Rough fuzzy approximations on two universes of discourse

Information Sciences

Volumn 178, Issue 3, 2008, Pages 892-906

  Li, Tong Jun ^a,b   Zhang, Wen Xiu ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b ZHEJIANG OCEAN UNIVERSITY   (China)

Author keywords

Binary relations; Coverings; Fuzzy sets; Rough fuzzy approximation operators; Two universes

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL OPERATORS; ROUGH SET THEORY;

BINARY RELATIONS; ROUGH FUZZY APPROXIMATION OPERATORS; TWO UNIVERSES;

FUZZY SETS;

EID: 35748956126     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2007.09.006     Document Type: Article

References (57)

1. Boixader D., Jacas J., and Recasens J. Upper and lower approximations of fuzzy sets. International Journal of General Systems 29 (2000) 555-568
2. Bonikowski Z., Bryniariski E., and Skardowska V.W. Extension and intensions in the rough set theory. Information Sciences 107 (1998) 149-167
3. Chakrabarty K., Biawas R., and Nanda S. Fuzziness in rough sets. Fuzzy Sets and Systems 10 (2000) 247-251
4. Dubois D., and Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17 (1990) 191-208
5. Dubois D., and Prade H. Putting fuzzy sets and rough sets together. In: Slowinski R. (Ed). Intelligence Decision Support (1992), Kluwer Academic, Dordrecht 203-232
6. T. Feng, J. Mi, W. Wu, Covering-based generalized rough fuzzy sets, in: G. Wang et al. (Eds.), RSKT 2006, LNAI 4062, 2006, pp. 208-215.
7. Ganter B., and Wille R. Formal Concept Analysis: Mathematical Foundations (1999), Springer-Verlag, New York
8. Greco S., Matarazzo B., and Slowinski R. Theory and methodology: rough approximation of a preference relation by dominance relations. European Journal of Operational Research 117 (1999) 63-83
9. Greco S., Matarazzo B., and Slowinski R. Rough approximation by dominance relations. International Journal of Intelligent Systems 17 (2002) 153-171
10. Huynh V.N., and Nakamori Y. A roughness measure for fuzzy sets. Information Sciences 173 (2005) 255-275
11. Inuiguchi M., and Tanino T. New fuzzy rough set based on certainty qualification. In: Pal S.K., Polkowski L., and Skowron A. (Eds). Rough-Neural Computing: Techniques for Computing with Words (2002), Springer-Verlag, Berlin 277-296
12. Kryszkiewicz M. Rough set approach to incomplete information systems. Information Sciences 112 (1998) 39-49
13. Kuncheva L.I. Fuzzy rough set: Application to feature selection. Fuzzy Sets and Systems 51 (1992) 147-153
14. T. Li, Rough approximation operators in covering approximation spaces, in: S. Greco et al. (Eds.), RSCTC 2006, LNAI 4259, 2006, pp. 174-182.
15. T.J. Li, W.X. Zhang, Rough approximations in formal contexts, in: Proceedings of ICMLC'05, 2005, pp. 18-21.
16. Mi J.-S., Leung Y., and Wu W.-Z. An uncertainty measure in partition-based fuzzy rough sets. International Journal of General Systems 34 (2005) 77-90
17. Mi J.-S., and Zhang W.-X. An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160 (2004) 235-249
18. Morsi N.N., and Yakout M.M. Axiomatics of fuzzy rough sets. Fuzzy Set and Systems 100 (1998) 327-342
19. Nakamura A. Fuzzy rough set. Note on Multiple-Valued Logic in Japan 9 8 (1998) 1-8
20. Nanda S., and Majumda S. Fuzzy rough set. Fuzzy Sets and Systems 45 (1992) 157-160
21. Orlowska E. Semantics analysis of inductive reasoning. Theoretical Computer Science 3 (1986) 81-89
22. Pawlak Z. Rough sets. International Journal of Computer and Information Science 11 (1982) 341-356
23. Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data (1991), Kluwer Academic Publisher, Boston
24. Pawlak Z., and Skowron A. Rudiments of rough sets. Information Sciences 177 1 (2007) 3-27
25. Pawlak Z., and Skowron A. Rough sets: some extensions. Information Sciences 177 1 (2007) 28-40
26. Pawlak Z., and Skowron A. Rough sets and Boolean reasoning. Information Sciences 177 1 (2007) 41-73
27. Pomykala J.A. Approximation operations in approximation space. Bulletin of the Polish Academy of Sciences: Mathematics 35 (1987) 653-662
28. Pomykala J.A. On definability in the nondeterministic information system. Bulletin of the Polish Academy of Sciences: Mathematics 36 (1988) 193-210
29. Radzikowska A.M., and Kerre E.E. A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126 (2002) 137-155
30. A.M. Radzikowska, E.E. Kerre, L-fuzzy rough sets, in: J.F. Peter et al. (Eds.), Artificial Intelligence and Soft Computing-ICAISC2004, LNCS 3135, vol. 3070. 2004, pp. 526-531.
31. G. Shafer, Belief functions and possibility measures, in: J.C. Bezdek (Eds.), Analysis of Fuzzy Information, vol. 1, 1987, pp. 51-84.
32. Slowinski R., and Stefanowski J. Medical information systems-problems with analysis and way of solution. In: Pal S.K., and Skowron A. (Eds). Rough Fuzzy Hybridization: A New Trend in Decision-making (1999), Springer-Verlag, Singapore 301-315
33. Slowinski R., and Vanderpooten D. A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12 2 (2000) 331-336
34. Skowron A., and Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245-253
35. A. Skowron, R. Swiniarski, P. Synak, Approximation spaces and information granulation, in: J.F. Peters, A. Skowron (Eds.), Transactions on Rough Sets III, LNCS 3400, 2005, pp. 175-189.
36. J. Stepaniuk, Approximation spaces in extensions of rough set theory, in: L. Polkowski, A. Skowron (Eds.), RSCTC'98, LNAI 1424, 1998, pp. 290-297.
37. S.K. Wong, L. Wang, Y. Yao, Interval structure: a framework for representing uncertain information, in: Proceedings of UAI'92, 1992, pp. 336-343.
38. Wong S.K., Wang L., and Yao Y. On modeling uncertainty with interval structures. Computational Intelligence 11 2 (1995) 406-426
39. 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
40. W.Z. Wu, Y. Leung, W.X. Zhang, On generalized rough fuzzy approximation operators, in: J.F. Peters, A. Skowron (Eds.), Transactions on Rough Sets V, LNCS 4100, 2006, pp. 263-284.
41. Wu W.-Z., Mi J.-S., and Zhang W.-X. Generalized fuzzy rough sets. Information Sciences 15 (2003) 263-282
42. Wu W.-Z., and Zhang W.-X. Neighborhood operator systems and approximations. Information Sciences 144 (2002) 201-217
43. Wu W.-Z., and Zhang W.-X. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences 159 (2004) 233-254
44. Wu W.Z., Zhang W.X., and Xu Z.B. Characterizating rough fuzzy sets in constructive and axiomatic approaches. The Chinese Journal of Computer 27 (2004) 197-203
45. Wybraniec-Skardowska U. On a generalization of approximation space. Bulletin of the Polish Academy of Sciences, Mathematics 37 (1989) 51-65
46. Yao Y.Y. Two views of the theory of rough sets in finite universe. International Journal of Approximate Reasoning 15 (1996) 291-317
47. Yao Y.Y. Combination of rough and fuzzy sets based on α-level sets. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining: Analysis for Imprecise Data (1997), Kluwer Academic Publishers, Boston 301-321
48. Yao Y.Y. Generalized rough set models. In: Polkowski L., et al. (Ed). Rough Sets in Knowledge Discovery. Methodology and Applications 1 (1998), Physical-Verlag, Heidelberg 286-318
49. Yao Y.Y. Constructive and algebraic methods of the theory of rough sets. Information Sciences 109 (1998) 21-47
50. Yao Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111 (1998) 239-259
51. Yao Y.Y. Rough sets, neighborhood systems, and granular computing. In: Meng (Ed). Proceedings of the 1999 IEEE Canadian Conference on Electrical and Computer Engineering, Edmonton, Canada (1999), IEEE press 1553-1558
52. 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
53. Yao Y.Y., Wong S.K.M., and Lin T.Y. A review of rough set models. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining: Analysis for Imprecise Data (1997), Kluwer Academic Publishers, Boston 47-75
54. Yao Y.Y., Wong S.K.M., and Wang L.S. A non-numeric approach to uncertain reasoning. International Journal of General System 23 (1995) 343-359
55. Zadeh L.A. Toward a generalized theory of uncertainty (GTU)-an outline. Information Sciences 172 (2005) 1-40
56. Zakowski W. Approximations in the space (U, Π). Demenstratio Mathematica XVI (1983) 761-769
57. Zhang W.-X., and Mi J.-S. Incomplete information system and its optimal selections. Computers and Mathematics with Applications 48 (2004) 691-698