Constructive and axiomatic approaches of fuzzy approximation operators

Information Sciences

Volumn 159, Issue 3-4, 2004, Pages 233-254

  Wu, Wei Zhi ^a,b   Zhang, Wen Xiu ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b ZHEJIANG OCEAN UNIVERSITY   (China)

Author keywords

Approximation operators; Binary relations; Fuzzy rough sets; Fuzzy sets; Rough fuzzy sets; Rough sets

Indexed keywords

APPROXIMATION THEORY; BOOLEAN ALGEBRA; FUZZY SETS; ROUGH SET THEORY;

APPROXIMATION OPERATORS; BINARY RELATIONS;

MATHEMATICAL OPERATORS;

EID: 1642525198     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2003.08.005     Document Type: Article

References (45)

1. Bodjanova S. Approximation of a fuzzy concepts in decision making. Fuzzy Sets and Systems. 85:1997;23-29.
2. Boixader D., Jacas J., Recasens J. Upper and lower approximations of fuzzy sets. International Journal of General Systems. 29(4):2000;555-568.
3. Chakrabarty K., Biswas R., Nanda S. Fuzziness in rough sets. Fuzzy Sets and Systems. 110:2000;247-251.
4. Chuchro M. On rough sets in topological Boolean algebras. Ziarko W. Rough Sets, Fuzzy Sets and Knowledge Discovery. 1994;157-160 Springer-Verlag, Berlin.
5. Chuchro M. A certain conception of rough sets in topological Boolean algebras. Bulletin of the Section of Logic. 22(1):1993;9-12.
6. Comer S. An algebraic approach to the approximation of information. Fundamenta Informaticae. 14:1991;492-502.
7. S. Comer, On connections between information systems, rough sets, and algebraic logic, in: C. Rauszer (Ed.), Algebraic Methods in Logic and Computer Science, vol. 28, Banach Center Publisher, Polish Academy of Sciences, 1993, pp. 117-127.
8. Dubois D., Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems. 17:1990;191-208.
9. Dubois D., Prade H. Twofold fuzzy sets and rough sets - some issues in knowledge representation. Fuzzy Sets and Systems. 23:1987;3-18.
10. Kortelainen J. On relationship between modified sets, topological space and rough sets. Fuzzy Sets and Systems. 61:1994;91-95.
11. Kuncheva L.I. Fuzzy rough sets: Application to feature selection. Fuzzy Sets and Systems. 51:1992;147-153.
12. T.Y. Lin, Neighborhood systems - application to qualitative fuzzy and rough sets, in: P.P. Wang (Ed.), Advances in Machine Intelligence and Soft-Computing, Department of Electrical Engineering, Duke University, Durham, NC, USA, 1997, pp. 132-155.
13. Lin T.Y., Liu Q. Rough approximate operators: axiomatic rough set theory. Ziarko W. Rough Sets, Fuzzy Sets and Knowledge Discovery. 1994;256-260 Springer, Berlin.
14. Morsi N.N., Yakout M.M. Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems. 100:1998;327-342.
15. Nakamura A., Gao J.M. On a KTB-modal fuzzy logic. Fuzzy Sets and Systems. 45:1992;327-334.
16. Nanda S., Majumda S. Fuzzy rough sets. Fuzzy Sets and Systems. 45:1992;157-160.
17. Pal S.K. Roughness of a fuzzy set. Information Sciences. 93:1996;235-246.
18. Pawlak Z. Information systems, theoretical foundations. Information Systems. 6:1981;205-218.
19. Pawlak Z. Rough sets. International Journal of Computer and Information Science. 11:1982;341-356.
20. Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. 1991;Kluwer Academic Publishers, Boston.
21. Pomykala J.A. Approximation operations in approximation space. Bulletin of the Polish Academy of Sciences: Mathematics. 35:1987;653-662.
22. Skowron A. The relationship between the rough set theory and evidence theory. Bulletin of Polish Academy of Science: Mathematics. 37:1989;87-90.
23. Skowron A. The rough sets theory and evidence theory. Fundamenta Informatica. XIII:1990;162-245.
24. Skowron A., Grzymala-Busse J. From rough set theory to evidence theory. Yager R.R., Fedrizzi M., Kacprzyk J. Advances in the Dempster-Shafer Theory of Evidence. 1994;193-236 Wiley, New York.
25. R. Slowinski, D. Vanderpooten, Similarity relation as a basis for rough approximations, in: P.P. Wang (Ed.), Advances in Machine Intelligence and Soft-Computing, Department of Electrical Engineering, Duke University, Durham, NC, USA, 1997, pp. 17-33.
26. Slowinski R., Vanderpooten D. A Generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering. 12(2):2000;331-336.
27. Thiele H. On axiomatic characterisations of crisp approximation operators. Information Sciences. 129:2000;221-226.
28. H. Thiele, On axiomatic characterisation of fuzzy approximation operators I, the fuzzy rough set based case, RSCTC 2000, Banff Park Lodge, Bariff, Canada, 19-19 October 2000, Conference Proceedings, pp. 239-247.
29. H. Thiele, On axiomatic characterisation of fuzzy approximation operators II, the rough fuzzy set based case, Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic, 2001, pp. 330-335.
30. H. Thiele, On axiomatic characterization of fuzzy approximation operators III, the fuzzy diamond and fuzzy box cases, The 10th IEEE International Conference on Fuzzy Systems 2001, vol. 2, pp. 1148-1151.
31. Vakarelov D. A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticae. 15:1991;61-79.
32. Wasilewska A. Conditional knowledge representation systems - model for an implementation. Bulletin of the Polish Academy of Sciences: Mathematics. 37:1990;63-69.
33. Wiweger R. On topological rough sets. Bulletin of Polish Academy of Sciences: Mathematics. 37:1989;89-93.
34. Wu W.-Z., Leung Y., Zhang W.-X. Connections between rough set theory and Dempster-Shafer theory of evidence. International Journal of General Systems. 31(4):2002;405-430.
35. Wu W.-Z., Mi J.-S., Zhang W.-X. Generalized fuzzy rough sets. Information Sciences. 151:2003;263-282.
36. Wu W.-Z., Zhang W.-X. Neighborhood operator systems and approximations. Information Sciences. 144(1-4):2002;201-217.
37. Wybraniec-Skardowska U. On a generalization of approximation space. Bulletin of the Polish Academy of Sciences: Mathematics. 37:1989;51-61.
38. Yao Y.Y. Constructive and algebraic methods of the theory of rough sets. Journal of Information Sciences. 109:1998;21-47.
39. Yao Y.Y. Generalized rough set model. Polkowski L., Skowron A. Rough Sets in Knowledge Discovery 1. Methodology and Applications. 1998;286-318 Physica-Verlag, Heidelberg.
40. Yao Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences. 111:1998;239-259.
41. Yao Y.Y. Combination of rough and fuzzy sets based on. α -level sets Lin T.Y., Cercone N. Rough Sets and Data Mining: Analysis for Imprecise Data. 1997;301-321 Kluwer Academic Publishers, Boston.
42. Yao Y.Y. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning. 15:1996;291-317.
43. Yao Y.Y., Lin T.Y. Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing, an International Journal. 2:1996;103-120.
44. Yao Y.Y., Lingras P.J. Interpretations of belief functions in the theory of rough sets. Information Sciences. 104:1998;81-106.
45. Zakowski W. On a concept of rough sets. Demonstratio Mathematica. XV:1982;1129-1133.