In regard to multiple criteria group decision making problems with linguistic information of criteria values which take the form of intuitionistic trapezoidal fuzzy numbers, a sort of group decision analysis method is proposed. Both of power average operator and power ordered weighted average operator are nonlinear weighted average aggregation operators, and all of their weighting vectors have a dependence on the input arguments. By using power operation, some new aggregation operators are introduced, including intuitionistic trapezoidal fuzzy generalized weighted power average (ITFGWPA) operator, intuitionistic trapezoidal fuzzy generalized ordered weighted power average (ITFGOWPA) operator and induced-intuitionistic trapezoidal fuzzy generalized ordered weighted power average (I-ITFGOWPA) operator. Accordingly, different types of families of I-ITFGOWPA operators in terms of the inducing variable, weighting vector and the generalized parameter are considered.