Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators

On the basis of Frank operators, the operational rules of intuitionistic fuzzy numbers are redefined, then the intuitionistic fuzzy Frank power average operator (IFFPA), intuitionistic fuzzy Frank power weighted average operator (IFFPWA) and intuitionistic fuzzy Frank power ordered weighted average operator (IFFPOWA) are proposed by combining Frank operations and power aggregation operators. At the same time, some desirable properties of these operators, such as idempotency, commutativity and boundedness, are studied, and some special cases are analyzed. Furthermore, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decision making methods based on IFFPWA and IFFPOWA operators are developed. Finally, an illustrative example is given to verify the proposed methods and to demonstrate their practicality and effectiveness.