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The Scientific World Journal
Volume 2014, Article ID 192957, 11 pages
http://dx.doi.org/10.1155/2014/192957
Research Article

On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2Mathematics and OR Section, Xi’an Research Institute of High-Tech Hongqing Town, Xi’an 710025, China

Received 8 February 2014; Accepted 30 June 2014; Published 20 July 2014

Academic Editor: Muhammad I. Ali

Copyright © 2014 Xiaoyan Liu 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. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 378–352, 1965. View at Google Scholar
  2. 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 MathSciNet
  3. 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
  4. H. Aktaş and N. Çağman, “Soft sets and soft groups,” Information Sciences, vol. 177, no. 13, pp. 2726–2735, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  5. 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
  6. 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
  7. 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
  8. N. O. Alshehri, M. Akram, and R. S. Al-ghamdi, “Applications of soft sets in K-algebras,” Advances in Fuzzy Systems, vol. 2013, Article ID 319542, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. L. Xin and W. T. Li, “Soft congruence relations over rings,” The Scientific World Journal, vol. 2014, Article ID 541630, 9 pages, 2014. View at Publisher · View at Google Scholar
  10. X. Ma and H. S. Kim, “M,N-soft intersection BL-algebras and their congruences,” The Scientific World Journal, vol. 2014, Article ID 461060, 6 pages, 2014. View at Publisher · View at Google Scholar
  11. J. H. Park, O. H. Kim, and Y. C. Kwun, “Filterness on soft topological spaces,” Journal of Computational Analysis and Applications, vol. 15, no. 2, pp. 280–293, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Shabir and M. Naz, “On soft topological spaces,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1786–1799, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Y. Zou and Z. Xiao, “Data analysis approaches of soft sets under incomplete information,” Knowledge-Based Systems, vol. 21, no. 8, pp. 941–945, 2008. View at Publisher · View at Google Scholar
  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
  15. K. Y. Qin and Z. Y. Hong, “On soft equality,” Journal of Computational and Applied Mathematics, vol. 234, no. 5, pp. 1347–1355, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  16. K. Gong, Z. Xiao, and X. Zhang, “The bijective soft set with its operations,” Computers & Mathematics with Applications, vol. 60, no. 8, pp. 2270–2278, 2010. View at Publisher · View at Google Scholar
  17. M. I. Ali, “A note on soft sets, rough soft sets and fuzzy soft sets,” Applied Soft Computing, vol. 11, pp. 3329–3332, 2011. View at Google Scholar
  18. F. Feng, C. Li, B. Davvaz, and M. Irfan Ali, “Soft sets combined with fuzzy sets and rough sets: a tentative approach,” Soft Computing, vol. 14, pp. 899–911, 2010. View at Publisher · View at Google Scholar
  19. F. Feng, X. Y. Liu, V. Leoreanu-Fotea, and Y. B. Jun, “Soft sets and soft rough sets,” Information Sciences, vol. 181, no. 6, pp. 1125–1137, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555–562, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir, “On some new operations in soft set theory,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1547–1553, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  22. M. I. Ali, M. Shabir, and M. Naz, “Algebraic structures of soft sets associated with new operations,” Computers and Mathematics with Applications, vol. 61, no. 9, pp. 2647–2654, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  23. P. K. Maji, R. Biswas, and A. R. Roy, “Fuzzy soft sets,” Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589–602, 2001. View at Google Scholar · View at MathSciNet
  24. P. Majumdar and S. K. Samanta, “Generalised fuzzy soft sets,” Computers & Mathematics with Applications, vol. 59, no. 4, pp. 1425–1432, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  25. X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li, and D. J. Yu, “Combination of interval-valued fuzzy set and soft set,” Computers & Mathematics with Applications, vol. 58, no. 3, pp. 521–527, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  26. Z. C. Liu, K. Y. Qin, and Z. Pei, “Similarity measure and entropy of fuzzy soft sets,” The Scientific World Journal, vol. 2014, Article ID 161607, 10 pages, 2014. View at Publisher · View at Google Scholar
  27. F. Feng, H. Fujita, Y. B. Jun, and M. Khan, “Decomposition of fuzzy soft sets with finite value spaces,” The Scientific World Journal, vol. 2014, Article ID 902687, 10 pages, 2014. View at Publisher · View at Google Scholar
  28. Y. B. Jun and X. Yang, “A note on the paper “Combination of interval-valued fuzzy set and soft set” [COMput. Math. Appl. 58 (2009) 521–527],” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1468–1470, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  29. X. Liu, F. Feng, and Y. B. Jun, “A note on generalized soft equal relations,” Computers & Mathematics with Applications, vol. 64, no. 4, pp. 572–578, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  30. 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
  31. F. Feng, Y. Li, and V. Leoreanu-Fotea, “Application of level soft sets in decision making based on interval-valued fuzzy soft sets,” Computers & Mathematics with Applications, vol. 60, no. 6, pp. 1756–1767, 2010. View at Publisher · View at Google Scholar · View at MathSciNet