Generalized fuzzy rough approximation operators determined by fuzzy implicators
|dc.identifier.citation||Wu, W. and Leung, Y. and Shao, M. 2013. Generalized fuzzy rough approximation operators determined by fuzzy implicators. International Journal of Approximate Reasoning. 54 (9): pp. 1388-1409.|
Abstract In this paper, a general framework for the study of dual fuzzy rough approximation operators determined by a fuzzy implication operator I in infinite universes of discourse is investigated. Lower and upper approximations of fuzzy sets with respect to a fuzzy approximation space in infinite universes of discourse are first introduced. Properties of I-fuzzy rough approximation operators are then examined. An operator-oriented characterization of fuzzy rough sets is further proposed, that is, I-fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper I-fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. Finally, a comparative study of I-fuzzy rough sets with fuzzy topological spaces is presented. It is proved that there exists a one-to-one correspondence between the set of all reflexive and T-transitive fuzzy approximation spaces and the set of all fuzzy Alexandrov spaces such that the lower and upper I-fuzzy rough approximation operators in a fuzzy approximation space are, respectively, the fuzzy interior and closure operators in a fuzzy topological space. © 2013 Elsevier Inc. All rights reserved.
|dc.title||Generalized fuzzy rough approximation operators determined by fuzzy implicators|
|dcterms.source.title||International Journal of Approximate Reasoning|
|curtin.department||Department of Electrical and Computer Engineering|
|curtin.accessStatus||Fulltext not available|
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