Choquet integral correlation coefficient of intuitionistic fuzzy sets and its applications

The Choquet integral is a very useful way of measuring the expected utility an uncertain event. In this paper, we use the Choquet integral to propose intuitionistic fuzzy Choquet integral correlation coefficient as a new extension of existing correlation coefficient for intuitionistic fuzzy correlation coefficient. The extended correlation coefficient not only globally consider the importance of the elements or their ordered positions, but also can overall reflect their correlations. Furthermore, when the weight information about criteria represented by intuitionistic fuzzy set (IFSs) is incomplete known, a fuzzy measure model for the optimal measures on criteria set is established, which can be used to determine the criteria fuzzy measure. Then, an evaluation formula of intuitionistic fuzzy Choquet integral correlation coefficient between an alternative and the ideal alternative is proposed. The considered alternatives can be ranked and the most desirable one is selected. To comparative analysis, we also apply the Ye's method [49] to solve the problem based on intuitionistic fuzzy correlation coefficient. Finally, a comparative analysis of the two methods is used to assess the green supply chain choice.