The Choquet integral correlation coefficient between intuitionistic fuzzy sets and the computing formula are obtained by Qu, but the results have contradiction with the nature of the Choquet integral correlation coefficient between intuitionistic fuzzy sets. It is found from the practical example that the range of the Choquet integral correlation coefficient between intuitionistic fuzzy sets is not appropriate, and through the study on the proof of its nature of the Choquet integral correlation coefficient, the cause of the problem existed is analyzed. Then based on the Choquet integral correlation of intuitionistic fuzzy sets, the new Choquet integral information energy of the intuitionistic fuzzy set and the Choquet integral correlation coefficient between intuitionistic fuzzy sets are defined, and their natures are also discussed. Finally, the Choquet correlation coefficient between the alternative and the positive ideal alterative is derived, and a method is developed to solve the multiple attribute decision making problem using the Choquet correlation coefficient, and an example is used to illustrate the feasibility and effectiveness of the proposed method.