Can fuzzy entropies be effective measures for evaluating the roughness of a rough set?

Information Sciences

Volumn 232, Issue , 2013, Pages 143-166

  Wei, Wei ^a   Liang, Jiye ^a   Qian, Yuhua ^a   Dang, Chuangyin ^b  

^a SHANXI UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Fuzzy entropy; Fuzzy set; Granular computing; Rough set; Roughness

Indexed keywords

BOUNDARY REGIONS; EFFECTIVE MEASURES; FUZZY ENTROPY; FUZZY MEMBERSHIP; ROUGH MEMBERSHIP;

ENTROPY; FUZZY SETS; GRANULAR COMPUTING; SURFACE ROUGHNESS;

ROUGH SET THEORY;

EID: 84875435236     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2012.12.036     Document Type: Article

References (59)

1. M. Banerjee, and S.K. Pal Roughness of a fuzzy set Information Sciences 93 1996 235 246
2. T. Beaubouef, F.E. Petry, and G. Arora Information-theoretic measures of uncertainty for rough sets and rough relational databases Information Sciences 109 1998 535 563
3. D. Bhandari, and N.R. Pal Some new information measure of fuzzy sets Information Sciences 67 1993 209 228
4. D. Bianucci, G. Cattaneo, Information entropy and granulation co-entropy of partitions and coverings: a summary, in: J.F. Peters et al. (Eds.), Transactions on Rough Sets 10, LNCS 5656, 2009, pp. 15-66.
5. K. Chakrabarty, R. Biswas, and S. Nanda Fuzziness in rough sets Fuzzy Sets and Systems 110 2000 247 251
6. D. Dubois, and H. Prade Rough fuzzy sets and fuzzy rough sets International Journal of General Systems 17 1990 191 208
7. D. Dubois, and H. Prade Putting fuzzy sets and rough sets together R. Slowiniski, Intelligent Decision Support 1992 Kluwer Academic Dordrecht 203 232
8. J.L. Fan, and W.X. Xie Distance measure and induced fuzzy entropy Fuzzy Sets and Systems 104 1999 305 314
9. J.L. Fan, Y.L. Ma, and W.X. Xie On some properties of distance measures Fuzzy Sets and Systems 117 2001 355 361
10. J.L. Fan, and Y.L. Ma Some new fuzzy entropy formulas Fuzzy Sets and Systems 128 2002 277 284
11. Q.H. Hu, Z.X. Xie, and D.R. Yu Fuzzy probabilistic approximation spaces and their information measures IEEE Transactions on Fuzzy Systems 14 2006 191 201
12. Q.H. Hu, D.R. Yu, and Z.X. Xie Information-preserving hybrid data reduction based on fuzzy-rough techniques Pattern Recognition Letters 27 2006 414 423
13. Q.H. Hu, Z.X. Xie, and D.R. Yu Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation Pattern Recognition 40 2007 3509 3521
14. Q.H. Hu, J.F. Liu, and C.X. Wu Neighborhood rough set based heterogeneous feature subset selection Information Sciences 178 18 2008 3577 3594
15. A. Kaufmann Introduction to the Theory of Fuzzy Subsets 1975 Academic Press New York
16. G.J. Klir Multivalued logics versus modal logics: alternative frameworks for uncertainty modelling P.P. Wang, Advances in Fuzzy Theory and Technology Department of Electrical Engineering 1994 Duke University Durham, North Carolina 3 47
17. G.J. Klir, and T.A. Fogler Fuzzy Sets Uncertainity and Information 1998 Prentice-Hall Int. (UK) Ltd.
18. B. Kosko Neural Networks and Fuzzy Systems 1992 Prentice-Hall Englewood Cliffs, NJ
19. J. Komorowski, Z. Pawlak, L. Polkowski, and A. Skowron Rough sets: a tutorial S.K. Pal, A. Skowron, Rough Fuzzy Hybridization: A New Trend in Decision-Making 1999 Springer-Verlag Singapore 3 98
20. J.Y. Liang, K.S. Chin, C.Y. Dang, and C.M. YAM. Richard A new method for measuring uncertainty and fuzziness in rough set theory International Journal of General Systems 31 4 2002 331 342
21. J.Y. Liang, and Z.Z. Shi The information entropy, rough entropy and knowledge granulation in rough set theory International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12 1 2004 37 46
22. J.Y. Liang, Z.Z. Shi, D.Y. Li, and M.J. Wireman The information entropy rough entropy and knowledge granulation in incomplete information systems International Journal of General Systems 34 1 2006 641 654
23. J.Y. Liang, J.H. Wang, and Y.H. Qian A new measure of uncertainty based on knowledge granulation for rough sets Information Sciences 179 4 2009 458 470
24. X.C. Liu Entropy, distance measure and similarity measure of fuzzy sets and their relations Fuzzy Sets and Systems 52 1992 305 318
25. A.D. Luca, and S. Termini A de1nition of a nonprobalistic entropy in the setting of fuzzy entropy Information and Control 20 1972 301 312
26. D. Malyszko, and J. Stepaniuk Standard and fuzzy rough entropy clustering algorithms in image segmentation Lecture Notes in Computer Science 5306 2008 409 418
27. D. Malyszko, J. Stepaniuk, and Adaptive rough entropy clustering algorithms in image segmentation Fundamenta Informaticae 98 2-3 2010 199 231
28. D. Malyszko, and J. Stepaniuk Adaptive multilevel rough entropy evolutionary thresholding Information Sciences 180 2010 1138 1158
29. J.S. Mi, and W.X. Zhang An aximatic characterization of a fuzzy generalization of rough sets Information Sciences 160 2004 235 249
30. S. Nanda Fuzzy rough sets Fuzzy Sets and Systems 45 1992 157 160
31. N.R. Pal, and S.K. Pal Entropy, a new definition and its applications IEEE Transactions on System, Man and Cybernetics 21 1991 1260 1270
32. N.R. Pal, and J.C. Bezdek Measuring fuzzy uncertainty IEEE Transactions on Fuzzy Systems 2 1994 107 118
33. N.R. Pal, and J.C. Bezdek Quantifying different facets of fuzzy uncertainty D. Dubas, H. Prade, Fundamentals of Fuzzy Sets 2000 Kluwer Academic Publishers. London 459 480
34. S.K. Pal, B.U. Shankar, and P. Mitra Granular computing rough entropy and object extraction Pattern Recognition Letters 26 2005 2509 2517
35. Z. Pawlak Information systems theoretical foundations Information Systems 6 3 1981 205 218
36. Z. Pawlak Rough sets International Journal of Computer and Information Sciences 11 1982 341 356
37. Z. Pawlak Rough sets and fuzzy sets Fuzzy Sets and Systems 17 1985 99 102
38. Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data 1991 Kluwer Academic Publishers Dordrecht
39. Z. Pawlak, and A. Skowron Rudiments of rough sets Information Sciences 177 2007 3 27
40. Y.H. Qian, J.Y. Liang, and C.Y. Dang Consistency measure, inclusion degree and fuzzy measure in decision tables Fuzzy Sets and Systems 159 2008 2353 2377
41. Y.H. Qian, J.Y. Liang, D.Y. Li, H.Y. Zhang, and C.Y. Dang Measures for evaluating the decision performance of a decision table in rough set theory Information Sciences 178 1 2008 181 202
42. Y.H. Qian, J.Y. Liang, W. Pedrycz, and C.Y. Dang Positive approximation: an accelerator for attribute reduction in rough set theory Artificial Intelligence 174 2010 597 618
43. A.M. Radzikowska, and E.E. Kerreb A comparative study of fuzzy rough sets Fuzzy Sets and Systems 126 2002 137 155
44. A. Renyi, On measures of entropy and information, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, vol. 1, 1960, pp. 547-561.
45. C.E. Shannon A mathematical theory of communication Bell System Technology Journal 21 1948 379 423 623-656
46. W. Wei, J.Y. Liang, Y.H. Qian, F. Wang, and C.Y. Dang Comparative study of decision performance of decision tables induced by attribute reductions International Journal of General Systems 39 8 2010 813 838
47. W.H. Xu, and W.X. Zhang Measuring roughness of generalized rough sets induced by a covering Fuzzy Sets and Systems 158 2007 2443 2455
48. R.R. Yager Measures of entropy and fuzziness related to aggregation operators Information Sciences 82 3-4 1995 147 166
49. R.R. Yager On the measure of fuzziness and negation-Part II: Lattices Information and Control 44 1980 236 260
50. R.R. Yager On the measure of fuzziness and negation-Part I: Membership in the unit interval International Journal of General Systems 5 1979 221 229
51. Y.J. Yang, and R. John Roughness bounds in rough set operations Information Sciences 176 2006 3256 3267
52. J. Yao, M. Dash, S.T. Tan, and H. Liu Entropy-based fuzzy clustering and fuzzy modeling Fuzzy Sets and Systems 113 2000 381 388
53. Y.Y. Yao A comparative study of fuzzy sets and rough sets Information Sciences 109 1-4 1998 227 242
54. Y.Y. Yao Constructive and algebraic methods of theory of rough sets Information Sciences 109 1998 21 47
55. Y.Y. Yao Neighborhood systems and approximate retrieval Information Sciences 176 23 2006 3431 3452
56. Y.Y. Yao Attribute reduction in decision-theoretic rough set models Information Sciences 178 2008 3356 3373
57. D.S. Yeung, D.G. Chen, E.C.C. Tsang, J.W.T. Lee, and X.Z. Wang On the generalization of fuzzy rough sets IEEE Transaction on Fuzzy Systems 13 3 2005 343 361
58. L.A. Zadeh Fuzzy sets Information Control 8 1965 338 353
59. L.A. Zadeh Forward E. Orlowska, Incomplete Information: Rough Set Analysis 1998 Physica-Verlag Heidelberg v vi