Abstract
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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ε</sup> ) operator, interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (IVIFOWG <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ε</sup> ) operator and interval-valued intuitionistic fuzzy Einstein hybrid geometric (IVIFHWG <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ε</sup> ) operator, which are the generalizations of the geometric aggregation operators based on AIFSs. Moreover, we establish various properties of these operators.
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