A compensatory value function for modeling risk tolerance and criteria interactions in preference disaggregation

Preference disaggregation is effective in inducing the preference models of decision makers from empirical data, which is of great significance for data-driven decision-making where there is a difficulty to interact with decision makers. Existing preference disaggregation techniques in multiple criteria decision making mainly employ additive value functions for aggregation, ignoring the interrelationship between criteria. This study aims to model the desired behavior of a value system in an interpretable manner. To do so, we introduce a compensatory value function by dividing the trade-off mechanism between criteria into independent and dependent parts. The independent part is used to model the importance of criteria additively, while the dependent part describes interactions between criteria and decision makers’ risk tolerance. In addition, we develop a preference disaggregation procedure using the compensatory value function as a preference structure to learn preference models compatible with historical or fictional decision examples through linear programming. The proposed procedure is demonstrated through five case studies based on real-world datasets. Experimental results indicate that our approach compares favorably with the value functions which consider limited preference factors.