Intuitionistic fuzzy numbers and their comparison laws were defined and prioritized aggregation operators for intuitionistic fuzzy numbers were proposed. For fuzzy multi-criteria decision making problems having a preference between criteria,in which the criteria values were intuitionistic fuzzy numbers and the changing weights of the criteria were unknown，an approach based on prioritized aggregation operators was proposed. By using these prioritized aggregation operators, the comparative satisfying index, comparative accuracy and the weights of each alternative under different criteria were calculated, then the values of the score function and accuracy function were attained. By comparing score function and accuracy function values, a ranking of the whole alternative set was attained. Analysis of an example shows that the method is of the feasibility and effectiveness.