Relationship between partition matroid and rough set through k-rank matroid

Journal of Information and Computational Science

Volumn 9, Issue 8, 2012, Pages 2151-2163

  Liu, Yanfang ^a   Zhu, William ^a   Zhang, Yuanping ^a  

^a MINNAN NORMAL UNIVERSITY   (China)

Author keywords

K rank matroid; Partition matroid; Restriction; Rough set

Indexed keywords

CLOSURE OPERATORS; LINEAR INDEPENDENCE; LOWER AND UPPER APPROXIMATIONS; MATHEMATICAL TOOLS; RANK FUNCTIONS; RESTRICTION; ROUGH SET; UPPER APPROXIMATION;

FORMAL LOGIC; MATRIX ALGEBRA; ROUGH SET THEORY;

COMBINATORIAL MATHEMATICS;

EID: 84865144645     PISSN: 15487741     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. Z. Pawlak, Rough sets. International Journal of Computer and Information Sciences, 11 (1982), 341-356
2. H. Zhang, H. Liang, D. Liu, Two new operators in rough set theory with applications to fuzzy sets. Information Sciences, 166 (2004), 147-165
3. B. Sun, Z. Gong, D. Chen, Fuzzy rough set theory for the interval-valued fuzzy information systems. Information Sciences, 178 (2008), 2794-2815
4. W. Wu, Attribute reduction based on evidence theory in incomplete decision systems. Information Sciences, 178 (2008), 1355-1371
5. Y. Yamauchi, M. Mukaidono, Probabilistic inference and Bayesian theorem on rough sets. In: Rough Sets and Current Trends in Computing. Volume 2005 of LNCS. 2000, 73-81
6. M. Kryszkiewicz, Rough set approach to incomplete information systems. Information Sciences, 112 (1998), 39-49
7. M. Kryszkiewicz, Rules in incomplete information systems. Information Sciences, 113 (1998), 271-292
8. Q. Liu, J. Wang, Semantic analysis of rough logical formulas based on granular computing. In: Granular Computing. (2006), 393-396
9. R. Slowinski, D. Vanderpooten, A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering, 12 (2000), 331-336
10. Y. Yao, A comparative study of fuzzy sets and rough sets. Information Sciences, 109 (1998), 227-242
11. Y. Yao, Constructive and algebraic methods of theory of rough sets. Information Sciences, 109 (1998), 21-47
12. Y. Yao, On generalizing pawlak approximation operators. In: Lecture Notes in Artificial Intelligence. Volume 1424, 1998, 298-307
13. Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences, 111 (1998), 239-259
14. W. Zhu, F. Wang, Binary relation based rough set. In: Fuzzy Systems and Knowledge Discovery. Volume 4223 of LNAI. 2006, 276-285
15. Z. Bonikowski, E. Bryniarski, U. Wybraniec-Skardowska, Extensions and intentions in the rough set theory. Information Sciences, 107 (1998), 149-167
16. W. Zhu, Topological approaches to covering rough sets. Information Sciences, 177 (2007), 1499-1508
17. W. Zhu, F. Wang, Reduction and axiomization of covering generalized rough sets. Information Sciences, 152 (2003), 217-230
18. W. Zhu, F. Wang, Axiomatic systems of generalized rough sets. In: Rough Set and Knowledge Technology. Volume 4062 of LNAI. 2006, 216-221
19. W. Zhu, F. Wang, A new type of covering rough sets. In: IEEE International Conference on Intelligent Systems 2006, London, 4-6 September, 2006, 444-449
20. W. Zhu, F. Wang, Relationships among three types of covering rough sets. In: Granular Computing. 2006, 43-48
21. Y. Yao, Three-way decisions with probabilistic rough sets. Information Sciences, 180 (2010), 341-353
22. Y. Yao, The superiority of three-way decisions in probabilistic rough set models. Information Sciences, 181 (2011), 1080-1096
23. T. Deng, Y. Chen, W. Xu, Q. Dai, A novel approach to fuzzy rough sets based on a fuzzy covering. Information Sciences, 177 (2007), 2308-2326
24. Z. Gong, B. Sun, D. Chen, Rough set theory for the interval-valued fuzzy information systems. Information Sciences, 178 (2008), 1968-1985
25. R. Jensen, Q. Shen, Semantics-preserving dimensionality reduction: Rough and fuzzy-rough-based approaches. IEEE Transactions on Knowledge and Data Engineering, 16 (2004), 1457-1471
26. E. Tay, L. Shen, Economic and financial prediction using rough sets model. European Journal of Operational Research, 141 (2002), 643-661
27. D. Yamaguchi, G. Li, M. Nagai, A grey-based rough approximation model for interval data processing. Information Sciences, 177 (2007), 4727-4744
28. R. Deja, Conict analysis. International Journal of Intelligent Systems, 17 (2002), 235-253
29. Z. Pawlak, Analysis of conicts. In: Joint Conference of Information Science, 1997, 350-352
30. R. Deja, D. Slezak, Rough set theory in conict analysis. In: International Symposia on AI 2001 Workshops. Volume 2253 of LNAI, 2001, 349-353
31. X. Li, S. Tian, D. Deng, J. Chen, A method of multi-agent system conict analysis based on rough set theory. In: Granular Computing. Volume 1, 2005, 180-184
32. M. Hall, G. Holmes, Benchmarking attribute selection techniques for discrete class data mining. IEEE Transactions on Knowledge and Data Engineering, 15 (2003), 1437-1447
33. F. Min, H. He, Y. Qian, W. Zhu, Test-cost-sensitive attribute reduction. Information Sciences, 181 (2011), 4928-4942
34. Y. Qian, J. Liang, W. Pedrycz, C. Dang, Positive approximation: An accelerator for attribute reduction in rough set theory. Artificial Intelligence, 174 (2010), 597-618
35. Y. Yao, F. Wang, J. Wang, "rule + exception" strategies for knowledge management and discovery. In: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Volume 3641 of LNAI. 2005, 69-78
36. H. Lai, Matroid Theory. Higher Education Press, Beijing, 2001
37. H. Mao, The relation between matroid and concept lattice. Advance in Mathematics, 35 (2006), 361-365
38. S. Wang, 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
39. S. Wang, W. Zhu, F. Min, Transversal and function matroidal structures of covering-based rough sets. In: Rough Sets and Knowledge Technology. 2011, 146-155
40. W. Zhu, S. Wang, Matroidal approaches to generalized rough sets based on relations. International Journal of Machine Learning and Cybernetics, 2 (2011), 273-279
41. E. Lawler, Combinatorial Optimization: Networks and Matroids. Dover Publications, 2001
42. J. Edmonds, Matroids and the greedy algorithm. Mathematical Programming, 1 (1971), 127-136
43. F. Zhu, H. He, Logical properties of rough sets. In: The Fourth International Conference on High Performance Computing in the Asia-Pacific Region. Volume 2, IEEE Press, 2000, 670-671
44. F. Zhu, H. He, The axiomization of the rough set. Chinese Journal of Computers, 23 (2000), 330-333
45. T. Y. Lin, Q. Liu, Rough approximate operators: Axiomatic rough set theory. In W. Ziarko, ed.: Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer, 1994, 256-260
46. J. G. Oxley, Matroid Theory. Oxford University Press, 1993
47. G. Liu, Q. Chen, Matroid. National University of Defence Technology Press, Changsha, 1994