Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making

For the multiple attribute group decision making (MAGDM) problems whereattribute values arethe interval-valued intuitionistic fuzzy numbers (IVIFNs), the group decision making method based on some generalized Einstein aggregation operators is developed. Firstly, interval-valued intuitionistic fuzzy generalized Einstein weighted averaging (IVIFGEWA) operator, interval-valued intuitionistic fuzzy generalized Einstein ordered weighted averaging (IVIFGEOWA) operator, and interval-valued intuitionistic fuzzy generalized Einstein hybrid weighted averaging (IVIFGEHWA) operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for MAGDM problems based on these operators was developed, and the operational processes were illustrated in detail. Finally, an illustrative example is given to show the decision steps of the proposed methods and to demonstrate their and effectiveness.