In this paper, the multi-criteria decision making problem with the assumption that the criteria are correlative is studied under intuitionistic fuzzy environment. Some new aggregation operators for intuitionistic fuzzy information are proposed, including the intuitionistic fuzzy geometric Heronian mean (IFGHM) operator and the intuitionistic fuzzy geometric weighed Heronian mean (IFGWHM) operator. We investigate the properties of the proposed operators, such as idempotency, monotonicity, permutation and boundary. Moreover, an approach is proposed for multi-criteria decision making based on IFGWHM operator. An example about talent introduction is given to illustrate the proposed method.