On characterizations of \((\mathcal J,\mathcal T)\)-fuzzy rough approximation operators. (English) Zbl 1074.03027

Summary: In rough set theory, the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties. Various fuzzy generalizations of rough approximations have been made in the literature. This paper proposes a general framework for the study of \((\mathcal J,\mathcal T)\)-fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper generalized fuzzy rough approximation operators, determined by an implicator \(\mathcal J\) and a triangular norm \(\mathcal T\), is first defined. Basic properties of \((\mathcal J,\mathcal T)\)-fuzzy rough approximation operators are investigated. The connections between fuzzy relations and fuzzy rough approximation operators are further established. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, \((\mathcal J,\mathcal T)\)-fuzzy approximation operators are defined by axioms. Different axiom sets of \(\mathcal T\)-upper and \(\mathcal J\)-lower fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. Finally, an open problem posed by A. M. Radzikowska and E. Kerre [Fuzzy Sets Syst. 126, 137–155 (2002; Zbl 1004.03043)] is solved.


03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence


Zbl 1004.03043
Full Text: DOI


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