The three-way decision model and multi-attribute decision-making: Methodological traps and challenges

The three-way decision (3WD) model has lately gained a lot of attention in data analysis and decision-making, and has even become a methodological framework that brings new insights into old problems. Our research is inspired by Bisht and Pal (2024) who introduced an innovative 3WD model which frames multi-attribute decision-making (MADM) problems. Considering both the loss and utility associated with various alternatives, they deduced the threshold values and directly integrated them to determine the final thresholds of 3WD. However, this approach does not fully address the precondition of the minimum expected cost or the maximum expected return inherent in the Bayesian decision procedure. In this paper, we would like to fill this research gap and discuss methodological aspects of establishing the decision thresholds of the 3WD model. Specifically, the experimental analysis demonstrates that the decision results generated by the decision model of Bisht and Pal (2024) may be inconsistent with the optimal decision results derived from the maximum expected return, thus potentially leading to conflicting outcomes. In the present paper, we address this problem and deduce more optimal expressions for the thresholds on the basis of the Bayesian decision procedure. In addition, through comparative experimental analysis, the rationality and effectiveness of the proposed threshold calculation method are verified. Finally, in the concrete derivation process, we also reveal the criteria for the existence of two-way decision, which makes our model applicable to more general situations.