In this paper, a hesitant fuzzy multiple attribute group decision making problem where there exists prioritization relationships over the attributes and decision makers is studied. First, some Einstein operations on hesitant fuzzy elements and their properties are presented. Then, several generalized hesitant fuzzy prioritized Einstein aggregation operators, including the generalized hesitant fuzzy prioritized Einstein weighted averaging operator and the generalized hesitant fuzzy prioritized Einstein weighted geometric operator, are introduced. Moreover, some desirable properties and special cases are investigated. It is shown that some existing hesitant fuzzy aggregation operators are the special cases of the proposed operators. Further, a new approach of hesitant fuzzy group decision making is developed based on the proposed operators. Finally, a practical example is provided to illustrate the developed approach.