Using one axiom to characterize rough set and fuzzy rough set approximations

Information Sciences

Volumn 223, Issue , 2013, Pages 285-296

  Liu, Guilong ^a  

^a BEIJING LANGUAGE AND CULTURE UNIVERSITY   (China)

Author keywords

Approximate reasoning; Approximation operators; Axioms; Fuzzy relations; Fuzzy rough sets; Inner products

Indexed keywords

APPROXIMATE REASONING; APPROXIMATION OPERATORS; AXIOMS; FUZZY RELATIONS; FUZZY-ROUGH SETS; INNER PRODUCT;

APPROXIMATION ALGORITHMS; FORMAL LOGIC; FUZZY SETS;

ROUGH SET THEORY;

EID: 84870251102     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2012.10.004     Document Type: Article

References (51)

1. M. Banerjee, and S.K. Pal Roughness of a fuzzy set Information Sciences 93 1996 235 246
2. R. Bello, and J.L. Verdegay Rough sets in the soft computing environment Information Sciences 212 2012 1 14
3. Z. Bonikowski Algebraic structure of rough sets W.P. Ziarko, Rough Sets Fuzzy Sets and Knowledge Discovery 1994 Springer-Verlag London 242 247
4. Z. Bonikowski, E. Bryniarski, and U. Wybraniec-Skardowska Extensions and intentions in the rough set theory Information Sciences 107 1998 149 167 (Pubitemid 128383778)
5. 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
6. X. Chen, and Q. Li Construction of rough approximations in fuzzy setting Fuzzy Sets and Systems 158 2007 2641 2653 (Pubitemid 47445752)
7. S. Comer An algebraic approach to the approximation of information Fundamenta Informaticae 14 1991 492 502
8. D. Dubois, and H. Prade Rough fuzzy sets and fuzzy rough sets International Journal of General Systems 17 1990 191 208
9. D. Dubois, and H. Prade Putting fuzzy sets and rough sets together R. Slowinski, Intelligent Decision Support 2004 Kluwer Academic Dordrecht 203 232
10. L. Guan, and G. Wang Generalized approximations defined by non-equivalence relations Information Sciences 193 2012 163 179
11. J.L. Kelley General Topology, Graduate Texts in Mathematics vol. 27 1955 Springer-Verlag
12. D. Kim, and S.Y. Bang A handwritten numeral character classification using tolerant rough set IEEE Transactions on Pattern Analysis and Machine Intelligence September 22 2000 923 937
13. T. Li, W. Zhang, J. Ma, Rough sets on atomic Boolean lattices, in: IEEE GrC2005, 2006, pp. 176-179.
14. Y. Li, J. Tang, K. Chin, X. Luo, and Y. Han Rough set-based approach for modeling relationship measures in product planning Information Sciences 193 2012 199 217
15. T.Y. Lin, Granular computing - structures, representations, and applications, in: LNAI, vol. 2639, 2003, pp. 16-24. (Pubitemid 36657931)
16. T.Y. Lin, and Q. Liu Rough approximate operators: axiomatic rough set theory W. Ziarko, Rough Sets, Fuzzy Sets and Knowledge Discovery 1994 Springer Berlin 256 260
17. G. Liu The axiomatization of the rough set upper approximation operations Fundamenta Informaticae 69 2006 331 342
18. G. Liu Generalized rough set over fuzzy lattices Information Sciences 178 2008 1651 1662
19. G. Liu Axiomatic systems for rough sets and fuzzy rough sets International Journal of Approximate Reasoning 48 2008 857 867
20. G. Liu, and Y. Sai A comparison of two types of rough sets induced by coverings International Journal of Approximate Reasoning 50 2009 521 528
21. G. Liu, and W. Zhu The algebraic structures of generalized rough set theory Information Sciences 178 2008 4105 4113
22. J. Medina Multi-adjoint property-oriented and object-oriented concept lattices Information Sciences 190 2012 95 106
23. Z. Meng, and Z. Shi Extended rough set-based attribute reduction in inconsistent incomplete decision systems Information Sciences 204 2012 44 69
24. J. Mi, Y. Leung, H. Zhao, and T. Feng Generalized fuzzy rough sets determined by a triangular norm Information Sciences 178 2008 3203 3213
25. J. Mi, and W. Zhang An axiomatic characterization of a fuzzy generalization of rough sets Information Sciences 160 2004 235 249
26. F. Min, and W. Zhu Attribute reduction of data with error ranges and test costs Information Sciences 211 2012 48 67
27. N.N. Morsi, and M.M. Yakout Axiomatics for fuzzy rough set Fuzzy Sets and Systems 100 1998 327 342
28. S. Nanda, and S. Majumdar Fuzzy rough sets Fuzzy sets and systems 45 1992 157 160
29. Z. Pawlak Rough sets International Journal of Computer and Information Sciences 11 1982 341 356
30. Z. Pawlak Rough Sets-Theoretical Aspects of Reasoning About Data 1991 Kluwer Academic Publishers Boston, MA
31. Z. Pawlak, and A. Skowron Rough sets: some extensions Information Sciences 177 2007 28 40 (Pubitemid 44556699)
32. D.W. Pei A generalized model of fuzzy rough sets International Journal of General Systems 34 2005 603 613
33. A.M. Radzikowska, and E.E. Kerre A comparative study of fuzzy rough sets Fuzzy Sets and Systems 126 2002 137 155 (Pubitemid 34116140)
34. R. Slowinski, and D. Vanderpooten A generalized definition of rough approximation IEEE Transactions on Data and Knowledge Engineering 12 2000 331 336
35. L. Wang, X. Yang, J. Yang, and C. Wu Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system Information Sciences 207 2012 66 78
36. W. Wei, J. Liang, and Y. Qian A comparative study of rough sets for hybrid data Information Sciences 190 2012 1 16
37. W. Wu, and W. Zhang Constructive and axiomatic approaches of fuzzy approximation operators Information Sciences 159 2004 233 254
38. Y. Yao Two views of the theory of rough sets in finite universes International Journal of Approximation Reasoning 15 1996 291 317 (Pubitemid 126414908)
39. Y. Yao Relational interpretations of neighborhood operators and rough set approximation operators Information Sciences 111 1998 239 259 (Pubitemid 128383897)
40. Y. Yao A comparative study of fuzzy sets and rough sets Information Sciences 109 1998 227 242
41. Y. Yao Constructive and algebraic methods of the theory of rough sets Information Sciences 109 1998 21 47
42. Y. Yao, and T.Y. Lin Generalization of rough sets using modal logic International Journal of Intelligent Automation and Soft Computing 2 1996 103 120
43. Y. Yao, B. Yao, Covering based rough set approximations, Information Sciences 200 (2012) 91-107.
44. D.S. Yeung, D. Chen, E.C.C. Tsang, J.W.T. Lee, and X. Wang On the generalization of fuzzy rough sets IEEE Transaction on Fuzzy Systems 13 2005 343 361 (Pubitemid 40914091)
45. L.A. Zadeh Fuzzy sets Information and Control 8 1965 338 353
46. X. Zhang, B. Zhou, and P. Li A general frame for intuitionistic fuzzy rough sets Information Sciences 216 2012 34 49
47. Y. Zhang, J. Li, and W. Wu On axiomatic characterizations of three pairs of covering based approximation operators Information Sciences 180 2010 274 287
48. Y. Zhang, and M. Luo On minimization of axiom sets characterizing covering-based approximation operators Information Sciences 181 2011 3032 3042
49. P. Zhu, and Q. Wen Information-Theoretic measures associated with rough set approximations Information Sciences 212 2012 33 43
50. W. Zhu Topological approaches to covering rough sets Information Sciences 177 2007 1499 1508 (Pubitemid 46037660)
51. W. Zhu Generalized rough sets based on relations Information Sciences 177 2007 4997 5011 (Pubitemid 47331457)