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On some interval-valued fuzzy hyperideals of semihypergroups

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Abstract

We first introduce the notion of some interval-valued fuzzy hyperideals of a semihypergroup and present some important structural results. Then we find some inter-relations between interval-valued fuzzy hyperideals and obtain some characterizations of regular semihypergroups, intra-regular semihypergroups by using interval-valued fuzzy hyperideals of semihypergroups.

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References

  1. Biswas, R.: Rosenfeld’s fuzzy subgroups with interval-valued membership functions. Fuzzy Sets Syst. 63(1), 87–90 (1994)

    Article  MATH  Google Scholar 

  2. Bonansinga, P., Corsini, P.: On semihypergroup and hypergroup homomorphisms. Unione Matematica Italiana B 1(2), 717–727 (1982)

    MathSciNet  Google Scholar 

  3. Chattopadhyay, S.: A semihypergroup associated with a \(\Gamma \)-semigroup. Analele Stiintifice Ale Universitatii “Ali Cuza” Din Iasi (S.N.) Mathematica 56(1), 209–225 (2010)

    MATH  MathSciNet  Google Scholar 

  4. Corsini, P.: Prolegomena of Hypergroup Theory, 2nd edn. Aviani Editore, Tricesimo (1993)

    Google Scholar 

  5. Corsini, P., Leoreanu, V.: Applications of Hyperstructure Theory, Advances in Mathematics. Kluwer Academic Publishers, Dordrecht (2003)

  6. Davvaz, B.: Fuzzy hyperideals in ternary semihyperrings. Iran J. Fuzzy Syst. 6, 21–36 (2009)

    MATH  MathSciNet  Google Scholar 

  7. Davvaz, B.: Fuzzy ideals of near-rings with interval valued membership functions. J. Sci. I. R. Iran 12(2), 171–175 (2001)

    MathSciNet  Google Scholar 

  8. Davvaz, B., Leoreanu-Fotea, V.: Hyperring Theory and Applications. International Academic Press, Palm Harbor (2007)

    MATH  Google Scholar 

  9. Davvaz, B.: Interval-valued fuzzy subhypergroup. Korean J. Comput. Appl. Math. 6(1), 197–202 (1999)

    MATH  MathSciNet  Google Scholar 

  10. Davvaz, B.: Some results on congruences on semihypergroups. Bull. Malays. Math. Sci. Soc. 23(2), 53–58 (2000)

    MATH  MathSciNet  Google Scholar 

  11. Davvaz, B.: \(T_H\) and \(S_H\)-interval valued fuzzy \(H_v\)-subgroups. Indian J. Pure Appl. Math. 35(1), 61–69 (2004)

    MATH  MathSciNet  Google Scholar 

  12. Davvaz, B., Leoreanu-Fotea, V.: Applications of interval valued fuzzy n-ary polygroups with respect to t-norms (t-conorms). Comput. Math. Appl. 57, 1413–1424 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Davvaz, B., Zhan, J., Shum, K.P.: Generalized fuzzy \(H_v\)-submodules endowed with interval valued membership functions. Inform. Sci. 178, 3147–3159 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Freni, D.: Strongly transitive geometric spaces: applications to hypergroups and semigroups theory. Commun. Algebra 32, 969–988 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gorzalczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21, 1–17 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Hasankhani, A.: Ideals in a semihypergroup and Green’s relations. Ratio Math. 13, 29–36 (1999)

    MATH  MathSciNet  Google Scholar 

  17. Hedayati, H.: Generalized fuzzy k-ideals of semirings with interval-valued membership functions. Bull. Malays. Math. Sci. Soc. 32, 409–424 (2009)

    MATH  MathSciNet  Google Scholar 

  18. Hila, K., Davvaz, B., Naka, K.: On quasi-hyperideals in semihypergroups. Commun. Algebra 39(11), 4183–4194 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  19. Kar, S., Shum, K.P., Sarkar, P.: Interval-valued prime fuzzy ideals of semigroups. Lobachevskii J. Math. 34(1), 11–19 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kar, S., Sarkar, P., Hila, K.: Interval-valued semiprime fuzzy ideals of semigroups. Adv. Fuzzy Syst. 2014, 1–10 (2014). http://dx.doi.org/10.1155/2014/842471

  21. Kar, S., Sarkar, P.: Interval-valued fuzzy completely regular subsemigroups of semigroups. Ann. Fuzzy Math. Inform. 5(3), 583–595 (2013)

    MathSciNet  Google Scholar 

  22. Marty, F.: Sur une generalization de la notion de group. In: Proceedings of the 8th Congres des Mathematiciens Scandinave, Stockholm, pp. 45–49 (1934)

  23. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems. Introduction and New Directions. Prentice-Hall, Upper Saddle River (2001)

  24. Narayanan, A.L., Manikantan, T.: Interval-valued fuzzy ideals generated by an interval-valued fuzzy subset in semigroups. J. Appl. Math. Comput. 20, 455–464 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Onipchuk, S.V.: Regular semihypergroups (Russian). Mat. Sb. 183, 43–54 (1992) [translation in Russian Acad. Sci. Sb. Math. 76, 155–164 (1993)]

  26. Roy, M.K., Biswas, R.: I-V fuzzy relations and Sanchezs approach for medical diagnosis. Fuzzy Sets Syst. 47, 35–38 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  27. Shabir, M., Mahmood, T.: Semihypergroups Characterized by \((\in,\in \vee q_k)\)-fuzzy Hyper ideals. Inf. Sci. Lett. 2(2), 101–121 (2013)

    Google Scholar 

  28. Turksen, I.B.: Interval-valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20, 191–210 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  29. Vougiouklis, T.: Some results on hyperstructures. Contemp. Math. 184, 427–431 (1995)

    Article  MathSciNet  Google Scholar 

  30. Vougiouklis, T.: Hyperstructures and Their Representations. Hadronic Press, Palm Harbor (1994)

    MATH  Google Scholar 

  31. Yamak, S., Kazanci, O., Davvaz, B.: Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups. Inform. Sci. 178, 3957–3972 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  32. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inform. Sci. 8, 199–249 (1975)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The second author would like to gratefully acknowledge the financial support of the Council of Scientific and Industrial Research (CSIR), India for carrying out this research work.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata-32, West Bengal, India

    S. Kar & P. Sarkar

  2. Faculty of Mathematics, Al.I. Cuza University, Iasi, Romania

    V. Leoreanu-Fotea

Authors
  1. S. Kar
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  2. P. Sarkar
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  3. V. Leoreanu-Fotea
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Correspondence to V. Leoreanu-Fotea.

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Kar, S., Sarkar, P. & Leoreanu-Fotea, V. On some interval-valued fuzzy hyperideals of semihypergroups. Afr. Mat. 26, 1171–1186 (2015). https://doi.org/10.1007/s13370-014-0273-8

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  • DOI: https://doi.org/10.1007/s13370-014-0273-8

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