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The Scientific World Journal
Volume 2014, Article ID 951796, 11 pages
http://dx.doi.org/10.1155/2014/951796
Research Article

Characterizations of MV-Algebras Based on the Theory of Falling Shadows

1School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
2School of Mathematics, Northwest University, Xi’an 710127, China

Received 24 June 2014; Accepted 28 July 2014; Published 28 August 2014

Academic Editor: Hee S. Kim

Copyright © 2014 Yongwei Yang 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. C. C. Chang, “Algebraic analysis of many valued logics,” Transactions of the American Mathematical Society, vol. 88, no. 2, pp. 467–490, 1958. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. Giuntini, “Quasilinear QMV algebras,” International Journal of Theoretical Physics, vol. 34, no. 8, pp. 1397–1407, 1995. View at Publisher · View at Google Scholar
  3. A. di Nola and A. Lettieri, “Perfect MV-algebras are categorically equivalent to abelian l-groups,” Studia Logica, vol. 53, no. 3, pp. 417–432, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. S. Hoo, “Fuzzy ideals of BCI and MV-algebras,” Fuzzy Sets and Systems, vol. 62, no. 1, pp. 111–114, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G. Dymek, “Fuzzy prime ideals of pseudo-MV algebras,” Soft Computing, vol. 12, no. 4, pp. 365–372, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. L. P. Belluce and A. di Nola, “Commutative rings whose ideals form an MV-algebra,” Mathematical Logic Quarterly, vol. 55, no. 5, pp. 468–486, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. C. Lele and J. B. Nganou, “MV-algebras derived from ideals in BL-algebras,” Fuzzy Sets and Systems, vol. 218, pp. 103–113, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. S. Hoo, “Fuzzy implicative and Boolean ideals of MV-algebras,” Fuzzy Sets and Systems, vol. 66, no. 3, pp. 315–327, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. B. Jun and A. Walendziak, “Fuzzy ideals of pseudo MV-algebras,” International Review of Fuzzy Mathematics, vol. 1, no. 1, pp. 21–31, 2006. View at Google Scholar · View at MathSciNet
  10. H. Hedayati, “A generalization of (implicative) (,q)-fuzzy ideals of pseudo-MV algebras,” Journal of Multiple-Valued Logic and Soft Computing, vol. 20, no. 5-6, pp. 625–651, 2013. View at Google Scholar · View at MathSciNet · View at Scopus
  11. I. R. Goodman, Fuzzy Sets as Equivalence Classes of Random Sets, Pergamon Press, Oxford, UK, 1982.
  12. P. Z. Wang and E. Sanchez, “Treating a fuzzy subset as a projectable random subset,” Electronic Research Laboratory, College of Engineering University of California, 1982.
  13. 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 MathSciNet · View at Scopus
  14. 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 · View at Scopus
  15. X. 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 · View at Scopus
  16. P. Z. Wang, Fuzzy Sets and Falling Shadows of Random Sets, Beijing Normal University Press, Beijing, China, 1985.
  17. M. Yu and G. Zhang, “Fuzzy ideal based on the theory of falling shadows of random set in BCI-algebras,” Journal of Dalian University, vol. 26, no. 2, pp. 1–4, 2005. View at Google Scholar
  18. 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 Scopus
  19. Y. B. Jun, S. S. Ahn, and K. J. Lee, “Falling d-ideals in d-algebras,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 516418, 14 pages, 2011. View at Publisher · View at Google Scholar
  20. B. Yu, J. Zhan, and B. Yu, “Falling fuzzy ideals of hemirings,” Journal of Intelligent Fuzzy Systems, vol. 25, no. 4, pp. 1037–1042, 2013. View at Google Scholar
  21. J. Zhan, Y. B. Jun, and H. K. Kim, “Some types of falling fuzzy filters of BL-algebras and its applications,” Journal of Intelligent & Fuzzy Systems, vol. 26, no. 4, pp. 1675–1685, 2014. View at Google Scholar
  22. P. Hájek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. L. O. Cignoli, I. M. L. D'Ottaviano, and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  24. A. Dvurecenskij and S. Pulmannová, New Trends in Quantum Structures, Dordrecht, The Netherlands, Kluwer Academic Publishers, 2000.
  25. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. P. Z. Wang, H. X. Li, J. P. Yan, G. Lu, and C. F. Huang, “Fuzzy set operations in the theory of falling shadow representation,” Fuzzy Systems and Mathematics, vol. 6, no. 2, pp. 86–92, 1992. View at Google Scholar · View at MathSciNet
  27. C. Lele and J. B. Nganou, “Pseudo-addition and fuzzy ideals in BL-algebras,” Annals of Fuzzy Mathematics and Informatics, vol. 8, no. 2, pp. 193–207, 2014. View at Google Scholar
  28. B. L. Meng and X. L. Xin, “On fuzzy ideals of BL-algebras,” The Scientific World Journal, vol. 2014, Article ID 757382, 12 pages, 2014. View at Publisher · View at Google Scholar