Some interval-valued intuitionistic fuzzy geometric aggregation operators based on einstein operations

The notion of interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of Atanassov´s intuitionistic fuzzy set (AIFS). The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. In this article, we develop some interval-valued intuitionistic fuzzy geometric operators based on Einstein operations, such as the interval-valued intuitionistic fuzzy Einstein weighted geometric (IVIFWG^ε) operator, interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (IVIFOWG^ε) operator and interval-valued intuitionistic fuzzy Einstein hybrid geometric (IVIFHWG^ε) operator, which are the generalizations of the geometric aggregation operators based on AIFSs. Moreover, we establish various properties of these operators.