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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 716435, 9 pages
http://dx.doi.org/10.1155/2013/716435
Research Article

Characterizations of Hemirings Based on Probability Spaces

Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China

Received 24 March 2013; Accepted 8 May 2013

Academic Editor: Qiankun Song

Copyright © 2013 Bin Yu and Jianming Zhan. 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. I. R. Goodman, “Fuzzy sets as equivalence classes of random sets,” in Recent Developments in Fuzzy Sets and Possibility Theory, R. Yager, Ed., Pergamon, New York, NY, USA,, 1982.
  3. P. Z. Wang and E. Sanchez, “Treating a fuzzy subset as a projectable random set,” in Fuzzy Information and Decision, M. M. Gupta and E. Sanchez, Eds., pp. 212–219, Pergamon, New York, NY, USA, 1982.
  4. S. K. Tan, P. Z. Wang, and E. S. Lee, “Fuzzy set operations based on the theory of falling shadows,” Journal of Mathematical Analysis and Applications, vol. 174, no. 1, pp. 242–255, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. K. Tan, P. Z. Wang, and X. Z. Zhang, “Fuzzy inference relation based on the theory of falling shadows,” Fuzzy Sets and Systems, vol. 53, no. 2, pp. 179–188, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X.-H. Yuan and E. S. Lee, “A fuzzy algebraic system based on the theory of falling shadows,” Journal of Mathematical Analysis and Applications, vol. 208, no. 1, pp. 243–251, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. B. Jun and M. S. Kang, “Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows,” Computers and Mathematics with Applications, vol. 61, no. 1, pp. 62–67, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Beasley and N. J. Pullman, “Linear operators strongly preserving idempotent matrices over semirings,” Linear Algebra and Its Applications, vol. 160, pp. 217–229, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Ghosh, “Matrices over semirings,” Information Sciences, vol. 90, no. 1–4, pp. 221–230, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. D. R. LaTorre, “On h-ideals and k-ideals in hemirings,” Publicationes Mathematicae Debrecen, vol. 12, pp. 219–226, 1965. View at MathSciNet
  11. S. Abdullah, B. Davvaz, and M. Aslam, “(α,β)-intuitionistic fuzzy ideals of hemirings,” Computers and Mathematics with Applications, vol. 62, no. 8, pp. 3077–3090, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Ahsan, K. Saifullah, and M. F. Khan, “Fuzzy semirings,” Fuzzy Sets and Systems, vol. 60, no. 3, pp. 309–320, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. Ahsan, J. N. Mordeson, and M. Shabir, “Fuzzy k-ideals of semirngs,” in Fuzzy Semiring With Applications Automata Theory, vol. 278 of Studies in Fuzziness and Soft Computing, pp. 53–82, 2012.
  14. T. K. Dutta and B. K. Biswas, “Fuzzy congruence and quotient semiring of a semiring,” Journal of Fuzzy Mathematics, vol. 4, no. 4, pp. 737–748, 1996. View at Zentralblatt MATH · View at MathSciNet
  15. H. Hedayati, “Fuzzy ideals of semirings,” in Neural Computing and Applications, vol. 20, pp. 1219–1228, 2011.
  16. Y. B. Jun, H. S. Kim, and M. A. Öztürk, “Fuzzy k-ideals in semirings,” Journal of Fuzzy Mathematics, vol. 13, no. 2, pp. 351–364, 2005. View at Zentralblatt MATH · View at MathSciNet
  17. J. Zhan and W. A. Dudek, “Fuzzy h-ideals of hemirings,” Information Sciences, vol. 177, no. 3, pp. 876–886, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Y. Q. Yin and H. X. Li, “The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings,” Information Sciences, vol. 178, no. 17, pp. 3451–3464, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Y. Q. Yin, X. K. Huang, D. H. Xu, and H. J. Li, “The characterization of h-semisimple hemirings,” International Journal of Fuzzy Systems, vol. 11, no. 2, pp. 116–122, 2009. View at MathSciNet
  20. W. A. Dudek, M. Shabir, and M. Irfan Ali, “(α,β)-fuzzy ideals of hemirings,” Computers and Mathematics with Applications, vol. 58, no. 2, pp. 310–321, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W. A. Dudek, M. Shabir, and R. Anjum, “Characterizations of hemirings by their h-ideals,” Computers and Mathematics with Applications, vol. 59, no. 9, pp. 3167–3179, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  22. X. Ma, Y. Yin, and J. Zhan, “Characterizations of h-intra- and h-quasi-hemiregular hemirings,” Computers and Mathematics with Applications, vol. 63, no. 4, pp. 783–793, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  23. X. Ma and J. Zhan, “Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings,” Information Sciences, vol. 179, no. 9, pp. 1249–1268, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  24. X. Ma and J. Zhan, “New fuzzy h-ideals in hemirings,” Politehnica University of Bucharest Scientific Bulletin A, vol. 74, no. 1, pp. 11–24, 2012. View at MathSciNet
  25. J. Zhan and Y. Yin, “A new view of fuzzy k-ideals of hemirings,” Journal of Intelligent and Fuzzy Systems, vol. 23, no. 5, pp. 169–176, 2012. View at MathSciNet
  26. B. Yu and J. Zhan, “Falling fuzzy ideals of hemirings,” Journal of Intelligent and Fuzzy Systems. In press. View at Publisher · View at Google Scholar