Topological properties in covering-based rough sets

Proceedings - Fourth International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2007

Volumn 1, Issue , 2007, Pages 289-293

  Zhu, William ^a,b   Wang, Fei Yue ^b,c  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b INSTITUTE OF AUTOMATION   (China)

^c University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COVERING BASED ROUGH SETS; ROUGH SET MODELS;

APPROXIMATION ALGORITHMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; TOPOLOGY;

ROUGH SET THEORY;

EID: 44049091239     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FSKD.2007.592     Document Type: Conference Paper

References (46)

1. Z. Bonikowski, E. Bryniarski, and U. WybraniecSkardowska. Extensions and intentions in the rough set theory. Information Sciences, 107:149-167, 1998.
2. G. Cattaneo. Abstract approximation spaces for rough theorie. In Rough Sets in Knowledge Discovery 1: Methodology and Applications, pages 59-98,1998.
3. M. Kondo. On the structure of generalized rough sets. Information Sciences, 176(5):589-600,2006.
4. T. Y. Lin. From rough sets to soft computing: Introduction. Information Sciences, 104(1-2): 1-2,1998.
5. T. Y. Lin. Granular computing - structures, representations, and applications. In LNAI, volume 2639, pages 16-24,2003.
6. T. Y. Lin and Q. Liu. Rough approximate operators: axiomatic rough set theory. In W. Ziarko, editor, Rough Sets, Fuzzy Sets and Knowledge Discovery, pages 256-260. Springer, 1994.
7. W.-J. Liu. Topological space properties of rough sets. In Proceedings of the Third International Conference on Machine Learning and Cybernetics, pages 26-29, August 2004.
8. S. Pal and P. Mitra. Case generation using rough sets with fuzzy representation. IEEE Trans. On Knowledge and Data Engineering, 16(3):292-300, 2004.
9. Z. Pawlak. Rough sets. Internat. J. Comput. Inform. Sci., 11:341-356, 1982.
10. Z. Pawlak. Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston, 1991.
11. L. Polkowski and A. Skowron, editors. Rough sets and current trends in computing, volume 1424. Springer, 1998.
12. L. Polkowski and A. Skowron, editors. Rough sets in knowledge discovery, volume 1. Heidelberg: Physica-Verlag, 1998.
13. L. Polkowski and A. Skowron, editors. Rough sets in knowledge discovery, volume 2. Heidelberg: Physica-Verlag, 1998.
14. J. Pomykala. Approximation, similarity and rough constructions. In ILLC Prepublication series, University of Amsterdam, volume CT-93-07,1993.
15. K. Qin and Z. Pei. On the topological properties of fuzzy rough sets. Fuzzy Sets and Systems, 151(3):601-613, May 2005.
16. A. Skowron and J. Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27:245-253,1996.
17. R. Slowinski and D. Vanderpooten. A generalized definition of rough approximations based on similarity. IEEE Trans. On Knowledge and Data Engineering, 12(2):331336,2000.
18. F.-Y. Wang. Outline of a computational theory for linguistic dynamic systems: Toward computing with words. International Journal of Intelligent Control and Systems, 2(2):211224,1998.
19. F.-Y. Wang. On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis. Information Sciences, 171(1-3):233-259, 2005.
20. Y. Yao. A comparative study of fuzzy sets and rough sets. Information Sciences, 109:227-242, 1998.
21. Y. Yao. Constructive and algebraic methods of theory of rough sets. Information Sciences, 109:21-47, 1998.
22. Y. Yao. On generalizing pawlak approximation operators. In LNAI, volume 1424, pages 298-307, 1998.
23. Y. Yao. A partition model of granular computing. LNCS, 3100:232-253, August 2004.
24. Y. Yao and N. Zhong. Potential applications of granular computing in knowledge discovery and data mining. In Proceedings of World Multiconference on Systemics, Cybernetics and Informatics, pages 573-580,1999.
25. Y. Y. Yao. Granular computing: basic issues and possible solutions. In Proceedings of the 5th Joint Conference on Information Sciences, volume 1, pages 186-189, 2000.
26. D. Yeung, D. Chen, E. Tsang, J. Lee, and W. Xizhao. On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems, 13(3):343-361, June 2005.
27. L. Zadeh. The concept of a linguistic variable and its application to approximate reasoning - I. Information Sciences, 8:199-249, 1975.
28. L. Zadeh. The concept of a linguistic variable and its application to approximate reasoning - II. Information Sciences, 8:301-357, 1975.
29. L. Zadeh. The concept of a linguistic variable and its application to approximate reasoning - III. Information Sciences, 9:43-80, 1975.
30. L. Zadeh. Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 4:103-111, 1996.
31. L.A.Zadeh. Fuzzy sets. Information and Control, 8:338353,1965.
32. W. Zakowski. Approximations in the space (u, π). Demonstratio Mathematica, 16:761-769, 1983.
33. B. Zhang and L. Zhang. Theory and Application of Problem Solving. Elsevier Science Publishers B. V., Noth-Holland, 1992.
34. L. Zhang and B. Zhang. The quotient space theory of problem solving. In RSFDGrC 2003, volume 2639 of LNCS, pages 11-15,2003.
35. N. Zhong. Rough sets in knowledge discovery and data mining. Journal of Japan Society for Fuzzy Theory and Systems, 13(6):581-591,2001.
36. N. Zhong, J. Z. Dong, and S. Ohsuga. Using rough sets with heuristics to feature selection. Journal of Intelligent Information Systems, 16(3):199-214, 2001.
37. N. Zhong, Y. Yao, and M. Ohshima. Peculiarity oriented multidatabase mining. IEEE Trans. On Knowledge and Data Engineering, 15(4):952-960, 2003.
38. F. Zhu and H.-C. He. The axiomization of the rough set. Chinese Journal of Computers,23(3):330-333, March 2000.
39. W. Zhu and F.-Y. Wang. Reduction and axiomization of covering generalized rough sets. Information Sciences, 152:217-230, 2003.
40. W. Zhu and F.-Y. Wang. Relationships among three types of covering rough sets. In IEEE GrC 2006, pages 43-48, May 2006.
41. W. Zhu and F.-Y. Wang. Covering based granular computing for conflict analysis. In IEEE ISI 2006, volume 3975 of LNCS, pages 566-571,2006.
42. W. Zhu and F.-Y. Wang. Binary relation based rough set. In IEEE FSKD 2006, volume 4223 of LNAI, pages 276-285, 2006.
43. W. Zhu and F.-Y. Wang. Properties of the first type of covering-based rough sets. In Proceedings of DM Workshop 06, ICDM 06, Hong Kong, China, December 18, 2006, pages 407-411, 2006.
44. W. Zhu. Properties of the second type of covering-based rough sets. In Workshop Proceedings of GrC&BI 06, IEEE WI06, Hong Kong, China, December 18, 2006, pages 494-497, 2006.
45. W. Zhu. Properties of the fourth type of covering-based rough sets. In HIS'06, AUT Technology Park, Auckland, New Zealand, December 13-15, 2006, pages 43-43, 2006.
46. W. Zhu. Topological approaches to covering rough sets. Information Sciences, 177(6): 1499-1508, 2007.