The induced generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric aggregation operator and their application to group decision-making.

For the multi-attribute group decision-making problems where attribute values are the interval-valued intuitionistic fuzzy numbers, the group decision-making method based on induced generalized Einstein geometric aggregation operators is developed. Firstly, induced generalized interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (I-GIVIFEOWG) aggregation operator and induced generalized interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric (I-GIVIFEHWG) aggregation operator, were proposed. Some general properties such as, idempotency, commutativity, monotonicity and boundedness, were discussed and some special cases were analyzed. Furthermore, the method for multi-attribute group decision-making problems was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. The proposed methods provide more general, more accurate and precise results. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision making problems to show the validity, practicality and effectiveness of the new approach.