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Journal of Applied Mathematics
Volume 2013, Article ID 915217, 10 pages
http://dx.doi.org/10.1155/2013/915217
Research Article

On Rough Hyperideals in Hyperlattices

1Department of Mathematics, Northwest University, Xi'an 710127, China
2Department of Mathematics, Hubei University for Nationalities, Enshi 445000, China

Received 30 March 2013; Revised 28 June 2013; Accepted 29 June 2013

Academic Editor: Hak-Keung Lam

Copyright © 2013 Pengfei He et al. 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. F. Marty, “Sur une généralisation de la notion de groupe,” in 8th Congrès des Mathématiciens Scandinaves, pp. 45–49, Stockholm, Sweden, 1934.
  2. J. Jantosciak, “Transposition hypergroups: noncommutative join spaces,” Journal of Algebra, vol. 187, no. 1, pp. 97–119, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. Rota, “Hyperaffine planes over hyperrings,” Discrete Mathematics, vol. 155, no. 1–3, pp. 215–223, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Konstantinidou and J. Mittas, “An introduction to the theory of hyperlattices,” Mathematica Balkanica, vol. 7, pp. 187–193, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Mittas and M. Konstantinidou, “Sur une nouvelle généralisation de la notion de treillis: les supertreillis et certaines de leurs propriétés générales,” Annales Scientifiques de l'Université de Clermont-Ferrand II. Mathématiques, no. 25, pp. 61–83, 1989. View at Google Scholar · View at MathSciNet
  6. A. Rahnamai-Barghi, “The prime ideal theorem and semiprime ideals in meet-hyperlattices,” Italian Journal of Pure and Applied Mathematics, no. 5, pp. 53–60, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Rahnamai-Barghi, “The prime ideal theorem for distributive hyperlattices,” Italian Journal of Pure and Applied Mathematics, no. 10, pp. 75–78, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. X. Z. Guo and X. L. Xin, “Hyperlattices,” Pure and Applied Mathematics, vol. 20, no. 1, pp. 40–43, 2004. View at Google Scholar · View at MathSciNet
  9. S. Rasouli and B. Davvaz, “Lattices derived from hyperlattices,” Communications in Algebra, vol. 38, no. 8, pp. 2720–2737, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Rasouli and B. Davvaz, “Construction and spectral topology on hyperlattices,” Mediterranean Journal of Mathematics, vol. 7, no. 2, pp. 249–262, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, vol. 5 of Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. View at MathSciNet
  12. B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
  13. Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. Biswas and S. Nanda, “Rough groups and rough subgroups,” Bulletin of Mathematics of Polish Academy of Sciences, vol. 42, no. 3, pp. 251–254, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. B. Davvaz, “Roughness in rings,” Information Sciences, vol. 164, no. 1–4, pp. 147–163, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. B. Davvaz and M. Mahdavipour, “Roughness in modules,” Information Sciences, vol. 176, no. 24, pp. 3658–3674, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. B. Jun, “Roughness of ideals in BCK-algebras,” Scientiae Mathematicae Japonicae, vol. 57, no. 1, pp. 165–169, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. N. Kuroki, “Rough ideals in semigroups,” Information Sciences, vol. 100, no. 1–4, pp. 139–163, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. N. Kuroki and J. N. Mordeson, “Structure of rough sets and rough groups,” Journal of Fuzzy Mathematics, vol. 5, no. 1, pp. 183–191, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. N. Kuroki and P. P. Wang, “The lower and upper approximations in a fuzzy group,” Information Sciences, vol. 90, no. 1–4, pp. 203–220, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. A. Estaji, M. R. Hooshmandasl, and B. Davvaz, “Rough set theory applied to lattice theory,” Information Sciences, vol. 200, pp. 108–122, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. V. Leoreanu-Fotea and B. Davvaz, “Roughness in n-ary hypergroups,” Information Sciences, vol. 178, no. 21, pp. 4114–4124, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  23. V. L. Fotea, “The lower and upper approximations in a hypergroup,” Information Sciences, vol. 178, no. 18, pp. 3605–3615, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. B. Davvaz, “Approximations in Hv-modules,” Taiwanese Journal of Mathematics, vol. 6, no. 4, pp. 499–505, 2002. View at Google Scholar · View at MathSciNet
  25. B. Davvaz, “A new view of the approximations in Hv-groups,” Soft Computing, vol. 10, no. 11, pp. 1043–1046, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Q. Yin, J. M. Zhan, and P. Corsini, “L-fuzzy roughness of n-ary polygroups,” Acta Mathematica Sinica, vol. 27, no. 1, pp. 97–118, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  27. Y. Yin, J. Zhan, and P. Corsini, “Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice,” Neural Computing and Applications, vol. 20, no. 1, pp. 41–57, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. Y.-Q. Yin and X.-K. Huang, “Fuzzy roughness in hyperrings based on a complete residuated lattice,” International Journal of Fuzzy Systems, vol. 13, no. 3, pp. 185–194, 2011. View at Google Scholar · View at MathSciNet
  29. N. Yaqoob, “Applications of rough sets to Γ-hyperideals in left almost Γ-semihypergroups,” Neural Computing and Applications, vol. 21, pp. 267–237, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. 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