Multi-criteria group decision making (MCGDM) is an important part of decision science and widely applied in several fields. To cope with the vagueness and ambiguity of the human evaluation in the MCGDM process, interval-valued intuitionistic fuzzy set (IVIFS) theory is introduced. In this study, the AHP method whose traditional form is frequently used in MCGDM problems is improved in the IVIF environment. Since the aim of AHP is to choose the most suitable criterion/alternative by making a rank from the most important to the least important, the improved IVIF-AHP method is based on the ranking functions. Some existing score and accuracy functions are analyzed and it is seen that these functions have some limitations to rank IVIF numbers. So, new score and accuracy functions of IVIFS are developed to overcome their limitations and these new functions are integrated into the IVIF-AHP method. The comparative results show that the improved IVIF-AHP method gives a consistent ranking for the criteria. Moreover, the proposed method steps are illustrated with a case study about prioritizing some technical and soft skills over industrial engineering and electrical engineering.