A Novel Coarse-Grained Fuzzy Model: Q-rung Orthopair Fuzzy Granular-Balls on Three-Way Multi-Attribute Decision-Making with Regret Theory for Pre-Diagnosis of Depression

Three-way multi-attribute decision-making (3W-MADM) in fuzzy environments provides an effective framework for handling uncertain information by introducing a boundary domain, which reduces misjudgment risks and enhances fault tolerance. However, existing 3W-MADM research is largely confined to fine-grained perspective and still faces shortcomings such as non-compliance with the computational principle of conditional probabilities, neglect of the decision-maker's psychological factors, and low decision-making efficiency. Based on this, this paper proposes a multi-granular 3W-MADM method with regret theory based on q-rung orthopair fuzzy granular-balls (q-ROFGBs) from a coarse-grained perspective. First, the q-ROFGBs are developed by combining qrung orthopair fuzzy sets with granular-balls and the generation algorithm is designed. Second, a computational method for conditional probabilities with proper semantic interpretation based on q-ROFGBs is introduced. Third, regret theory is incorporated to account for the influence of psychological factors in decision-making. Next, a new 3W-MADM method with regret theory based on q-ROFGBs is established. Finally, the effectiveness, practicality, and flexibility of the proposed method are demonstrated through experimental analysis on both small-scale synthetic datasets and a large-scale real-world depression dataset. Compared with existing 3WMADM methods, the proposed method not only incorporates the impact of regret psychology but also achieves the shorter decision-making time.