Title: On Modeling Multi-Criteria Decision Making with Uncertain Information using Probabilistic Rules

Abstract: Decision-making processes often involve dealing with uncertainty, which is traditionally addressed through probabilistic models. However, in practical scenarios, assessing probabilities reliably can be challenging, compounded by diverse perceptions of probabilistic information among decision makers. To address this variability and accommodate diverse preferences regarding uncertainty, we introduce the Probabilistic Abstract Decision Framework (PADF). PADF offers a structured approach for reasoning across different decision criteria, encompassing the optimistic, pessimistic, and Laplace perspectives, each tailored to distinct perceptions of uncertainty. We illustrate how PADF facilitates the computation of optimal decisions aligned with these criteria by leveraging probabilistic rules. Furthermore, we present strategies for optimizing the computational efficiency of these rules, leveraging appropriate independence assumptions to navigate the extensive search space inherent in PADF. Through these contributions, our framework provides a robust and adaptable tool for effectively navigating the complexities of decision-making under uncertainty.