Table of Contents
Algebra
Volume 2016, Article ID 2752681, 7 pages
http://dx.doi.org/10.1155/2016/2752681
Research Article

Characterizations of Algebras

School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China

Received 11 July 2015; Revised 20 November 2015; Accepted 8 December 2015

Academic Editor: Antonio M. Cegarra

Copyright © 2016 Fang-an Deng 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. M. Baczynski and B. Jayaram, Fuzzy Implications, Springer, 2008.
  2. M. Mas, M. Monserrat, J. Torrens, and E. Trillas, “A survey on fuzzy implication functions,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1107–1121, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Massanet, G. Mayor, R. Mesiar, and J. Torrens, “On fuzzy implications: an axiomatic approach,” International Journal of Approximate Reasoning, vol. 54, no. 9, pp. 1471–1482, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. W. M. Wu, “Fuzzy implication algebra,” Fuzzy Systems and Mathematics, vol. 4, no. 1, pp. 56–64, 1990. View at Google Scholar
  5. Z. W. Li and G. H. Li, “Some properties of fuzzy implication algebras,” Fuzzy Systems and Mathematics, vol. 14, supplement 1, pp. 19–21, 2000 (Chinese). View at Google Scholar
  6. Z. W. Li and G. H. Li, “Characterization of fuzzy implication algebras,” Journal of Mathematics, vol. 28, no. 6, pp. 701–705, 2008 (Chinese). View at Google Scholar · View at MathSciNet
  7. W. Chen, “Some chararacters of regular fuzzy implication algebras,” Fuzzy System and Mathematics, vol. 15, no. 4, pp. 24–27, 2001 (Chinese). View at Google Scholar
  8. Z. W. Li, L. M. Sun, and C. Y. Zheng, “Regular fuzzy implication algebras,” Fuzzy System and Mathematics, vol. 16, no. 2, pp. 22–26, 2002 (Chinese). View at Google Scholar
  9. D. Wu, “Commutative fuzzy implication algebras,” Fuzzy Systems and Mathematics, vol. 13, no. 1, pp. 27–30, 1999 (Chinese). View at Google Scholar · View at MathSciNet
  10. F. A. Deng and J. L. Li, “Wd-fuzzy implication algebras,” Journal of Harbin Normal University (Natural Science Edition), vol. 12, no. 2, pp. 18–21, 1996 (Chinese). View at Google Scholar
  11. H. R. Zhang and L. C. Wang, “Properties of LFI-algebras and residuated lattice,” Fuzzy System and Mathematics, vol. 18, no. 2, pp. 13–17, 2004 (Chinese). View at Google Scholar
  12. C. H. Liu and L. X. Xu, “MP-filters of fuzzy implication algebras,” Fuzzy Systems and Mathematics, vol. 23, no. 2, pp. 1–6, 2009 (Chinese). View at Google Scholar · View at MathSciNet
  13. C. H. Liu and L. X. Xu, “Various concepts of fuzzy filters in FI-algebras,” Fuzzy Systems and Mathematics, vol. 24, no. 2, pp. 21–27, 2010. View at Google Scholar · View at MathSciNet
  14. Y. Zhu and Y. Xu, “On filter theory of residuated lattices,” Information Sciences, vol. 180, no. 19, pp. 3614–3632, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Kondo and W. A. Dudek, “Filter theory of BL-algebras,” Soft Computing, vol. 12, no. 5, pp. 419–423, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Haveshki and E. Eslami, “n-fold filters in BL-algebras,” Mathematical Logic Quarterly, vol. 54, no. 2, pp. 176–186, 2008. View at Publisher · View at Google Scholar
  17. R. A. Borzooei, S. K. Shoar, and R. Ameri, “Some types of filters in MTL-algebras,” Fuzzy Sets and Systems, vol. 187, no. 1, pp. 92–102, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. Haveshki, A. Saeid, and E. Eslami, “Some types of filters in BL algebras,” Soft Computing, vol. 10, no. 8, pp. 657–664, 2006. View at Publisher · View at Google Scholar
  19. B. Q. Hu, “Equivalence of fuzzy implication algebras and bounded BCK-algebras,” Applied Mathematics, vol. 6, no. 2, pp. 233–234, 1993 (Chinese). View at Google Scholar
  20. H. Jiang and F. A. Deng, “Relations between fuzzy mplication algebras and bouned BCK-algebras,” Fuzzy system and Mathematics, vol. 5, no. 1, pp. 88–89, 1991 (Chinese). View at Google Scholar
  21. Z. W. Li and C. Y. Zheng, “Relations between fuzzy implication algebra and MV algebra,” Journal of Fuzzy Mathematics, vol. 9, no. 1, pp. 201–205, 2001 (Chinese). View at Google Scholar · View at MathSciNet
  22. S. L. Chen, “Rough sets and fuzzy implication algebras,” Computing Science and Engineering, vol. 31, no. 4, pp. 134–136, 2009 (Chinese). View at Google Scholar
  23. H. X. Wei and X. Q. Li, “Rough set algebras and fuzzy implication algebras,” Computer Engineering and Applications, vol. 45, no. 18, pp. 38–39, 2009 (Chinese). View at Google Scholar
  24. Y. Q. Zhu, “A logic system based on FI-algebras and its completeness,” Fuzzy Systems and Mathematics, vol. 19, no. 2, pp. 25–29, 2005 (Chinese). View at Google Scholar · View at MathSciNet
  25. D. Pei, “A survey of fuzzy implication algebras and their axiomatization,” International Journal of Approximate Reasoning, vol. 55, no. 8, pp. 1643–1658, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. Y. B. Jun, “Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras,” Fuzzy Sets and Systems, vol. 121, no. 2, pp. 353–357, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. Y. B. Jun and S. Z. Song, “On fuzzy implicative filters of lattice implication algebras,” Journal of Fuzzy Mathematics, vol. 10, no. 4, pp. 893–900, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. L. Liu and K. Li, “Fuzzy implicative and Boolean filters of R0-algebras,” Information Sciences, vol. 171, pp. 61–71, 2005. View at Google Scholar
  29. L. Liu and K. Li, “Fuzzy filters of BL-algebras,” Information Sciences, vol. 173, no. 1–3, pp. 141–154, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. L. Liu and K. Li, “Fuzzy Boolean and positive implicative filters of BL-algebras,” Fuzzy Sets and Systems, vol. 152, no. 2, pp. 333–348, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. J. Siekmann and P. Z. Szabó, “The undecidability of the DA-unification problem,” The Journal of Symbolic Logic, vol. 54, no. 2, pp. 402–414, 1989. View at Publisher · View at Google Scholar
  32. F.-A. Deng and Y. Xu, “On N(2,2,0) algebra,” Journal of Southwest Jiaotong University, vol. 131, pp. 457–463, 1996. View at Google Scholar
  33. F.-A. Deng and L.-Q. Yong, “Regular smeigroup of N(2, 2, 0) algebra,” Advances in Mathematics, vol. 6, pp. 655–662, 2012 (Chinese). View at Google Scholar
  34. I. Chajda and J. Paseka, “Tense operators in fuzzy logic,” Fuzzy Sets and Systems, vol. 276, no. 1, pp. 100–113, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  35. F. Abdullahu and A. Zejnullahu, “Notes on semimedial semigroups,” Commentationes Mathematicae Universitatis Carolinae, vol. 50, no. 3, pp. 321–324, 2009. View at Google Scholar · View at MathSciNet
  36. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, San Diego, Calif, USA, 1976. View at MathSciNet
  37. M. Brion, “On algebraic semigroups and monoids, II,” Semigroup Forum, vol. 88, no. 1, pp. 250–272, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. Y. Luo and X. Li, “The maximum idempotent-separating congruence on eventually regular semigroups,” Semigroup Forum, vol. 74, no. 2, pp. 306–318, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. H. Mitsch, “Semigroups and their lattice of congruences,” Semigroup Forum, vol. 26, no. 1-2, pp. 1–63, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. Y. B. Jun and S. Song, “Int-soft (generalized) Bi-ideals of semigroups,” The Scientific World Journal, vol. 2015, Article ID 198672, 6 pages, 2015. View at Publisher · View at Google Scholar
  41. N. Kehayopulu and M. Tsingelis, “Archimedean ordered semigroups as ideal extensions,” Semigroup Forum, vol. 78, no. 2, pp. 343–348, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  42. J. Fountain and G. M. S. Gomes, “Finite abundant semigroups in which the idempotents form a subsemigroup,” Journal of Algebra, vol. 295, no. 2, pp. 303–313, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus