An axiomatic characterization of a fuzzy generalization of rough sets

Information Sciences

Volumn 160, Issue 1-4, 2004, Pages 235-249

  Mi, Ju Sheng ^a,b   Zhang, Wen Xiu ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b HEBEI NORMAL UNIVERSITY   (China)

Author keywords

Approximation operators; Composition of approximation spaces; Fuzzy relation; Rough set; Triangular norm

Indexed keywords

APPROXIMATION THEORY; INFORMATION DISSEMINATION; KNOWLEDGE ENGINEERING; THEOREM PROVING;

FUZZY RELATIONS; ROUGH SETS;

FUZZY SETS;

EID: 1342328031     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2003.08.017     Document Type: Article

References (38)

1. Abdel-Hamid A.A., Morsi N.N. On the relationship of extended necessity measures to implication operators on the unit interval. Information Sciences. 82:1995;129-145.
2. Comer S. An algebraic approach to approximation of information. Fundamenta Informaticae. 14:1991;492-502.
3. Comer S. On connections between information system rough sets and algebraic logic. Algebraic Methods in Logic and Computer Science. vol. 28:1993;117-124 Banach Center Publications.
4. Dubois D., Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems. 17:1990;191-209.
5. Greco S., Matarazzo B., Slowinski R. Rough set processing of vague information using fuzzy similarity relations. Calude C.S., Paun G. Finite Versus Infinite - Contributions to an Eternal Dilemma. 2002;149-173 Springer-Verlag, London.
6. Inuiguchi M., Greco S., Slowinski R., Tanino T. Possibility and necessity measure specification using modifiers for decision making under fuzziness. Fuzzy Sets and Systems. 137:2003;151-175.
7. Kuncheva L.I. Fuzzy rough sets: Application to feature selection. Fuzzy Sets and Systems. 51:1992;147-153.
8. 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.
9. Lin T.Y. A rough logic formalism for fuzzy controllers: A hard and soft computing view. International Journal of Approximate Reasoning. 15:1996;395-414.
10. Lin T.Y. Granular computing: fuzzy logic and rough sets. Zadeh L.A., Kacprzyk J. Computing with Words in Information/Intelligent Systems. 1999;183-200 Physica-Verlag, New York.
11. Lin T.Y. Topological and fuzzy rough sets. Slowinski R. Decision Support by Experience - Application of the Rough Set Theory. 1992;287-304 Kluwer Academic Publishers, Boston.
12. Morsi N.N., Yakout M.M. Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems. 100:1998;327-342.
13. Nguyen H.T. Intervals in Boolean rings: approximation and logic. Foundations of Computer and Decision Sciences. 17:1992;131-138.
14. Pawlak Z. Rough sets. International Journal of Computer Information Sciences. 11:1982;145-172.
15. Pawlak Z. Rough Sets - Theoretical Aspects to Reasoning about Data. 1991;Kluwer Academic Publisher, Boston.
16. Pawlak Z. Rough set and fuzzy set. Fuzzy Sets and Systems. 17:1985;99-102.
17. Quafatou M. α -RST: a generalization of rough set theory Information Sciences. 124:2000;301-316.
18. Skowron A., Stepaniuk J. Generalized approximation spaces. Lin T.Y., Wildberger A.M. Soft Computing. 1995;18-21 The Society for Computer Simulation, San Diego.
19. Skowron A. The relationship between the rough set theory and evidence theory. Bulletin of Polish Academy of Science: Mathematics. 37:1989;87-90.
20. Skowron A. The rough sets theory and evidence theory. Fundamenta Informatica. XIII:1990;245-262.
21. 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.
22. Slowinski R., Vanderpooten D. Similarity relation as a basis for rough approximations. Wang P.P. Advances in Machine Intelligence and Soft-Computing. 1997;17-33 Department of Electrical Engineering, Duke University, Durham, NC, USA.
23. 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.
24. R. Slowinski, S. Greco, B. Matarazzo, Fuzzy rough sets applied to multicriteria and multiattribute classification, in: Z. Suraj (Ed.), Proceedings of Sixth International Conference on Soft Computing and Distributed Processing, Rzeszow, June 24-25, 2002, pp. 129-132.
25. Thiele H. On axiomatic characterization of crisp approximation operators. Information Sciences. 129:2000;221-226.
26. H. Thiele, On axiomatic characterization of fuzzy approximation operators I, the fuzzy rough set based case, in: RSCTC 2000 Conference Proceedings, Banff Park Lodge, Bariff, Canada, October 19, 2000, pp. 239-247.
27. H. Thiele, On axiomatic characterization of fuzzy approximation operators II, the rough fuzzy set based case, in: Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic, 2001, pp. 330-335.
28. Wasilewska A. Conditional knowledge representation systems-model for an implementation. Bulletin of the Polish Academy of Sciences: Mathematics. 37:1990;63-69.
29. Wiweger A. On topological rough sets. Bulletin of the Polish Academy of Sciences: Mathematics. 37:1989;89-93.
30. Wu W.-Z., Mi J.-S., Zhang W.-X. Generalized fuzzy rough sets. Information Sciences. 151:2003;263-282.
31. Wybraniec-Skardowska U. On a generalization of approximation space. Bulletin of the Polish Academy of Sciences: Mathematics. 37:1989;51-61.
32. 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.
33. Yao Y.Y. Two views of the theory of rough sets in finite universe. International Journal of Approximate Reasoning. 15:1996;291-317.
34. Yao Y.Y. Constructive and algebraic methods of the theory of rough sets. Information Sciences. 109:1998;21-47.
35. Yao Y.Y., Wong S.K.M., Lin T.Y. A review of rough set models. Lin T.Y., Cercone N. Rough Sets and Data Mining: Analysis for Imprecise Data. 1997;47-75 Kluwer Academic Publishers, Boston.
36. Zakowski W. On a concept of rough sets. Demonstration Mathematic. XV:1982;1129-1133.
37. Zhang W.-X., Wang G.-J. Fuzzy Mathematics. 1991;Xi'an Jiaotong University Press, Xi'an.
38. Ziarko W. Variable precision rough set model. Journal of Computer and System Sciences. 46(1):1993;39-59.