Rough matroid

Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011

Volumn , Issue , 2011, Pages 817-822

  Zhu, William ^a   Wang, Shiping ^b  

^a MINNAN NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Poset matroid; Rough greedoid; Rough matroid

Indexed keywords

GENERALIZED ROUGH SET; GREEDOIDS; LOWER AND UPPER APPROXIMATIONS; ROUGH SET;

GRANULAR COMPUTING; MATRIX ALGEBRA; ROUGH SET THEORY;

COMBINATORIAL MATHEMATICS;

EID: 84863060737     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/GRC.2011.6122704     Document Type: Conference Paper

References (39)

1. G. Liu, "Axiomatic systems for rough sets and fuzzy rough sets," International Journal of Approximate Reasoning, vol. 48, no. 3, pp. 857-867, 2008.
2. W. Wu and W. Zhang, "Constructive and axiomatic approaches of fuzzy approximation operators," Information Sciences, vol. 159, no. 3-4, pp. 233-254, Feb. 2004.
3. Y. Zhang, J. Li, and W. Wu, "On axiomatic characterizations of three pairs of covering based approximation operators,"Information Sciences, vol. 180, no. 2, pp. 274-287, 2010.
4. W. Zhu and F. Wang, "On three types of covering rough sets,"IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 8, pp. 1131-1144, 2007.
5. A. Skowron and J. Stepaniuk, "Tolerance approximation spaces," Fundamenta Informaticae, vol. 27, pp. 245-253, 1996.
6. 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.
7. C. Wu, X. Hu, and J. Yang, "On blocks and coverings based on semi-equivalence relation in pansystems methodology,"Kybernetes, vol. 37, no. 6, pp. 739-748, 2008.
8. W. Zhu, "Generalized rough sets based on relations," Information Sciences, vol. 177, no. 22, pp. 4997-5011, 2007. (Pubitemid 47331457)
9. G. Liu and Y. Sai, "Invertible approximation operators of generalized rough sets and fuzzy rough sets," Information Sciences, vol. 180, no. 11, pp. 2221-2229, 2010.
10. W. Zhu, "Topological approaches to covering rough sets,"Information Sciences, vol. 177, no. 6, pp. 1499-1508, 2007. (Pubitemid 46037660)
11. W. Zhu and S. Wang, "Matroidal approaches to generalized rough sets based on relations," to appear in International Journal of Machine Learning and Cybernetics, 2011.
12. W. Bartol, J. Miro, K. Pioro, and F. Rossello, "On the coverings by tolerance classes," Information Sciences, vol. 166, no. 1-4, pp. 193-211, 2004.
13. D. Bianucci, G. Cattaneo, and D. Ciucci, "Entropies and co-entropies of coverings with application to incomplete information systems," Fundamenta Informaticae, vol. 75, no. 1-4, pp. 77-105, 2007. (Pubitemid 46381787)
14. W. Zhu, "Relationship among basic concepts in covering-based rough sets," Information Sciences, vol. 179, no. 14, pp. 2478-2486, 2009.
15. -, "Relationship between generalized rough sets based on binary relation and covering," Information Sciences, vol. 179, no. 3, pp. 210-225, 2009.
16. W. Zhu and F. Wang, "Reduction and axiomization of covering generalized rough sets," Information Sciences, vol. 152, no. 1, pp. 217-230, 2003.
17. M. Diker, "Textural approach to generalized rough sets based on relations," Information Sciences, vol. 180, no. 8, pp. 1418-1433, 2010.
18. Z. Meng and Z. Shi, "A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets," Information Sciences, vol. 179, no. 16, pp. 2774-2793, 2009.
19. Y. Ouyang, Z. Wang, and H. Zhang, "On fuzzy rough sets based on tolerance relations," Information Sciences, vol. 180, no. 4, pp. 532-542, 2010.
20. 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.
21. D. Slezak, "Foundations of entropy based bayesian networks: theoretical results and rough set based extraction from data."[Online]. Available: citeseer.ist.psu.edu/333748.html
22. D. Slezak and W. Ziarko, "The investigation of the bayesian rough set model," International Journal of Approximate Reasoning, vol. 40, pp. 81-91, 2006.
23. Y. Yamauchi and M. Mukaidono, "Probabilistic inference and bayesian theorem on rough sets," in Rough Sets and Current Trends in Computing, ser. LNCS, vol. 2005, 2000, pp. 73-81.
24. Y. Yao, "Three-way decisions with probabilistic rough sets,"Information Sciences, vol. 180, no. 3, pp. 341-353, 2010.
25. 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.
26. Z. Gong, B. Sun, and D. Chen, "Rough set theory for the interval-valued fuzzy information systems," Information Sciences, vol. 178, no. 8, pp. 1968-1985, 2008.
27. R. Jensen and Q. Shen, "Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 12, pp. 1457-1471, 2004. (Pubitemid 40010921)
28. T. Li and W. Zhang, "Rough fuzzy approximations on two universes of discourse," Information Sciences, vol. 178, no. 3, pp. 892-906, 2008. (Pubitemid 350050972)
29. S. Wang, F. Min, and W. Zhu, "Quantitative analysis for covering-based rough sets on boolean algebra," Submitted to Information Sciences, 2011.
30. S. Wang and W. Zhu, "Matroidal structure of covering-based rough sets through the upper approximation number,"to appear in International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2011.
31. T. Deng, Y. Chen, W. Xu, and Q. Dai, "A novel approach to fuzzy rough sets based on a fuzzy covering," Information Sciences, vol. 177, no. 11, pp. 2308-2326, 2007. (Pubitemid 46435493)
32. T. Hong, L. Tseng, and B. Chien, "Mining from incomplete quantitative data by fuzzy rough sets," Expert Systems with Applications, vol. 37, pp. 2644-2653, 2010.
33. O. Kazanci, S. Yamak, and B. Davvaz, "The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets," Information Sciences, vol. 178, no. 10, pp. 2349-2359, 2008.
34. J. Li, "Topological methods on the theory of covering generalized rough sets," Pattern Recognition and Artificial Intelligence (in Chinese), vol. 17, no. 1, pp. 7-10, 2004.
35. K. Qin and Z. Pei, "On the topological properties of fuzzy rough sets," Fuzzy Sets and Systems, vol. 151, no. 3, pp. 601-613, May 2005. (Pubitemid 40305080)
36. A. Skowron, "On topology in information system," Bull. Polish Acad. Sci. Math., vol. 36, pp. 477-480, 1988.
37. P. Rajagopal and J. Masone, Discrete mathematics for computer science. Saunders College, Canada, 1992.
38. H. Lai, Matroid theory. Higher Education Press, 2001.
39. Y. Li, "Some researches on fuzzy matroids," Ph.D. dissertation, Shaanxi Normal University, 2007.