Interval three-way decision model based on data envelopment analysis and prospect theory

Since the three-way decision theory was proposed, two paradigms, "narrow sense" and "broad sense", have gradually evolved, each demonstrating unique advantages in handling multi- granularity information and uncertainty analysis. These approaches provide a systematic theoretical framework for solving complex decision-making problems. However, the traditional three-way decision model has limitations in multi-input-output scenarios, and the current method is still insufficient in characterizing the risk attitudes and psychological characteristics of decision-makers. To address these challenges, this paper proposes an interval three-way decision model based on Data Envelopment Analysis (DEA) and Prospect theory for multi-input-output decision problems. First, we define a many-valued decision information system based on DEA, using benefit scores from various orientations as decision attributes to formulate decision strategies. Second, to mitigate the subjective bias introduced by reference points in Prospect theory, we introduce triangular fuzzy reference points that account for interval uncertainty. Additionally, we propose a calculation method for the multi-input-output interval membership function of Decision-Making Units (DMUs) and a construction method for the value function. Comprehensive decision rules are derived by calculating the overall prospect value. Finally, the effectiveness of the proposed model is validated using a series of experiments across multiple datasets, with comparisons to over ten existing methods. The results indicate that the model achieves competitive performance in terms of classification accuracy and decision-making efficiency, demonstrating its strengths in addressing uncertain multi-input-output decision problems while incorporating decision-makers' risk preferences in an interval environment.