A general frame for intuitionistic fuzzy rough sets

Intuitionistic fuzzy rough sets are investigated in a general framework which includes generalizations of many related results in early literatures. A new definition of intuitionistic fuzzy rough sets is given with the analysis of its basic properties based on the notion of two universes, general binary relations, and a pair (T(T, I)I) of intuitionistic fuzzy t  -norm TT and intuitionistic fuzzy implicator II. For t-representable intuitionistic fuzzy t-norms and its residual implicators, intuitionistic fuzzy rough approximation operators are defined by axioms, and its connections with special intuitionistic fuzzy relations are investigated.