Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making

Intuitionistic fuzzy information aggregation plays an important part in the intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on the intuitionistic fuzzy sets, such as Hamacher sum, Hamacher product, Hamacher exponentiation, etc., and further develop some new Hamacher aggregation operators, such as the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, the intuitionistic fuzzy Hamacher ordered weighted averaging (IFHOWA) operator and the intuitionistic fuzzy Hamacher hybrid averaging (IFHHA) operator. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. Then, we apply the intuitionistic fuzzy Hamacher hybrid averaging (IFHHA) operator to deal with multiple attribute decision making with Intuitionistic fuzzy information. Finally, an illustrative example for evaluating the enterprise financial performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.