Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/16878
Title: On the generalization of fuzzy rough sets
Authors: Yeung, DS
Chen, D
Tsang, ECC
Lee, JWT
Wang, X
Keywords: Approximation operators
Completely distributive lattice
Fuzzy rough sets
Fuzzy topology
Rough sets
Issue Date: 2005
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on fuzzy systems, 2005, v. 13, no. 3, p. 343-361 How to cite?
Journal: IEEE transactions on fuzzy systems 
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.
URI: http://hdl.handle.net/10397/16878
ISSN: 1063-6706
EISSN: 1941-0034
DOI: 10.1109/TFUZZ.2004.841734
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