In order to solve the prioritized multi-criteria decision-making problem under intuitionistic fuzzy environment, the
intuitionistic fuzzy POWA(IFPOWA) operator is defined. The method of determining the weighting vector related with the
operator is formulated based on priority relationship and revised scoring function. Some properties on the IFPOWA operator
are presented. A novel method for prioritized multi-criteria decision-making problem under intuitonistic fuzzy environment
utilizing the IFPOWA operator is developed. Finally, a practical example shows the effectiveness of the proposed method.