Generalized intuitionistic fuzzy rough sets based on an intuitionistic fuzzy residual implicator

This paper presents a general study of generalized intuitionistic fuzzy rough sets integrating the rough set theory with the intuitionistic fuzzy set theory by a constructive approach. By employing an intuitionistic fuzzy residual implicator and its dual operator, generalized upper and lower intuitionistic fuzzy rough approximation operators with respect to an arbitrary intuitionistic fuzzy approximation space are first defined. Then some interesting properties of intuitionistic fuzzy rough approximation operators are examined. Finally, the connections between special types of intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are also established.