Three-way decision with regret theory and T-spherical fuzzy interactional Aczél-Alsina aggregation operators for multi-attribute decision-making

The three-way decision (TWD) has attracted extensive attention in multi-attribute decision-making (MADM) for its ability to incorporate decision-makers' (DMs') preferences in uncertain environments. However, models often struggle to effectively integrate objective evaluation values with DMs' psychological behaviors when handling T-spherical fuzzy (T-SF) information, leading to inadequate performance in comparing and classifying alternatives. To address this issue, we proposed a novel regret-theory-based TWD approach in the T-SF environment. First, a relative utility function (RUF) was constructed by integrating regret theory (RT) to reasonably reflect DMs' psychological expectations and relative utility differences in different scenarios. Second, the T-spherical fuzzy interactional Aczél-Alsina (T-SFIAA) aggregation operator enabled robust aggregation information, and the TOPSIS method was employed to compute probabilities, enabling the construction of an action-set-based decision model. Third, thresholds for three-way partitions were adaptively derived, and finally, extensive parameter analysis and comparative experiments with existing methods demonstrated the superior stability and effectiveness of the novel approach. The results indicated that the proposed method significantly enhances the scientific validity and feasibility of MADM in complex and uncertain environments, offering a novel solution for decision-making in the T-SF context.