Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings

Study mainly investigates generalized intuitionistic fuzzy (IF) rough sets based on IF coverings. By using an IF covering, an IF triangular norm, and an IF implicator, two pairs of generalized lower and upper IF rough approximation operators have been constructed, and some fundamental properties are examined. Then, we give some conditions under which the generalized lower IF rough approximation operator is an IF interior operator and the generalized upper IF rough approximation operator is an IF closure operator. Furthermore, the duality of the generalized IF rough approximation operators is discussed. In addition, we propose some concepts and conditions for two intuitionistic coverings to generate an identical lower IF rough approximation operator and an identical upper IF rough approximation operator with the purpose of removing the redundancy in an IF covering. Finally, we compare the IF-neighborhood-oriented IF rough approximation operators with IF-neighborhood-operator-oriented IF rough approximation operators and obtain the conditions under which some or all of these approximation operators are equivalent.