A Novel Group Three-Way Decision Method Integrating Regret Theory and Consensus Reaching Process for Decision-Making Problems with Interval-Valued Uncertain Information

This study presents a novel group Three-Way Decision (TWD) method that effectively addresses decision-making problems characterized by interval-valued uncertain information by integrating regret theory and the Consensus Reaching Process (CRP) model. The proposed method explores several key principles derived from regret theory to transform the loss functions into regret theory-based interval-valued loss functions. Additionally, improvements are made to the TOPSIS method for calculating conditional probabilities of alternatives under an interval-valued uncertain environment. Subsequently, several novel interval-valued TWD rules are established to classify alternatives into three predefined decision regions without the requirements for information transformation. Moreover, a personalized CRP model is developed based on the classification results, assisting experts with low consensus in revising their opinions to achieve the desired consensus. To assess the effectiveness of the proposed method, an illustrative example is presented, accompanied by comparative and sensitivity analyses that highlight its advantages and robustness. The results emphasize the innovative perspective and methodology provided by the proposed method for effectively addressing practical decision problems in uncertain and risk-laden environments.