A extended intuitionistic fuzzy Choquet integral correlation coefficient based on Shapley index in multi-criteria decision making

An intuitionistic fuzzy set (IFS) consists of two parts, the membership function and non-membership function which is a generalized form of a fuzzy set (FS), supporting a more exemplary and flexible access to assign values for each element in the domain. Intuitionistic fuzzy correlation coefficient between variables plays a significant role in a variety of areas. In the present paper, we use the Choquet integral and Shapley index to propose intuitionistic fuzzy Shapley Choquet integral correlation coefficient as a new extension of existing correlation coefficient for intuitionistic fuzzy correlation coefficient. Then, an evaluation formula of intuitionistic fuzzy Shapley 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 as well. Finally, we present a comparative analysis of the three methods in green sustainable supply chain choice to show the effectiveness of the developed methods.