholar 

  11. B. Davvaz,Fuzzy H v -groups, Fuzzy Sets and Systems101 (1999), 191–195.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  13. B. Davvaz,Interval-valued fuzzy subhypergroups, J. Appl. Math. & Computing(old:KJCAM)6 (1999), 197–202.

    MATH  MathSciNet  Google Scholar 

  14. B. Davvaz,On H v -subgroups and anti fuzzy H v -subgroups, J. Appl. Math. & Computing(old:KJCAM)5 (1998), 181–190.

    MATH  MathSciNet  Google Scholar 

  15. W. A. Dudek,Fuzzy subquasigroups, Quasigroups and Related Systems.5 (1998), 81–98.

    MATH  MathSciNet  Google Scholar 

  16. W. A. Dudek and Y. B. Jun,Fuzzy subquasigroups over a t-norm, Quasigroup and Related Systems,6 (1999), 87–98.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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. D. Frei,A new characterization of the derived hypergroup via strongly regular equivalence, Comm in Algebra30 (2002), 3977–3989.

    Article  Google Scholar 

  20. T. Iwinski,Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math.35 (1987), 673–683.

    MATH  MathSciNet  Google Scholar 

  21. K. H. Kim, W. A. Dudek and Y. B. Jun,Intuitionistic fuzzy subquasigroups of quasigroups, Quasigroups and Related Systems7 (2000), 15–28.

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  23. N. Kuroki and P. P. Wang,The lower and upper approximation in a group, Inform Sci.90 (1996), 203–220.

    Article  MATH  MathSciNet  Google Scholar 

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

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  28. S. Spartalis and T. Vougiouklis,The relation on H v -rings, Rivista Math. Pura. Math.14 (1994), 7–20.

    MATH  MathSciNet  Google Scholar 

  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. 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. T. Vougiouklis,The fundamental relations in Hyperstructures, Bull. Greek Math. Soc.42 (1999), 113–118.

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  33. L. A. Zadeh,Fuzzy sets, Inform and Control8 (1965), 338–353.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hubei Institute for Nationalities, 445000, Enshi, Hubei Province, P. R. China

    Jianming Zhan & Zhisong Tan

Authors
  1. Jianming Zhan
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  2. Zhisong Tan
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Correspondence to Jianming Zhan.

Additional information

This work was supported by the Education Committee of Hubei Province(2004Z002,D200529001).

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Zhan, J., Tan, Z. Approximations in hyperquasigroups. J. Appl. Math. Comput. 21, 485–494 (2006). https://doi.org/10.1007/BF02896422

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  • DOI: https://doi.org/10.1007/BF02896422

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