In this paper, some series of new intuitionistic fuzzy averaging aggregation operators has been presented under the intuitionistic fuzzy sets environment. For this, some shortcoming of the existing operators are firstly highlighted and then new operational law, by considering the hesitation degree between the membership functions, has been proposed to overcome these. Based on these new operation laws, some new averaging aggregation operators namely, intuitionistic fuzzy Hamacher interactive weighted averaging, ordered weighted averaging and hybrid weighted averaging operators, labeled as IFHIWA, IFHIOWA and IFHIHWA respectively has been proposed. Furthermore, some desirable properties such as idempotency, boundedness, homogeneity etc. are studied. Finally, a multi-criteria decision making method has been presented based on proposed operators for selecting the best alternative. A comparative concelebration between the proposed operators and the existing operators are investigated in detail.