Multigranulation behavioral three-way group decisions under hesitant fuzzy linguistic environment

Bounded rationality of decision-makers and interaction among criteria plays a key role in the actual multi-criteria group decision-making (MCGDM) process. This paper aims to offer a decision approach to a MCGDM problem under hesitant fuzzy linguistic (HFL) uncertainty, by means of behavioral multigranulation decision-theoretic rough set (DTRS), where criteria interaction is handled by Choquet integral, and decision-makers’ psychological preferences are considered by prospect theory. In specific, we firstly define the behavioral DTRS over two universes, where the threshold parameters are obtained by maximizing expected utility, rather than minimizing expected risk. Then, from the perspective of the difference of alternatives, we develop the calculation methods of loss and benefit functions, and provide the determination of the overall threshold parameters by Choquet integral, in consideration of criteria interaction. With these discussions, the behavioral multigranulation DTRS over two universes in the HFL context is proposed, and the two special cases, i.e., optimistic and pessimistic versions are also discussed. Thus, solutions to a MCGDM issue, green supplier selection, by utilizing the proposed behavioral multigranulation HFL DTRS over two universes, are designed, along with key steps and algorithm. Ultimately, an illustrative example is given to elaborate the practicability and feasibility of our presented model.