In view of the deficiency of axiomatic definitions of intuitionistic fuzzy sets among current researches, an improved axiomatic definition of the intuitionistic fuzzy entropy is presented, and a corresponding formula is structured. In order to minimize the influence of abnormal data for information aggregation, a power parameter is introduced to define the generalized power average(GPA) operator. The related properties of GPA are proposed and verified, and an approach for determining the power parameters is also presented. Furthermore, the GPA operator is extended to intuitionistic fuzzy environments to proposed the generalized intuitionistic fuzzy power average operator. In a framework of complex system whose performance is evaluated as intuitionistic fuzzy numbers(IFNs), with respect to a multiple criteria group decision making(MCGDM) problem, in which there are both interactions among decision-makers, and criteria and decision-makers’ weights and criterion weights are both unknown, an interdependent MCGDM method based on an intuitionistic fuzzy entropy and a generalized intuitionistic fuzzy power average operator is proposed. A practical example illustrates the effectiveness and feasibility of the proposed decision-making methods.