Three-way group decision based on regret theory under dual hesitant fuzzy environment: An application in water supply alternatives selection

For actual multi-criteria group decision-making (MCGDM) issues with complexity and uncertainty, decision-makers may not be completely rational, and the psychological characteristics generally exert influences on the decision process. As an effective cognitive model, three-way decision (TWD) dedicates to handling uncertainty and is widely used in distinct fields. In this regard, this study incorporates regret emotion into TWD in the dual hesitant fuzzy (DHF) context, and accordingly designs a decision model for uncertain MCGDM issues considering bounded rationality. Specifically, by means of distance measures and score functions of dual hesitant fuzzy elements (DHFEs), the calculation method of loss functions and conditional probability are proposed firstly. Meanwhile, drawing from regret theory, the TWD rules considering regret emotion are generated under the DHF environment. Further, based on this, a detailed three-way group decision model based on regret theory, aimed at solving MCGDM problems under DHF uncertainty, water supply alternatives selection, is constructed. Lastly, a numerical example is employed to elaborate the application of the model.