A regret-based three-way decision with novel intuitionistic fuzzy similarity in an intuitionistic fuzzy information...

Three-way decision theory partitions the universe into positive, negative, and boundary regions, providing a flexible framework for decision-making under uncertainty that allows decisions to be deferred when information is insufficient, thereby controlling costs and reducing risks. Its core advantage lies in permitting deferred decisions when information is insufficient, thereby effectively controlling costs and reducing risks. Although the introduction of intuitionistic fuzzy sets can further capture the hesitation information within alternatives and enhance the model's expressiveness for fuzziness, existing research still faces dual challenges. On the one hand, traditional similarity measures mostly rely on distance formulas, which are prone to introducing bias and struggle to accurately capture the intrinsic relationships between intuitionistic fuzzy sets. On the other hand, existing frameworks are mostly based on the assumption of complete rationality, overlooking irrational decision-making under the combined influence of fuzzy information and psychological factors. To address these issues, this paper introduces a regret-joy function into intuitionistic fuzzy information systems and constructs a novel three-way decision method that integrates psychological behavioral characteristics. The main contributions are as follows: (1) To more accurately capture the intrinsic relationships among intuitionistic fuzzy sets and to effectively avoid biases in similarity judgments caused by distance measures, we propose a novel intuitionistic fuzzy similarity measure under an intuitionistic fuzzy information system that is based directly on hesitancy and does not rely on distance. (2) Based on the new intuitionistic fuzzy similarity measure and combined with ideal positive degree to construct objective weights, we provide methods for computing intuitionistic fuzzy similarity classes and conditional probabilities. (3) By integrating objective weights with regret-joy functions, we construct a relative loss function that better aligns with decision-makers' psychology. (4) Combining the relative loss function with conditional probability, we propose a novel three-way decision method in intuitionistic fuzzy information systems; this method can effectively handle uncertain decisions and enhance decision rationality and applicability. Finally, the effectiveness and rationality of the proposed method are verified through case analysis and experimental comparison. This study not only offers a new perspective on similarity measures in intuitionistic fuzzy information systems but also lays a solid foundation for the deepening and broader application of behavioral three-way decision theory.