On structure of generalized intuitionistic fuzzy rough sets

Intuitionistic fuzzy sets, originally proposed by Atanassov in 1986, are an attractive extension of fuzzy sets, which enriches the latter with extra features to represent uncertainty. The concept of IF rough sets comes from the combination of IF sets and rough sets. This paper studies axiomatic characterization of IF rough sets. The lower and upper approximations are respectively characterized by two simple axioms. We also consider lattice theoretical properties of IF rough sets and show that the set of all definable IF sets is a completely distributive lattice.