The algebraic structures of generalized rough set theory

Information Sciences

Volumn 178, Issue 21, 2008, Pages 4105-4113

  Liu, Guilong ^a   Zhu, William ^b  

^a BEIJING LANGUAGE AND CULTURE UNIVERSITY   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Approximation operators; Generalized rough sets; Granular computing; Rough sets; Solitary sets

Indexed keywords

ALGEBRA; BOOLEAN ALGEBRA; BOOLEAN FUNCTIONS; FUZZY SETS; MATRIX ALGEBRA; SET THEORY;

ALGEBRAIC STRUCTURES; APPROXIMATION OPERATORS; BELIEF FUNCTIONS; BINARY RELATIONS; BOOLEAN ALGEBRAS; DEFINABLE SETS; GENERALIZED ROUGH SETS; GRANULAR COMPUTING; KNOWLEDGE DISCOVERY IN DATABASES; ROUGH SETS; SOLITARY SETS; SUBALGEBRAS; UPPER APPROXIMATIONS;

ROUGH SET THEORY;

EID: 49849093407     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.06.021     Document Type: Article

References (38)

1. Banerjee M., and Pal S. Toughness of a fuzzy set. Information Sciences 93 (1996) 235-246
2. Chen D., Zhang W., Yeung D., and Tsang E. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Information Sciences 176 (2006) 1829-1848
3. Denoeux T. Modeling vague beliefs using fuzzy-valued belief structures. Fuzzy Sets and Systems 116 (2000) 167-199
4. Dubois D., and Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17 2-3 (1990) 191-209
5. Kondo M. Algebraic approach to generalized rough sets. Lecture Notes in Artificial Intelligence 3641 (2005) 132-140
6. Kondo M. On the structure of generalized rough sets. Information Sciences 176 (2006) 589-600
7. Liu G.L. The axiomatization of the rough set upper approximation operations. Fundamenta Informaticae 69 (2006) 331-342
8. Morsi N.N., and Yakout M.M. Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems 100 1-3 (1998) 327-342
9. Pawlak Z. Rough sets. International Journal of Computer and Information Sciences 11 (1982) 341-356
10. Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic Publishers, Boston
11. Pawlak Z., and Skowron A. Rudiments of rough sets. Information Sciences 177 1 (2007) 3-27
12. Pawlak Z., and Skowron A. Rough sets: some extensions. Information Sciences 177 1 (2007) 28-40
13. Pawlak Z., and Skowron A. Rough sets and boolean reasoning. Information Sciences 177 1 (2007) 41-73
14. Pei D. A generalized model of fuzzy rough sets. International Journal of General Systems 34 5 (2005) 603-613
15. Polkowski L. Rough Sets: Mathematical Foundations, Advances in Soft Computing (2002), Physica-Verlag, Heidelberg
16. In: Polkowski L., and Skowron A. (Eds). Rough Sets in Knowledge Discovery vol. 1 (1998), Physica-Verlag, Heidelberg
17. In: Polkowski L., and Skowron A. (Eds). Rough Sets in Knowledge Discovery vol. 2 (1998), Physica-Verlag, Heidelberg
18. Qi G., and Liu W. Rough operations on Boolean algebras. Information Sciences 173 (2005) 49-63
19. A.M. Radzikowska, E.E. Kerre, Fuzzy rough sets based on residuated lattices, in: Transactions on Rough Sets, Lecture Notes in Computer Science, vol. 3135, 2004, pp. 278-296.
20. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press
21. Skowron A. The rough set theory and evidence theory. Fundamenta Informaticae 13 (1990) 245-262
22. Skowron A., and Grzymała-Busse J.W. From rough set theory to evidence theory. In: Yager R., Fedrizzi M., and Kacprzyk J. (Eds). Advances in the Dempster-Shafer Theory of Evidence (1994), John Wiley & Sons, New York, NY 193-236
23. Skowron A., and Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245-253
24. Slowinski R., and Vanderpooten D. A generalized definition of rough approximations based on similarity. IEEE Transaction on Knowledge and Data Engineering 12 2 (1990) 331-336
25. Wu W.Z., Leung Y., and Zhang W.X. Connections between rough set theory and Dempster-Shafer theory of evidence. International Journal of General Systems 31 4 (2002) 405-430
26. Yao Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111 1-4 (1998) 239-259
27. Yao Y.Y. Constructive and algebraic methods of theory of rough sets. Information Sciences 109 (1998) 21-47
28. Yao Y.Y., and Lingras P.J. Interpretations of belief functions in the theory of rough sets. Information Sciences 104 1-2 (1998) 81-106
29. Yao Y.Y. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15 (1996) 291-317
30. 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
31. Yeung D., Chen D., Tsang E., Lee J., and Xizhao W. On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems 13 3 (2005) 343-361
32. Zhang H., Liang H., and Liu D. Two new operators in rough set theory with applications to fuzzy sets. Information Sciences 166 1-4 (2004) 147-165
33. Zhao Y., Yao Y., and Luo F. Data analysis based on discernibility and indiscernibility. Information Sciences 177 22 (2007) 4959-4976
34. Zadeh L.A. Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23 (1968) 421-427
35. Zhu W., and Wang F.Y. Reduction and axiomization of covering generalized rough sets. Information Sciences 152 (2003) 217-230
36. Zhu W. Topological approaches to covering rough sets. Information Sciences 177 6 (2007) 1499-1508
37. Zhu W., and Wang F.Y. On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering 19 8 (2007) 1131-1144
38. Zhu W. Generalized rough sets based on relations. Information Sciences 177 22 (2007) 4997-5011