The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
On the generalization of fuzzy rough sets
Abstract
Rough sets and fuzzy sets have been proved to be powerful mathematical tools to deal with uncertainty, it soon raises a natural question of whether it is possible to connect rough sets and fuzzy sets. The existing generalizations of fuzzy rough sets are all based on special fuzzy relations (fuzzy similarity relations, T-similarity relations), it is advantageous to generalize the fuzzy rough sets by means of arbitrary fuzzy relations and present a general framework for the study of fuzzy rough sets by using both constructive and axiomatic approaches. In this paper, from the viewpoint of constructive approach, we first propose some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations and study the relations among them, the connections between special fuzzy relations and upper and lower approximation operators of fuzzy sets are also examined. In axiomatic approach, we characterize different classes of generalized upper and lower approximation operators of fuzzy sets by different sets of axioms. The lattice and topological structures of fuzzy rough sets are also proposed. In order to demonstrate that our proposed generalization of fuzzy rough sets have wider range of applications than the existing fuzzy rough sets, a special lower approximation operator is applied to a fuzzy reasoning system, which coincides with the Mamdani algorithm.
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Cites
Pawlak, Z. (1982) · International Journal of Computer & Information Sciences · doi:10.1007/bf01001956 · Cited by 12,322
Rough Sets: Theoretical Aspects of Reasoning about Data
Pawlak, Z. (1991) · Our Digital Library (Warsaw University of Technology) · Cited by 8,343
Pawlak, Z. (1991) · Springer eBooks · doi:10.1007/978-94-011-3534-4 · Cited by 3,040
ROUGH FUZZY SETS AND FUZZY ROUGH SETS*
Dubois, D., & Prade, H. M. (1990) · International Journal of General Systems · doi:10.1080/03081079008935107 · Cited by 3,012
Rough set approach to incomplete information systems
Kryszkiewicz, M. (1998) · Information Sciences · doi:10.1016/s0020-0255(98)10019-1 · Cited by 1,314
Rough Sets in Knowledge Discovery 2
(1998) · Studies in fuzziness and soft computing · doi:10.1007/978-3-7908-1883-3 · Cited by 1,002
A comparative study of fuzzy rough sets
Radzikowska, A. M., & Kerre, E. E. (2002) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(01)00032-x · Cited by 976
Fuzzy topological spaces and fuzzy compactness
Löwen, R. (1976) · Journal of Mathematical Analysis and Applications · doi:10.1016/0022-247x(76)90029-9 · Cited by 896
Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory
(1992) · Springer eBooks · doi:10.1007/978-94-015-7975-9 · Cited by 836
Intelligent decision support. Handbook of applications and advances of the rough sets theory
(1993) · Fuzzy Sets and Systems · doi:10.1016/0165-0114(93)90040-o · Cited by 803
Cited by
Neighborhood rough set based heterogeneous feature subset selection
Hu, Q., Yu, D., Liu, J., & Wu, C. (2008) · Information Sciences · doi:10.1016/j.ins.2008.05.024 · Cited by 1,085
Classification of BGP anomalies using decision trees and fuzzy rough sets
Li, Y., Xing, H.-J., Hua, Q., Wang, X.-Z., Batta, P., Haeri, S., & Trajkovic, L. (2014) · 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC) · doi:10.1109/smc.2014.6974096 · Cited by 36
Metadata
- Authors
- Yeung, D. S., Chen, D., Tsang, E. C. C., Lee, J. W. T., & Xizhao, W.
- Venue
- IEEE Transactions on Fuzzy Systems
- Published
- 2005-06
- Volume
- 13
- Issue
- 3
- Pages
- 343-361
- ISSN
- 1063-6706 (ISSN-L)
- OpenAlex
- W2137396323
- Cited by
- 448
- References
- 18
- FWCI
- 19.45
- Type
- journal article
- Language
- en
- Open access
- closed
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- Yeung, D. S., Chen, D., Tsang, E. C. C., Lee, J. W. T., & Xizhao, W. (2005). On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/tfuzz.2004.841734
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