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The Scientific World Journal
Volume 2014, Article ID 348683, 13 pages
http://dx.doi.org/10.1155/2014/348683
Research Article

Rough Atanassov’s Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications

Shuqun Luo and Weihua Xu

School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 26 August 2013; Accepted 18 November 2013; Published 13 May 2014

Academic Editors: E. Haghverdi, M. Mansour, and H. Xu

Copyright © 2014 Shuqun Luo and Weihua Xu. 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. Z. Pawlak, “Rough sets,” International Journal of Computer & Information Sciences, vol. 11, no. 5, pp. 341–356, 1982. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Pawlak, Rough Set: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
  3. Z. Pawlak and R. Sowinski, “Rough set approach to multi-attribute decision analysis,” European Journal of Operational Research, vol. 72, no. 3, pp. 443–459, 1994. View at Google Scholar · View at Scopus
  4. V. S. Ananthanarayana, M. N. Murty, and D. K. Subramanian, “Tree structure for efficient data mining using rough sets,” Pattern Recognition Letters, vol. 24, no. 6, pp. 851–862, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Cheng, Z. Mo, and J. Wang, “Notes on the lower and upper approximations in a fuzzy group and rough ideals in semigroups,” Information Sciences, vol. 177, no. 22, pp. 5134–5140, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping,” The Annals of Mathematical Statistics, vol. 38, pp. 325–339, 1967. View at Google Scholar
  7. I. Düntsch and G. Gediga, “Uncertainty measures of rough set prediction,” Artificial Intelligence, vol. 106, no. 1, pp. 109–137, 1998. View at Google Scholar · View at Scopus
  8. R. Jensen and Q. Shen, “Fuzzy-rough sets assisted attribute selection,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 1, pp. 73–89, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Mi and W. Zhang, “An axiomatic characterization of a fuzzy generalization of rough sets,” Information Sciences, vol. 160, no. 1–4, pp. 235–249, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Pawlak, “Rough sets, decision algorithms and Bayes' theorem,” European Journal of Operational Research, vol. 136, no. 1, pp. 181–189, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. Pawlak, “Some remarks on conflict analysis,” European Journal of Operational Research, vol. 166, no. 3, pp. 649–654, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Pawlak and A. Skowron, “Rudiments of rough sets,” Information Sciences, vol. 177, no. 1, pp. 3–27, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Zhou and W. Wu, “Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory,” Computers and Mathematics with Applications, vol. 62, no. 1, pp. 282–296, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Zhang, “An interval-valued rough intuitionistic fuzzy set model,” International Journal of General Systems, vol. 39, no. 2, pp. 135–164, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. W. Xu, Q. Wang, and X. Zhang, “Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space,” International Journal of Fuzzy Systems, vol. 13, no. 4, pp. 246–259, 2011. View at Google Scholar · View at Scopus
  16. W. H. Xu, Y. F. Liu, and W. X. Sun, “Uncertainty measure of intuitionistic fuzzy T equivalence information systems,” Journal of Intelligent and Fuzzy Systems. In press.
  17. Y. Shen and F. Wang, “Variable precision rough set model over two universes and its properties,” Soft Computing, vol. 15, no. 3, pp. 557–567, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Yan, J. Zheng, J. Liu, and Y. Zhai, “Research on the model of rough set over dual-universes,” Knowledge-Based Systems, vol. 23, no. 8, pp. 817–822, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Z. Sun, W. M. Ma, and Q. Liu, “An approach to decision making based on intuitionistic fuzzy rough sets over two universes,” Journal of the Operational Research Society, vol. 64, pp. 1079–1089, 2013. View at Publisher · View at Google Scholar
  20. T. Li and W. Zhang, “Rough fuzzy approximations on two universes of discourse,” Information Sciences, vol. 178, no. 3, pp. 892–906, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Liu, “Rough set theory based on two universal sets and its applications,” Knowledge-Based Systems, vol. 23, no. 2, pp. 110–115, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. W. H. Xu, Y. F. Liu, and W. X. Sun, “Uncertainty measure of Atanassov's intuitionistic fuzzy T equivalence information systems,” Journal of Intelligent and Fuzzy Systems, vol. 26, no. 4, pp. 1799–1811, 2014. View at Publisher · View at Google Scholar
  23. L. Shu and X. Z. He, “Rough set model with double universe of discourse,” in Proceedings of the IEEE International Conference on Information Reuse and Integration (IRI '07), pp. 492–495, Las Vegas, Nev, USA, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. B. Sun and W. Ma, “Fuzzy rough set model on two different universes and its application,” Applied Mathematical Modelling, vol. 35, no. 4, pp. 1798–1809, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Zhang, W. Zhang, and W. Wu, “On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse,” International Journal of Approximate Reasoning, vol. 51, no. 1, pp. 56–70, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Google Scholar · View at Scopus
  27. K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Application, Physica, Heidelberg, Germany, 1999.
  28. D. Dubois and H. Prade, “Rough fuzzy sets and fuzzy rough sets,” International Journal of General Systems, vol. 17, pp. 191–209, 1990. View at Google Scholar
  29. W. H. Xu, W. X. Sun, Y. F. Liu, and W. X. Zhang, “Fuzzy rough set models over two universes,” International Journal of Machine Learning and Cybernetics, vol. 4, no. 6, pp. 631–645, 2012. View at Publisher · View at Google Scholar
  30. Z. Xu, “Intuitionistic fuzzy aggregation operators,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1179–1187, 2007. View at Publisher · View at Google Scholar · View at Scopus