A comparison of two types of rough sets induced by coverings

International Journal of Approximate Reasoning

Volumn 50, Issue 3, 2009, Pages 521-528

  Liu, Guilong ^a   Sai, Ying ^b  

^a BEIJING LANGUAGE AND CULTURE UNIVERSITY   (China)

^b SHANDONG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Approximation operators; Coverings; Generalized rough sets; Granular computing; Rough sets; Topology

Indexed keywords

FUZZY SETS; GRANULAR COMPUTING;

APPROXIMATION OPERATORS; AXIOMATIC SYSTEMS; COVERINGS; GENERALIZED ROUGH SETS; KNOWLEDGE DISCOVERY IN DATABASE; LOWER AND UPPER APPROXIMATIONS; ROUGH SET MODELS; ROUGH SETS;

ROUGH SET THEORY;

EID: 60849093738     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2008.11.001     Document Type: Article

References (41)

1. Bonikowski Z., Bryniarski E., and Wybraniec U. Extensions and intentions in the rough set theory. Information Sciences 107 (1998) 149-167
2. Chen D., Zhang W., Yeung D., and Tsang E. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Information Sciences 176 (2006) 1829-1848
3. Chen D., Wang C., and Hu Q. A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Information Sciences 177 (2007) 3500-3518
4. Dai J.H. Rough 3-valued algebras. Information Sciences 178 (2008) 1986-1996
5. Dubois D., and Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17 (1990) 191-209
6. Eric C.C.T., Chen D., and Yeung D.S. Approximations and reducts with covering generalized rough sets. Computers and Mathematics with Applications 56 (2008) 279-289
7. Kelley J.L. General topology. Graduate Texts in Mathematics vol. 27 (1955), Springer-Verlag
8. Kondo M. Algebraic approach to generalized rough sets. Lecture Notes in Artificial Intelligence 3641 (2005) 132-140
9. Kondo M. On the structure of generalized rough sets. Information Sciences 176 (2006) 589-600
10. Li T.J., Leung Y., and Zhang W.X. Generalized fuzzy rough approximation operators based on fuzzy coverings. International Journal of Approximate Reasoning 48 3 (2008) 836-856
11. Liu G.L. The axiomatization of the rough set upper approximation operations. Fundamenta Informaticae 69 (2006) 331-342
12. Liu G.L. Generalized rough sets over fuzzy lattices. Information Sciences 178 (2008) 1651-1662
13. Liu G.L. Axiomatic systems for rough sets and fuzzy rough sets. International Journal of Approximate Reasoning 48 (2008) 857-867
14. Liu G.L., and Zhu W. The algebraic structures of generalized rough set theory. Information Sciences 178 (2008) 4105-4113
15. Mi J.S., and Zhang W.X. An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160 (2004) 235-249
16. Pawlak Z. Rough sets. International Journal of Computer and Information Sciences 11 (1982) 341-356
17. Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic Publishers, Boston
18. Pawlak Z., and Skowron A. Rudiments of rough sets. Information Sciences 177 1 (2007) 3-27
19. Pawlak Z., and Skowron A. Rough sets: some extensions. Information Sciences 177 1 (2007) 28-40
20. Pawlak Z., and Skowron A. Rough sets and boolean reasoning. Information Sciences 177 1 (2007) 41-73
21. Qi G., and Liu W. Rough operations on Boolean algebras. Information Sciences 173 (2005) 49-63
22. Radzikowska A.M., and Kerre E.E. A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126 (2002) 137-155
23. A.M. Radzikowska, E.E. Kerre, Fuzzy rough sets based on residuated lattices, in: Transactions on Rough Sets, vol. 3135, LNCS, 2004, pp. 278-296.
24. Skowron A., and Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245-253
25. Slowinski R., and Vanderpooten D. A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12 2 (1990) 331-336
26. Wu W.Z., Mi J.S., and Zhang W.X. Generalized fuzzy rough sets. Information Sciences 151 (2003) 263-282
27. Wu W.Z., and Zhang W.X. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences 159 (2004) 233-254
28. Wu W.Z., Leung Y., and Mi J.S. On characterizations of (I, T)-fuzzy rough approximation operators. Fuzzy Sets and Systems 154 (2005) 76-102
29. W.Z. Wu, W.X. Zhang, Rough set approximations vs. measurable spaces, in: IEEE International Conference on Granular Computing, 2006, pp. 329-332.
30. Xu W.H., and Zhang W.X. Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets and Systems 158 (2007) 2443-2455
31. J.T. Yao, A ten-year review of granular computing, in: Proceedings of 2007 IEEE International Conference on Granular Computing, 2007, pp. 734-739.
32. Yao Y.Y. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15 (1996) 291-317
33. Yao Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111 1-4 (1998) 239-259
34. Yao Y.Y. Constructive and algebraic methods of theory of rough sets. Information Sciences 109 (1998) 21-47
35. Yao Y.Y., and Lin T.Y. Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing, An International Journal 2 (1996) 103-120
36. Zhang H., Liang H., and Liu D. Two new operators in rough set theory with applications to fuzzy sets. Information Sciences 166 1-4 (2004) 147-165
37. Zhu W., and Wang F.Y. Reduction and axiomization of covering generalized rough sets. Information Sciences 152 (2003) 217-230
38. Zhu W. Topological approaches to covering rough sets. Information Sciences 177 6 (2007) 1499-1508
39. Zhu W., and Wang F.Y. On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering 19 8 (2007) 1131-1144
40. Zhu W. Generalized rough sets based on relations. Information Sciences 177 22 (2007) 4997-5011
41. Zhu W. Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179 (2009) 210-225