Multi-attribute group decision making based on Choquet integral under interval-valued intuitionistic fuzzy environment

In this paper, we propose new methods to represent interdependence among alternative attributes and experts' opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interval-valued intuitionistic fuzzy Choquet integral is defined, and some elementary properties are studied in detail. Next, an axiomatic system of interval-valued intuitionistic fuzzy measure is established by delivering a series of mathematical proofs. Then, with fuzzy entropy and Shapely-values in game theory, we propose the interval-valued intuitionistic fuzzy measure development methods in order to form the importance measure of attributes and correlation measure of the experts, respectively. Based on the results of theoretical analysis, a new method is proposed to handle the interval-valued intuitionistic fuzzy group decision making problems. A numerical example illustrates the procedure of the proposed methods and verifies the validity and effectiveness of our new proposed methods.