Unified Bayesian Frameworks for Multi-criteria Decision-making Problems

This paper presents Bayesian frameworks for different tasks within multi-criteria decision-making (MCDM) based on a probabilistic interpretation of the MCDM methods and problems. Owing to the flexibility of Bayesian models, the proposed frameworks can address several long-standing and fundamental challenges in MCDM, including group decision-making problems and criteria correlation, in a statistically elegant manner. Also, the models can accommodate different forms of uncertainty in the preferences of the decision makers (DMs), such as normal and triangular distributions as well as interval preferences. Further, a probabilistic mixture model is developed that can group the DMs into several exhaustive classes. A probabilistic ranking scheme is also designed for both criteria and alternatives, where it identifies the extent to which one criterion/alternative is more important than another based on the DM(s) preferences. The experiments validate the outcome of the proposed frameworks on several numerical examples and highlight its salient features compared to other methods.