Multi-criteria decision-making (MCDM) methods are susceptible to the subjectivity of experts when especially they use linguistic terms for assessment. This subjectivity and vagueness in the evaluation process have been handled by the recent extensions of ordinary fuzzy sets such as type-2 fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and neutrosophic sets. Pythagorean fuzzy sets are superior to the other extensions with a more flexible definition of membership function. A novel Pythagorean fuzzy AHP method has been developed for MCDM. The developed method has been applied to a landfill site selection problem for the city of Istanbul in Turkey. The proposed method has successfully evaluated the landfill location alternatives with respect to the considered criteria. The results are compared with ordinary fuzzy AHP, and it is revealed that the proposed method produces consistent and informative outcomes better representing the uncertainty of decision-making environment. Robustness of the decision given by the proposed method is ensured by conducting one-at-a-time sensitivity analysis.