In this paper, we firstly propose some generalized prioritized aggregation operators to aggregate the intuitionistic fuzzy values (IFVs), such as the generalized intuitionistic fuzzy prioritized weighted geometric
(GIFPWG) operator and the generalized intuitionistic fuzzy prioritized weighted average (GIFPWA) operator. It is shown that some existing intuitionistic fuzzy aggregation operators are the special cases of our proposed operators. Then, we study serials of properties of these operators, such as Non-compensatory, Boundary and Monotonicity. In addition, we apply the two proposed aggregation operators to multi-criteria decision making under intuitionistic fuzzy environment and an example about talent recruitment is provided to illustrate the developed approach.