Pythagorean hesitant fuzzy set, which can not only describe the fuzzy phenomenon that the sum of membership degree and nonmembership degree may be bigger than 1 but their square sum is equal to or less than 1, but also express hesitations in membership degree and nonmembership degree, can be considered as a powerful tool for expressing uncertain information in the process of decision making. Considering that correlation measures play important role in statistics and management science, in this paper, correlation measures of the Pythagorean hesitant fuzzy set is studied. On the basis of the definition of the informational energy of the Pythagorean hesitant fuzzy set, the correlation coefficients between Pythagorean hesitant fuzzy sets are defined, and their natures are discussed. Then, the weights of attributes are often taken into account, and the concept of the weighted correlation coefficient between Pythagorean hesitant fuzzy sets is also introduced, and the natures are studied. Finally, through the weighted correlation coefficients between each alternative and the positive ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be identified. An example is given to illustrate the feasibility and applicability of the proposed method.