Matroidal structure of rough sets and its characterization to attribute reduction

Knowledge-Based Systems

Volumn 36, Issue , 2012, Pages 155-161

  Wang, Shiping ^a   Zhu, Qingxin ^a   Zhu, William ^b   Min, Fan ^b  

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

^b MINNAN NORMAL UNIVERSITY   (China)

Author keywords

2 Circuit matroid; Attribute reduction; Information system; Isomorphism; Matroid; Rank function; Rough set

Indexed keywords

ATTRIBUTE REDUCTION; ATTRIBUTE REDUCTION ALGORITHM; CLOSURE OPERATORS; DATA PREPROCESSING; EQUIVALENCE RELATIONS; GREEDY ALGORITHMS; INDEPENDENT SET; ISOMORPHISM; LINEAR INDEPENDENCE; MATROIDAL STRUCTURE; NP-HARD; RANK FUNCTIONS; ROUGH SET;

ALGORITHMS; COMBINATORIAL MATHEMATICS; INFORMATION SYSTEMS; MATRIX ALGEBRA;

ROUGH SET THEORY;

EID: 84867863748     PISSN: 09507051     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.knosys.2012.06.006     Document Type: Article

References (46)

1. P. Bosc, and O. Pivert About approximate inclusion and its axiomatization Fuzzy Sets and Systems 157 2006 1438 1454
2. D. Chen, C. Wang, and Q. Hu A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets Information Sciences 177 2007 3500 3518
3. Y. Chen, D. Miao, R. Wang, and K. Wu A rough set approach to feature selection based on power set tree Knowledge-Based Systems 24 2011 275 281
4. J. Dai, W. Wang, Q. Xu, and H. Tian Uncertainty measurement for interval-valued decision systems based on extended conditional entropy Knowledge-Based Systems 27 2012 443 450
5. D. Dubois, and H. Prade Rough fuzzy sets and fuzzy rough sets International Journal of General Systems 17 1990 191 209
6. Z. Gong, B. Sun, and D. Chen Rough set theory for the interval-valued fuzzy information systems Information Sciences 178 2008 1968 1985
7. M. Hall, and G. Holmes Benchmarking attribute selection techniques for discrete class data mining IEEE Transactions on Knowledge and Data Engineering 15 2003 1437 1447
8. Q. He, C. Wu, D. Chen, and S. Zhao Fuzzy rough set based attribute reduction for information systems with fuzzy decisions Knowledge-Based Systems 24 2011 689 696
9. Q. Hu, J. Liu, and D. Yu Mixed feature selection based on granulation and approximation Knowledge-Based Systems 21 2007 294 304
10. Q. Hu, D. Yu, J. Liu, and C. Wu Neighborhood rough set based heterogeneous feature subset selection Information Sciences 178 2008 3577 3594
11. O. Kazanci, S. Yamak, and B. Davvaz The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets Information Sciences 178 2008 2349 2359
12. M. Kondo On the structure of generalized rough sets Information Sciences 176 2006 589 600
13. M. Kryszkiewicz Rough set approach to incomplete information systems Information Sciences 112 1998 39 49
14. H. Lai Matroid Theory 2001 Higher Education Press Beijing
15. E. Lashin, A. Kozae, A.A. Khadra, and T. Medhat Rough set theory for topological spaces International Journal of Approximate Reasoning 40 2005 35 43
16. X. Li, and S. Liu Matroidal approaches to rough set theory via closure operators International Journal of Approximate Reasoning 53 2012 513 527
17. Y. Li, Some Researches on Fuzzy Matroids, Ph.D. thesis, Shaanxi Normal University, 2007 (in Chinese).
18. G. Liu Generalized rough sets over fuzzy lattices Information Sciences 178 2008 1651 1662
19. D. Miao, C. Gao, N. Zhang, and Z. Zhang Diverse reduct subspaces based co-training for partially labeled data International Journal of Approximate Reasoning 52 2011 1103 1117
20. F. Min, H. He, Y. Qian, and W. Zhu Test-cost-sensitive attribute reduction Information Sciences 181 2011 4928 4942
21. F. Min, and Q. Liu A hierarchical model for test-cost-sensitive decision systems Information Sciences 179 2009 2442 2452
22. H.S. Nguyen, S.K. Pal, and A. Skowron Rough sets and fuzzy sets in natural computing Theoretical Computer Science 412 2011 5816 5819
23. S. Pal, S. Mitra, and P. Mitra Rough-fuzzy mlp: modular evolution, rule generation, and evaluation IEEE Transactions on Knowledge and Data Engineering 15 2003 15 24
24. Z. Pawlak Rough sets International Journal of Computer and Information Sciences 11 1982 341 356
25. Y. Qian, J. Liang, W. Pedrycz, and C. Dang Positive approximation: an accelerator for attribute reduction in rough set theory Artificial Intelligence 174 2010 597 618
26. K. Qin, J. Yang, and Z. Pei Generalized rough sets based on reflexive and transitive relations Information Sciences 178 2008 4138 4141
27. A. Skowron, J. Stepaniuk, and R. Swiniarski Modeling rough granular computing based on approximation spaces Information Sciences 184 2012 20 43
28. H. Thiele On axiomatic characterisations of crisp approximation operators Information Sciences 129 2000 221 226
29. S. Tsumoto, An approach to statistical extention of rough set rule induction, in: Rough Sets and Current Trends in Computing, volume 2005 of LNCS, 2000, pp. 362-369.
30. G. Wang, H. Yu, and D. Yang Decision table reduction based on conditional information entropy Chinese Journal of Computers 2 2002 759 766
31. S. Wang, P. Zhu, and W. Zhu Structure of covering-based rough sets International Journal of Mathematical and Computer Sciences 6 2010 147 150
32. 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 2 2011 141 148
33. S. Wang, W. Zhu, Q. Zhu, and F. Min Covering base Journal of Information and Computational Science 9 2012 1343 1355
34. W. Wu, Y. Leung, and J. Mi On characterizations of (I, T)-fuzzy rough approximation operators Fuzzy Sets and Systems 154 2005 76 102
35. Q. Xiong Modern Algebra 1984 Wuhan University Press Wuhan
36. Y. Yao Constructive and algebraic methods of theory of rough sets Information Sciences 109 1998 21 47
37. Y. Yao, and B. Yao Covering based rough set approximations Information Sciences 200 2012 91 107
38. Y. Yao, and Y. Zhao Attribute reduction in decision-theoretic rough set models Information Sciences 178 2008 3356 3373
39. D. Yeung, D. Chen, E. Tsang, J. Lee, and X. Wang On the generalization of fuzzy rough sets IEEE Transactions on Fuzzy Systems 13 2005 343 361
40. P. Zhu An axiomatic approach to the roughness measure of rough sets Fundamenta Informaticae 109 2011 463 480
41. W. Zhu Generalized rough sets based on relations Information Sciences 177 2007 4997 5011
42. W. Zhu Topological approaches to covering rough sets Information Sciences 177 2007 1499 1508
43. W. Zhu Relationship between generalized rough sets based on binary relation and covering Information Sciences 179 2009 210 225
44. W. Zhu, and F. Wang Reduction and axiomization of covering generalized rough sets Information Sciences 152 2003 217 230
45. W. Zhu, and F. Wang On three types of covering rough sets IEEE Transactions on Knowledge and Data Engineering 19 2007 1131 1144
46. W. Zhu, and S. Wang Matroidal approaches to generalized rough sets based on relations International Journal of Machine Learning and Cybernetics 2 2011 273 279