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Journal of Applied Mathematics
Volume 2012, Article ID 429737, 16 pages
http://dx.doi.org/10.1155/2012/429737
Research Article

Matroidal Structure of Rough Sets Based on Serial and Transitive Relations

Yanfang Liu and William Zhu

Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

Received 2 August 2012; Accepted 5 November 2012

Academic Editor: Hector Pomares

Copyright © 2012 Yanfang Liu and William Zhu. 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 Zentralblatt MATH
  2. S. Calegari and D. Ciucci, “Granular computing applied to ontologies,” International Journal of Approximate Reasoning, vol. 51, no. 4, pp. 391–409, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. A. Hall and G. Holmes, “Benchmarking attribute selection techniques for discrete class data mining,” IEEE Transactions on Knowledge and Data Engineering, vol. 15, no. 6, pp. 1437–1447, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. D. Q. Miao, Y. Zhao, Y. Y. Yao, H. X. Li, and F. F. Xu, “Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model,” Information Sciences, vol. 179, no. 24, pp. 4140–4150, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. F. Min, H. He, Y. Qian, and W. Zhu, “Test-cost-sensitive attribute reduction,” Information Sciences, vol. 18, pp. 4928–4942, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Zhang, G. Qiu, and W. Wu, “A general approach to attribute reduction in rough set theory,” Science in China Series F, vol. 50, no. 2, pp. 188–197, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Chen, D. Miao, and R. Wang, “A rough set approach to feature selection based on ant colony optimization,” Pattern Recognition Letters, vol. 31, no. 3, pp. 226–233, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Dai and Q. Xu, “Approximations and uncertainty measures in incomplete information systems,” Information Sciences, vol. 198, pp. 62–80, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. Kryszkiewicz, “Rough set approach to incomplete information systems,” Information Sciences, vol. 112, no. 1–4, pp. 39–49, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Q. Liu and J. Wang, “Semantic analysis of rough logical formulas based on granular computing,” in Proceedings of the IEEE International Conference on Granular Computing, pp. 393–396, May 2006. View at Scopus
  11. K. Qin, J. Yang, and Z. Pei, “Generalized rough sets based on reflexive and transitive relations,” Information Sciences, vol. 178, no. 21, pp. 4138–4141, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. Slowinski and D. Vanderpooten, “A generalized definition of rough approximations based on similarity,” IEEE Transactions on Knowledge and Data Engineering, vol. 12, no. 2, pp. 331–336, 2000. View at Google Scholar · View at Scopus
  13. Y. Y. Yao, “Constructive and algebraic methods of the theory of rough sets,” Information Sciences, vol. 109, no. 1–4, pp. 21–47, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. Y. Yao, “Relational interpretations of neighborhood operators and rough set approximation operators,” Information Sciences, vol. 111, no. 1–4, pp. 239–259, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Z. Bonikowski, E. Bryniarski, and U. Wybraniec-Skardowska, “Extensions and intentions in the rough set theory,” Information Sciences, vol. 107, no. 1–4, pp. 149–167, 1998. View at Google Scholar · View at Scopus
  16. 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
  17. 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
  18. H. Lai, Matroid Theory, Higher Education Press, Beijing, China, 2001.
  19. Y. Liu and W. Zhu, “Characteristic of partition-circuit matroid through approximation number,” in Proceedings of the IEEE International Conference on Granular Computing, pp. 376–381, 2012.
  20. Y. Liu, W. Zhu, and Y. Zhang, “Relationship between partition matroid and rough set through k-rank matroid,” Journal of Information and Computational Science, vol. 8, pp. 2151–2163, 2012. View at Google Scholar
  21. J. Tang, K. She, and W. Zhu, “Matroidal structure of rough sets from the viewpoint of graph theory,” Journal of Applied Mathematics, vol. 2012, Article ID 973920, 27 pages, 2012. View at Publisher · View at Google Scholar
  22. S. Wang, Q. Zhu, W. Zhu, and F. Min, “Matroidal structure of rough sets and its characterization to attribute reduction,” Knowledge-Based Systems, vol. 36, pp. 155–161, 2012. View at Publisher · View at Google Scholar
  23. W. Zhu and S. Wang, “Matroidal approaches to generalized rough sets based on relations,” International Journal of Machine Learning and Cybernetics, vol. 2, pp. 273–279, 2011. View at Publisher · View at Google Scholar
  24. S. Zhang, X. Wang, T. Feng, and L. Feng, “Reduction of rough approximation space based on matroid,” in Proceedings of the International Conference on Machine Learning and Cybernetics, vol. 2, pp. 267–272, 2011.
  25. S. Wang and W. Zhu, “Matroidal structure of covering-based rough sets through the upper approximation number,” International Journal of Granular Computing, Rough Sets and Intelligent Systems, vol. 2, pp. 141–148, 2011. View at Publisher · View at Google Scholar
  26. S. Wang, Q. Zhu, W. Zhu, and F. Min, “Quantitative analysis for covering-based rough sets through the upper approximation number,” Information Sciences, vol. 220, pp. 483–491, 2013. View at Google Scholar
  27. M. Aigner and T. A. Dowling, “Matching theory for combinatorial geometries,” Transactions of the American Mathematical Society, vol. 158, pp. 231–245, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. H. Mao, “The relation between matroid and concept lattice,” Advances in Mathematics, vol. 35, pp. 361–365, 2006. View at Google Scholar
  29. F. Matúš, “Abstract functional dependency structures,” Theoretical Computer Science, vol. 81, no. 1, pp. 117–126, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. 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
  31. P. Rajagopal and J. Masone, Discrete Mathematics for Computer Science, Saunders College, Toronto, Canada, 1992.
  32. J. Kortelainen, “On relationship between modified sets, topological spaces and rough sets,” Fuzzy Sets and Systems, vol. 61, no. 1, pp. 91–95, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  33. L. Yang and L. Xu, “Topological properties of generalized approximation spaces,” Information Sciences, vol. 181, no. 17, pp. 3570–3580, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  34. J. G. Oxley, Matroid Theory, Oxford University Press, 1993.