The direct assignment of decimal numbers for membership and non-membership degrees of an element in intuitionistic fuzzy sets is not practical. The problem is that the expert cannot assign the same values to the degrees of membership, non-membership and hesitancy in decimal numbers for the same proposition in every attempt. Rather than the former, the assignment of proportional relationships between membership and non-membership degrees is more appropriate. We propose proportion-based models for intuitionistic fuzzy sets that include arithmetic and aggregation operators. Proportional intuitionistic fuzzy (PIF) sets require only the proportion relations between an intuitionistic fuzzy set's parameters. These models will make it easier to define intuitionistic fuzzy sets with more accurate data that better represents expert judgments. We transform AHP method, one of the traditional multi-criteria decision making methods, to PIF AHP using PIF sets. We compare the proposed PIF AHP method by interval-valued intuitionistic fuzzy AHP method existing in the literature. A wind turbine selection problem is handled to show the validity of the proposed PIF AHP method.