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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 973920, 27 pages
http://dx.doi.org/10.1155/2012/973920
Research Article

Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory

1School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2School of Computer Science and Engineering, XinJiang University of Finance and Economics, Urumqi 830012, China
3Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

Received 4 February 2012; Revised 30 April 2012; Accepted 18 May 2012

Academic Editor: Mehmet Sezer

Copyright © 2012 Jianguo Tang 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. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic, Boston, Mass, USA, 1991.
  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 Zentralblatt MATH
  3. J. Pomykala, Approximation, Similarity and Rough Constructions, vol. CT-93-07 of ILLC Prepublication, University of Amsterdam, 1993.
  4. R. Slowinski and D. Vanderpooten, “Similarity relation as a basis for rough approximations,” ICS Research Report 53/95, Warsaw University of Technology, 1995, Also in Advances in Machine Intelligence and Soft-Computing, P. P. Wang, Ed., pp. 17–33, Raleigh, NC, USA: Bookwrights, 1997. View at Google Scholar
  5. A. Skowron and J. Stepaniuk, “Tolerance approximation spaces,” Fundamenta Informaticae, vol. 27, no. 2-3, pp. 245–253, 1996. View at Google Scholar · View at Zentralblatt MATH
  6. E. Bryniarski, “A calculus of rough sets of the first order,” Bulletin of the Polish Academy of Sciences, vol. 36, no. 16, pp. 71–77, 1989. View at Google Scholar · View at Zentralblatt MATH
  7. J. A. Pomykała, “Approximation operations in approximation space,” Bulletin of the Polish Academy of Sciences, vol. 35, no. 9-10, pp. 653–662, 1987. View at Google Scholar · View at Zentralblatt MATH
  8. W. Zhu, “Generalized rough sets based on relations,” Information Sciences, vol. 177, no. 22, pp. 4997–5011, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. W. Zhu and F. Y. Wang, “On three types of covering-based rough sets,” IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 8, pp. 1131–1144, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Zhu and F. Y. Wang, “Reduction and axiomization of covering generalized rough sets,” Information Sciences, vol. 152, pp. 217–230, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Q. Hu, D. Yu, J. Liu, and C. Wu, “Neighborhood rough set based heterogeneous feature subset selection,” Information Sciences, vol. 178, no. 18, pp. 3577–3594, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. Y. Y. Yao, “Neighborhood systems and approximate retrieval,” Information Sciences, vol. 176, no. 23, pp. 3431–3452, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. F. Min, H. He, Y. Qian, and W. Zhu, “Test-cost-sensitive attribute reduction,” Information Sciences, vol. 181, no. 22, pp. 4928–4942, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Wang, L. Shu, and X. Ding, “Reduction of neighborhood-based generalized rough sets,” Journal of Applied Mathematics, vol. 2011, Article ID 409181, 22 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. D. Dubois and H. Prade, “Rough fuzzy sets and fuzzy rough sets,” International Journal of General Systems, vol. 17, no. 2-3, pp. 191–209, 1990. View at Google Scholar · View at Scopus
  16. G. L. Liu, “Generalized rough sets over fuzzy lattices,” Information Sciences, vol. 178, no. 6, pp. 1651–1662, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. S. Mi and W. X. 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 Zentralblatt MATH
  18. D. Pei, “A generalized model of fuzzy rough sets,” International Journal of General Systems, vol. 34, no. 5, pp. 603–613, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. W. Zhu, “A Class of covering-based fuzzy rough sets,” in Proceedings of the 4th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD '07), vol. 1, pp. 7–11, Haikou, China, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. T. J. Li, W. X. Zhang, and J. M. Ma, “Rough sets on atomic boolean lattices,” in Proceedings of IEEE International Conference on Granular Computing, vol. 1, pp. 176–179, July 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. Pawlak and A. Skowron, “Rough sets and Boolean reasoning,” Information Sciences, vol. 177, no. 1, pp. 41–73, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. Y. Y. Yao, “A comparative study of fuzzy sets and rough sets,” Information Sciences, vol. 109, no. 1–4, pp. 227–242, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. Qi and W. Liu, “Rough operations on Boolean algebras,” Information Sciences, vol. 173, no. 1–3, pp. 49–63, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. E. F. Lashin, A. M. Kozae, A. A. Abo Khadra, and T. Medhat, “Rough set theory for topological spaces,” International Journal of Approximate Reasoning, vol. 40, no. 1-2, pp. 35–43, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. W. J. Liu, “Topological space properties of rough sets,” in Proceedings of The 3rd International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2353–2355, August 2004. View at Scopus
  26. A. Wasilewska, “Topological rough algebras,” in Rough Sets and Data Mining, T. Y. Lin and N. Cercone, Eds., pp. 411–425, Kluwer Academic, Boston, Mass, USA, 1997. View at Google Scholar
  27. W. Zhu, “Topological approaches to covering rough sets,” Information Sciences, vol. 177, no. 6, pp. 1499–1508, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. D. G. Chen, W. X. Zhang, D. Yeung, and E. Tsang, “Rough approximations on a complete completely distributive lattice with applications to generalized rough sets,” Information Sciences, vol. 176, no. 13, pp. 1829–1848, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. H. R. Li, W. X. Zhang, and H. Wang, “Classification and reduction of attributes in concept lattices,” in Proceedings of IEEE International Conference on Granular Computing, pp. 142–147, May 2006. View at Scopus
  30. W. X. Zhang, Y. Y. Yao, and Y. Liang, Rough Set and Concept Lattice, Xi'an Jiaotong University Press, 2006.
  31. Y. Y. Yao and T. Y. Lin, “Generalization of rough sets using modal logics,” Intelligent Automation and Soft Computing, vol. 2, pp. 103–120, 1996. View at Google Scholar
  32. W. Zhu and S. Wang, “Matroidal approaches to generalized rough sets based on relations,” International Journal of Machine Learning and Cybernetics, vol. 2, no. 4, pp. 273–279, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. S. P. Wang, W. Zhu, and F. Min, “Transversal and function matroidal structures of covering-based rough sets,” in Rough Sets and Knowledge Technology, pp. 146–155, 2011. View at Google Scholar
  34. H. Whitney, “On the abstract properties of linear dependence,” American Journal of Mathematics, vol. 57, no. 3, pp. 509–533, 1935. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  35. R. J. Wilson, “An introduction to matroid theory,” The American Mathematical Monthly, vol. 80, pp. 500–525, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  36. W. Zhu and F. Y. Wang, “Topological properties in covering-based rough sets,” in Proceedings of the 4th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD '07), vol. 1, pp. 289–293, Haikou, China, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  37. B. Bollobás, Modern Graph Theory, vol. 184 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar
  38. D. B. West, Introduction to Graph Theory, Prentice Hall, 2nd edition, 2000.
  39. H. J. Lai, Matroid Theory, New Frontiers of Science, Higher Education Press, 2002.
  40. P. J. Cameron, “Notes on matroids and codes,” 1998.
  41. Wikipedia: Glossary of graph theory—wikipedia, the free encyclopedia, 2011.
  42. J. A. Bondy and U. S. R. Murty, Graph Theory, vol. 244 of Graduate Texts in Mathematics, Springer, 2008. View at Publisher · View at Google Scholar
  43. Y. Y. Yao, S. K. M. Wong, and T. Y. Lin, “A review of rough set models,” in Rough Sets and Data Mining, Kluwer Academic, Boston, Mass, USA, 1997. View at Google Scholar