Hesitant fuzzy three-way decision-making for large-scale data based on a new distance measure and behavioral theory

In highly uncertain real-world environments, making robust decisions amid incomplete information and the cognitive biases of decision-makers remain critical challenges in project management and other complex system decision-making-related domains. Although the three-way decision-making (3WD) method based on hesitant fuzzy (HF) environments provides an effective approach for managing uncertainty, the current research still has shortcomings in several key areas. On the one hand, the distance formulas that are commonly used for computing hesitant fuzzy elements (HFEs) generally suffer from insufficient sensitivity to the information captured by the score function and weak discriminative power. On the other hand, the process of determining loss functions is subjective and fails to consider the behavioral psychological factors of decision-makers, making it difficult to reflect the cognitive characteristics of humans during actual decision-making processes. These issues collectively limit the adaptability and practicality of the existing decision-making methods in complex real-world environments. To address the aforementioned issues, this study is aimed at constructing an HF 3WD framework that possesses both cognitive rationality and computational robustness. To this end, the core contributions of this work are as follows. First, a novel HF distance measure is developed, significantly improving the ability to distinguish fuzzy information differences. Second, a novel o -dominance relation is introduced, and the conditional probability is calculated using a data-driven approach, eliminating the reliance on expert scoring and thereby improving the objectivity and accuracy of the conditional probability. Finally, an objective loss function is established, effectively capturing the decision-maker’s nonlinear value perceptions and comparative psychology in gain and loss scenarios. Furthermore, comparative experiments and parameter analyses are conducted in big data scenarios to validate the fact that the proposed method outperforms the existing methods in terms of classification accuracy and decision stability, demonstrating superior effectiveness and robustness. We believe that by simulating human judgments made under uncertainty, this method opens up new avenues for implementing artificial intelligence-based decision-making systems in high-risk scenarios.