On measurements of covering rough sets based on granules and evidence theory

Information Sciences

Volumn 317, Issue , 2015, Pages 329-348

  Chen, Degang ^a   Zhang, Xiaoxia ^a   Li, Wanlu ^a  

^a NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

Author keywords

Covering rough sets; Distinctive degree; Evidence theory; Knowledge granulation; Precision degree; Rough degree

Indexed keywords

APPROXIMATION ALGORITHMS; GRANULATION;

COVERING ROUGH SETS; DISTINCTIVE DEGREE; EVIDENCE THEORIES; KNOWLEDGE GRANULATION; PRECISION DEGREE; ROUGH DEGREES;

ROUGH SET THEORY;

EID: 84930170930     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2015.04.051     Document Type: Article

References (75)

1. D. Bianucci, G. Cattaneo, and D. Ciucci Entropies and co-entropies of coverings with application to incomplete information systems Fundam. Inform. 75 2007 77 105
2. Z. Bonikowski, E. Bryniarski, and U.W. Skardowska Extensions and intentions in the rough set theory Inform. Sci. 107 1998 149 167
3. G. Cattaneo, Abstract approximation spaces for rough theories, in: Rough Sets in Knowledge Discovery 1: Methodology and Applications, 1998, pp. 59-98.
4. D.G. Chen, W.L. Li, and X. Zhang Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets Int. J. Approx. Reason. 55 2014 908 923
5. D.G. Chen, C.Z. Wang, and Q.H. Hu A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets Inform. Sci. 177 2007 3500 3518
6. Y.M. Chen, K.S. Wu, and X.H. Chen An entropy-based uncertainty measurement approach in neighborhood systems Inform. Sci. 279 2014 239 250
7. D.G. Chen, W.X. Zhang, and D. Yeung Rough approximations on a complete completely distributive lattice with applications to generalized rough sets Inform. Sci. 176 13 2006 1829 1848
8. P.M. Cohn Universal Algebra 1965 Harper and Row Publishers New York
9. I. Couso, and D. Dubois Rough sets coverings and incomplete information Fundam. Inform. 180 3 2001 1001 1024
10. J.H. Dai, W.T. Wang, and J.S. Mi Uncertainty measurement for interval-valued information systems Inform. Sci. 251 2013 63 78
11. J.H. Dai, and Q. Xu Approximations and uncertainty measures in incomplete information systems Inform. Sci. 198 2012 62 80
12. D. Dubois, and H. Prade Rough fuzzy sets and fuzzy rough sets Int. J. General Syst. 17 2-3 1990 191 209
13. A.P. Dempster Upper and lower probabilities induced by a multi valued mapping Ann. Math. Stat. 1967 325 339
14. I. Duntsch, and G. Gediga Uncertainty measures of rough set prediction Artif. Intell. 106 1998 109 137
15. S. Greco, B. Matarazzo, and R. Slowinski A new rough set approach to multi-criteria and multi-attribute classification Lecture Notes Artif. Intell. 1424 1998 60 67
16. J. Hu, G. Wang, and Q. Zhang Uncertainty measure of covering generated rough set Proceedings of the 2006 IEEE/WIC/ACM international conference on Web Intelligence and Intelligent Agent Technology 2006 IEEE Computer Society 498 504
17. M. Kryszkiewicz Rough set approach to incomplete information systems Inform. Sci. 112 1998 39 49
18. T.J. Li Rough approximation operators in covering approximation spaces Rough Sets and Current Trends in Computing 2006 Springer Berlin, Heidelberg 174 182
19. F. Li, and Y. Yin Approaches to knowledge reduction of covering decision systems based on information theory Inform. Sci. 179 11 2009 1694 1704
20. J.Y. Liang, K.S. Chin, C.Y. Dang, and R.C.M. Yam A new method for measuring uncertainty and fuzziness in rough set theory Int. J. General Syst. 31 2002 331 342
21. J.Y. Liang, J.H. Wang, and Y.H. Qian A new measure of uncertainty based on knowledge granulation for rough sets Inform. Sci. 179 2009 458 470
22. J. Liu, Z.H. Liao, The sixth type of covering-based rough sets, in: IEEE International Conference on IEEE Granular Computing, GrC 2008, 2008, pp. 438-441.
23. G.L. Liu, and Y. Sai A comparison of two types of rough sets induced by coverings Int. J. Approx. Reason. 50 3 2009 521 528
24. F. Min, H. He, Y. Qian, and W. Zhu Test-cost-sensitive attribute reduction Inform. Sci. 181 2011 4928 4942
25. Z. Pawlak Rough sets Int. J. Comput. Inform. Sci. 11 1982 341 356
26. Z. Pawlak, and A. Skowron Rough sets: some extensions Inform. Sci. 177 2006 28 40
27. Z. Pawlak, and A. Skowron Rudiments of rough sets Inform. Sci. 177 2007 3 27
28. Z. Pawlak, and A. Skowron Rough sets and boolean reasoning Inform. Sci. 177 2007 41 73
29. Z. Pawlak, Rough sets: theoretical aspects of reasoning about data, system theory, in: Knowledge Engineering and Problem Solving, vol. 9, 1991.
30. W. Pedrycz, and G. Vukovich Granular neural networks Neurocomputing 36 1 2001 205 224
31. W. Pedrycz, Associations and rules in data mining: a linkage analysis, in: Proceedings of the 2002 IEEE International Conference 2, 2002, pp. 867-871.
32. W. Pedrycz Granular Computing: Analysis and Design of Intelligent Systems 2013 CRC Press/Francis Taylor Boca Raton
33. J.A. Pomykala Approximation operations in approximation space Bull. Polish Acad. Sci.: Math. 35 1987 653 662
34. Y.H. Qian, and J.Y. Liang Combination entropy and combination granulation in rough set theory Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 16 2008 179 193
35. Y. H Qian, J. Y Liang, and W. Pedrycz Positive approximation: an accelerator for attribute reduction in rough set theory Artif. Intell. 174 9 2010 597 618
36. Y. H Qian, J. Y Liang, and W. Pedrycz An efficient accelerator for attribute reduction from incomplete data in rough set framework Pattern Recogn. 44 8 2011 1658 1670
37. K.Y. Qin, Y. Gao, Z. Pei, On covering rough sets, in: J.T. Yao et al. (Eds.), RSKT, LNCS (LNAI), vol. 4481, 2007, pp. 34-41.
38. P. Samanta, and M.K. Chakraborty Covering Based Approaches to Rough Sets and Implication Lattices Rough Sets, Fuzzy Sets, Data Mining and Granular Computing 2009 Springer Berlin, Heidelberg
39. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton
40. Z.H. Shi, and Z.T. Gong The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models Inform. Sci. 180 19 2010 3745 3763
41. A. Skowron, and J. Grzymala-Busse From rough set theory to evidence theory R.R. Yager, M. Fedrizzi, J. Kacprzyk, Advance in the Dempster-Shafer Theory of Evidence 1994 Wiley NewYork 193 236
42. A. Skowron Tolerance approximation spaces Fundam. Inform. 27 1996 245 253
43. R. Slowinski, and D. Vanderpooten A generalized definition of rough approximations based on similarity IEEE Trans. Knowl. Data Eng. 12 2 2000 331 336
44. M.L. Song, and W. Pedrycz From local neural networks to granular neural networks: a study in information granulation Neurocomputing 74 18 2011 3931 3940
45. E.C.C.C. Tsang, D.G. Chen, J. Lee, et al., On the upper approximations of covering generalized rough sets, in: Proc. 3rd International Conf. Machine Learning and Cybernetics, 2004, pp. 4200-4203.
46. E.C.C.C. Tsang, D.G. Chen, and D.S. Yeung Approximations and reducts with covering generalized rough sets Comput. Math. Appl. 56 2008 279 289
47. C.Z. Wang, Q. He, and D.G. Chen A novel method for attribute reduction of covering decision systems Inform. Sci. 254 2014 181 196
48. S. P Wang, W. Zhu, and Q.X. Zhu Four matroidal structures of covering and their relationships with rough sets Int. J. Approx. Reason. 54 2013 1361 1372
49. M.J. Wierman Measuring uncertainty in rough set theory Int. J. General Syst. 28 1999 283 297
50. W.Z. Wu, Y. Leung, and W.X. Zhang Connections between rough set theory and Dempster-Shafer theory of evidence Int. J. General Syst. 31 2002 405 430
51. W.Z. Wu, M. Zhang, H.Z. Li, and J.S. Mi Knowledge reduction in random information systems via Dempster-Shafer theory of evidence Inform. Sci. 174 2005 143 164
52. W. Wu, and W. Zhang Constructive and axiomatic approaches of fuzzy approximation operators Inform. Sci. 159 2004 233 254
53. U. Wybraniec-Skardowska On a generalization of approximation space Bull. Polish Acad. Sci.: Math. 37 1989 51 61
54. T. Yang, and Q.G. Li Reduction about approximation spaces of covering generalized rough sets Int. J. Approx. Reason. 51 3 2010 335 345
55. Y.Y. Yao Relational interpretations of neighborhood operators and rough set approximation operators Inform. Sci. 101 1998 239 259
56. Y.Y. Yao, and P.J. Lingras Interpretations of belief functions in the theory of rough sets Inform. Sci. 104 1998 81 106
57. Y.Y. Yao, On generalizing rough set theory, in: Proceedings of the Ninth International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, LNCS (LNAI) 2639, 2003, pp. 44-51.
58. Y.Y. Yao, Y.H. Chen, Subsystem based generalizations of rough set approximations, in: Proceedings of the Fifteenth International Symposium on Foundations of Intelligent Systems, LNCS (LNAI) 3488, 2005, pp. 210-218.
59. Y.Y. Yao, and P.J. Lingras Interpretations of belief functions in the theory of rough sets Inform. Sci. 104 1998 81 106
60. Y.Y. Yao, and B.X. Yao Covering based rough set approximations Inform. Sci. 200 2012 91 107
61. Y.Y. Yao Probabilistic approaches to rough sets Expert Syst. 20 5 2003 287 297
62. Z. Yun, X. Ge, and X. Bai Axiomatization and conditions for neighborhoods in a covering to form a partition Inform. Sci. 181 9 2011 1735 1740
63. W. Zakowski Approximations in the space (U, Π) Demonstr. Math. 16 1983 761 769
64. W.X. Zhang, W.Z. Wu, J.Y. Liang, and D.Y. Li Theory and Method of Rough Sets 2001 Science Press Beijing
65. W. Zhu, and F.Y. Wang Reduction and axiomization of covering generalized rough sets Inform. Sci. 152 2003 217 230
66. W. Zhu, and F.Y. Wang On three types of covering-based rough sets IEEE Trans. Knowl. Data Eng. 19 8 2007 1131 1144
67. W. Zhu Topological approaches to covering rough sets Inform. Sci. 177 6 2007 1499 1508
68. W. Zhu Relationship between generalized rough sets based on binary relation and covering Inform. Sci. 179 3 2009 210 225
69. W. Zhu Relationship among basic concepts in covering-based rough sets Inform. Sci. 179 2009 2478 2486
70. W. Zhu Rough matroids based on relations Inform. Sci. 232 2013 241 252
71. P. Zhu, and Q.Y. Wen Information-theoretic measures associated with rough set approximations Inform. Sci. 212 2012 33 43
72. P. Zhu, and Q.Y. Wen Entropy and co-entropy of a covering approximation space Int. J. Approx. Reason. 53 2012 528 540
73. W. Zhu, F.Y. Wang, Binary relation based rough set, in: Proceeding Third International Conference of Fuzzy Systems and Knowledge Discovery (FSKD' 06), 2006, pp. 276-285.
74. W. Zhu, and S. Wang Rough matroid Granular Comput. 2011 817 822
75. W.P. Ziarko, and Y. Tao Proceedings of the 2nd International Conference on Rough Sets and Current Trends in Computing (RSCTC'2000), Banff, Canada Lecture Notes in Artificial Intelligence vol. 2005 2001 Springer-Verleg Heidelberg