About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 560698, 9 pages
http://dx.doi.org/10.1155/2013/560698
Research Article

Structure of Intuitionistic Fuzzy Sets in -Semihyperrings

1Department of Mathematics, Yildiz Technical University, 34210 Istanbul, Turkey
2Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran

Received 21 October 2012; Accepted 27 December 2012

Academic Editor: Feyzi Başar

Copyright © 2013 Bayram Ali Ersoy and Bijan Davvaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Zentralblatt MATH · View at MathSciNet
  2. A. Rosenfeld, “Fuzzy groups,” Journal of Mathematical Analysis and Applications, vol. 35, pp. 512–517, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. J. Liu, “Fuzzy invariant subgroups and fuzzy ideals,” Fuzzy Sets and Systems, vol. 8, no. 2, pp. 133–139, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. T. Atanassov, “New operations defined over the intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 61, no. 2, pp. 137–142, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. T. Atanassov, Intuitionistic Fuzzy Sets, Theory and Applications, vol. 35 of Studies in Fuzziness and Soft Computing, Physica, Heidelberg, Germany, 1999. View at MathSciNet
  7. R. Biswas, “Intuitionistic fuzzy subgroups,” Notes on Intuitionistic Fuzzy Sets, vol. 3, no. 2, pp. 3–11, 1997. View at Zentralblatt MATH · View at MathSciNet
  8. K. H. Kim and Y. B. Jun, “Intuitionistic fuzzy ideals of semigroups,” Indian Journal of Pure and Applied Mathematics, vol. 33, no. 4, pp. 443–449, 2002. View at Zentralblatt MATH · View at MathSciNet
  9. C. Gunduz and B. Davvaz, “The universal coefficient theorem in the category of intuitionistic fuzzy modules,” Utilitas Mathematica, vol. 81, pp. 131–156, 2010. View at Zentralblatt MATH · View at MathSciNet
  10. K. H. Kim, “On intuitionistic fuzzy subhypernear-rings of hypernear-rings,” Turkish Journal of Mathematics, vol. 27, no. 3, pp. 447–459, 2003. View at Zentralblatt MATH · View at MathSciNet
  11. M. Uçkun, M. A. Öztürk, and Y. B. Jun, “Intuitionistic fuzzy sets in Γ-semigroups,” Bulletin of the Korean Mathematical Society, vol. 44, no. 2, pp. 359–367, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. E. Barnes, “On the Γ-rings of Nobusawa,” Pacific Journal of Mathematics, vol. 18, pp. 411–422, 1966. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Luh, “On the theory of simple Γ-rings,” The Michigan Mathematical Journal, vol. 16, pp. 65–75, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. Kyuno, “On prime Γ-rings,” Pacific Journal of Mathematics, vol. 75, no. 1, pp. 185–190, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. N. K. Saha, “On Γ-semigroup. II,” Bulletin of the Calcutta Mathematical Society, vol. 79, no. 6, pp. 331–335, 1987. View at MathSciNet
  16. M. K. Sen and N. K. Saha, “On Γ-semigroup. I,” Bulletin of the Calcutta Mathematical Society, vol. 78, no. 3, pp. 180–186, 1986. View at MathSciNet
  17. M. M. K. Rao, “Γ-semirings. I,” Southeast Asian Bulletin of Mathematics, vol. 19, no. 1, pp. 49–54, 1995. View at Zentralblatt MATH · View at MathSciNet
  18. F. Marty, “Sur une generalization de la notion de groupe,” in Proceedings of the 8th Scandinavian Congress of Mathematicians, pp. 45–49, Stockholm, Sweden, 1934.
  19. P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, Tricesimo, Italy, 1993. View at MathSciNet
  20. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, vol. 5 of Advances in Mathematics, Kluwer Academic, Dordrecht, The Netherlands, 2003. View at MathSciNet
  21. B. . Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, vol. 115, International Academic Press, Palm Harber, Fla, USA, 2007.
  22. T. Vougiouklis, Hyperstructures and Their Representations, vol. 115, Hadronic Press, Palm Harbor, Fla, USA, 1994. View at MathSciNet
  23. S. M. Anvariyeh, S. Mirvakili, and B. Davvaz, “On Γ-hyperideals in Γ-semihypergroups,” Carpathian Journal of Mathematics, vol. 26, no. 1, pp. 11–23, 2010. View at MathSciNet
  24. S. M. Anvariyeh, S. Mirvakili, and B. Davvaz, “Pawlak's approximations in Γ-semihypergroups,” Computers & Mathematics with Applications, vol. 60, no. 1, pp. 45–53, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  25. D. Heidari, S. O. Dehkordi, and B. Davvaz, “Γ-semihypergroups and their properties,” Scientific Bulletin A, vol. 72, no. 1, pp. 195–208, 2010. View at Zentralblatt MATH · View at MathSciNet
  26. S. O. Dehkordi and B. Davvaz, “Γ-semihyperrings: approximations and rough ideals,” Bulletin of the Malaysian Mathematical Sciences Society. In press.
  27. S. O. Dehkordi and B. Davvaz, “Γ-semihyperrings: ideals, homomorphisms and regular relations,” submitted.
  28. S. O. Dehkordi and B. Davvaz, “Ideal theory in Γ-semihyperrings,” submitted.
  29. H. Hedayati and B. Davvaz, “Fundamental relation on Γ-hyperrings,” Ars Combinatoria, vol. 100, pp. 381–394, 2011. View at MathSciNet
  30. B. Davvaz, “Fuzzy Hν-groups,” Fuzzy Sets and Systems, vol. 101, no. 1, pp. 191–195, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  31. V. Leoreanu-Fotea and B. Davvaz, “Fuzzy hyperrings,” Fuzzy Sets and Systems, vol. 160, no. 16, pp. 2366–2378, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. I. Cristea and B. Davvaz, “Atanassov's intuitionistic fuzzy grade of hypergroups,” Information Sciences, vol. 180, no. 8, pp. 1506–1517, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. B. Davvaz and V. Leoreanu-Fotea, “Intuitionistic fuzzy n-ary hypergroups,” Journal of Multiple-Valued Logic and Soft Computing, vol. 16, no. 1-2, pp. 87–103, 2010. View at MathSciNet
  34. B. Davvaz, P. Corsini, and V. Leoreanu-Fotea, “Atanassov's intuitionistic (S, T)-fuzzy n-ary sub-hypergroups and their properties,” Information Sciences, vol. 179, no. 5, pp. 654–666, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  35. B. Davvaz and S. K. Majumder, “Atanassov's intuitionistic fuzzy interior ideals of Γ-semigroups,” Scientific Bulletin A, vol. 73, no. 3, pp. 45–60, 2011. View at MathSciNet