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The Scientific World Journal
Volume 2014, Article ID 595160, 12 pages
http://dx.doi.org/10.1155/2014/595160
Research Article

Classes of Int-Soft Filters in Residuated Lattices

1Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea
2Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea
3Department of Mathematics Education, Hannam University, Daejeon 306-791, Republic of Korea

Received 12 July 2014; Accepted 13 August 2014; Published 27 August 2014

Academic Editor: Xiaolong Xin

Copyright © 2014 Young Bae Jun 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. R. Bělohlávek, “Some properties of residuated lattices,” Czechoslovak Mathematical Journal, vol. 53, no. 1, pp. 161–171, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. K. Blount and C. Tsinakis, “The structure of residuated lattices,” International Journal of Algebra and Computation, vol. 13, no. 4, pp. 437–461, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. R. A. Borzooei, S. Khosravi Shoar, and R. Ameri, “Some types of filters in MTL-algebras,” Fuzzy Sets and Systems, vol. 187, pp. 92–102, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. H. Kim, Q. Zhang, and Y. B. Jun, “On fuzzy filters of MTL-algebras,” Journal of Fuzzy Mathematics, vol. 10, no. 4, pp. 981–989, 2002. View at Google Scholar · View at MathSciNet
  5. J. Shen and X. Zhang, “On filters of residuated lattice,” Chinese Quarterly Journal of Mathematics, vol. 21, no. 3, pp. 443–447, 2006. View at Google Scholar · View at MathSciNet
  6. E. Turunen, “BL-algebras of basic fuzzy logic,” Mathware & Soft Computing, vol. 6, pp. 49–61, 1999. View at Google Scholar
  7. E. Turunen, “Boolean deductive systems of BL-algebras,” Archive for Mathematical Logic, vol. 40, no. 6, pp. 467–473, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. X. H. Zhang, “On filters in MTL-algebras,” Advances in Systems Science and Applications, vol. 7, pp. 32–38, 2007. View at Google Scholar
  9. D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. U. Acar, F. Koyuncu, and B. Tanay, “Soft sets and soft rings,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3458–3463, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. S. Ahn, N. O. Alshehri, and Y. B. Jun, “Int-soft filters of BE-algebras,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 602959, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. H. Aktas and N. Çagman, “Soft sets and soft groups,” Information Science, vol. 177, pp. 2726–2735, 2007. View at Google Scholar
  13. A. O. Atagün and A. Sezgin, “Soft substructures of rings, fields and modules,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 592–601, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. N. Çağman and S. Enginoğlu, “Soft set theory and uni–int decision making,” European Journal of Operational Research, vol. 207, no. 2, pp. 848–855, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. F. Feng, Y. Li, and N. Çağman, “Generalized uni–int decision making schemes based on choice value soft sets,” European Journal of Operational Research, vol. 220, no. 1, pp. 162–170, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. N. Çağman and S. Enginoğlu, “FP-soft set theory and its applications,” Annals of Fuzzy Mathematics and Informatics, vol. 2, no. 2, pp. 219–226, 2011. View at Google Scholar · View at MathSciNet
  17. F. Feng, “Soft rough sets applied to multicriteria group decision making,” Annals of Fuzzy Mathematics and Informatics, vol. 2, no. 1, pp. 69–80, 2011. View at Google Scholar · View at MathSciNet
  18. F. Feng, Y. B. Jun, and X. Zhao, “Soft semirings,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2621–2628, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Y. B. Jun, “Soft BCK/BCI-algebras,” Computers & Mathematics with Applications, vol. 56, pp. 1408–1413, 2008. View at Google Scholar
  20. Y. B. Jun, K. J. Lee, and C. H. Park, “Soft set theory applied to ideals in d-algebras,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 367–378, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. B. Jun, K. J. Lee, and J. Zhan, “Soft p-ideals of soft BCI-algebras,” Computers & Mathematics with Applications, vol. 58, no. 10, pp. 2060–2068, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Y. B. Jun and C. H. Park, “Applications of soft sets in ideal theory of BCK/BCI-algebras,” Information Sciences, vol. 178, no. 11, pp. 2466–2475, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. Y. B. Jun, S. S. Ahn, and K. J. Lee, “Intersection-soft filters in R0-algebras,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 950897, 7 pages, 2013. View at Publisher · View at Google Scholar
  24. J. Zhan and Y. B. Jun, “Soft BL-algebras based on fuzzy sets,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 2037–2046, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. F. Feng and Y. Li, “Soft subsets and soft product operations,” Information Sciences, vol. 232, pp. 44–57, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. F. Esteva and L. Godo, “Monoidal t-norm based logic: towards a logic for left-continuous t-norms,” Fuzzy Sets and Systems, vol. 124, no. 3, pp. 271–288, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. P. Hájek, Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic—Studia Logica Library, Kluwer Academic, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  28. X. H. Zhang and W. H. Li, “On fuzzy logic algebraic system MTL,” Advances in Systems Science and Applications, vol. 5, pp. 475–483, 2005. View at Google Scholar
  29. Y. Q. 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