Abstract
Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated.
Highlights
Rough sets theory [1, 2] proposed by Pawlak is a mathematical tool to deal with uncertainties and imprecision
In [24], an interval-valued intuitionistic fuzzy rough model has been proposed by combining the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory
To provide certain theoretical basis for dealing with such problem, we propose rough type-2 fuzzy set model by combining the classical Pawlak rough set theory with the general type2 fuzzy set theory in this paper
Summary
Rough sets theory [1, 2] proposed by Pawlak is a mathematical tool to deal with uncertainties and imprecision. In [24], an interval-valued intuitionistic fuzzy rough model has been proposed by combining the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory. General type-2 fuzzy sets and rough sets have important applications, a few results about the combination of general type-2 fuzzy set theory and rough set theory were presented [36,37,38]. The interval type-2 rough fuzzy set model proposed in [39] may be suitable to deal with these information systems with interval values. To provide certain theoretical basis for dealing with such problem, we propose rough type-2 fuzzy set model by combining the classical Pawlak rough set theory with the general type fuzzy set theory in this paper.
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