Rough approximations of intuitionistic fuzzy sets in crisp approximation spaces

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The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfy many interesting properties. Many types of generalized rough set models have been developed in the literature. This paper presents a general framework for the study of rough intuitionistic fuzzy sets in which intuitionistic fuzzy sets are approximated with respect to a crisp approximation space. A pair of lower and upper rough intuitionistic fuzzy approximation operators are first defined. Properties of rough intuitionistic fuzzy approximations are then examined. The relationships between special types of crisp binary relations and properties of rough intuitionistic fuzzy approximation operators are further established.