This study Present 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. In addition, 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.

中文翻译：

---

一种结合遗憾理论和共识达成过程的新型群体三向决策方法，解决区间值不确定信息决策问题


本研究提出了一种新颖的群体三向决策（TWD）方法，通过整合遗憾理论和共识达成过程（CRP）模型，有效解决以区间值不确定信息为特征的决策问题。该方法探索了从后悔理论导出的几个关键原理，将损失函数转换为基于后悔理论的区间值损失函数。此外，对计算区间值不确定环境下备选方案条件概率的TOPSIS方法进行了改进。随后，建立了一些新颖的区间值 TWD 规则，将备选方案分类为三个预定义的决策区域，而无需进行信息转换。此外，根据分类结果开发个性化的CRP模型，帮助共识度较低的专家修改意见，以达到期望的共识。为了评估所提出方法的有效性，提出了一个说明性示例，并进行了比较和敏感性分析，突出了其优点和鲁棒性。结果强调了所提出的方法为有效解决不确定和充满风险的环境中的实际决策问题提供的创新视角和方法。