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Aggregation of fuzzy information is a new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, which has attracted significant interest from researchers in recent years. In this paper, we treat the intuitionistic fuzzy aggregation operators with the help of Einstein operations. We first introduce some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication. Then, we develop some intuitionistic fuzzy aggregation operators, such as the intuitionistic fuzzy Einstein weighted averaging operator and the intuitionistic fuzzy Einstein ordered weighted averaging operator, which extend the weighted averaging operator and the ordered weighted averaging operator to aggregate Atanassov's intuitionistic fuzzy values, respectively. We further establish various properties of these operators and analyze the relations between these operators and the existing intuitionistic fuzzy aggregation operators. Moreover, we give some numerical examples to illustrate the developed aggregation operators. Finally, we apply the intuitionistic fuzzy Einstein weighted averaging operator to multiple attribute decision making with intuitionistic fuzzy information.