Abstract
In this paper, concepts of intuitionistic fuzzy measurable spaces and intuitionistic fuzzy σ-algebras are first introduced. Relationships between intuitionistic fuzzy rough approximations and intuitionistic fuzzy measurable spaces are then discussed. It is proved that the family of all intuitionistic fuzzy definable sets induced from an intuitionistic fuzzy serial approximation space forms an intuitionistic fuzzy σ-algebra. Conversely, for an intuitionistic fuzzy σ-algebra generated by a crisp algebra in a finite universe, there must exist an approximation space such that the family of all intuitionistic fuzzy definable sets is the class of all measurable sets in the given intuitionistic fuzzy measurable space.
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