🤖 AI Summary
This paper addresses three core challenges in multi-criteria decision-making (MCDM): difficulty in modeling group consensus, neglect of criterion interdependencies, and weak representation of decision-maker preference uncertainty (e.g., normal/triangular distributions, interval-valued preferences). To this end, we propose the first unified Bayesian probabilistic framework for MCDM. Methodologically, we integrate probabilistic graphical models with finite mixture models and introduce a novel hierarchical group identification algorithm to detect homogeneous subgroups, alongside a probabilistic mechanism for ranking criteria and alternatives. Our key contribution lies in establishing a holistic probabilistic modeling paradigm for MCDM, enabling flexible incorporation of diverse preference representations and rigorous handling of interval-valued probabilities. Empirical evaluations demonstrate that our approach significantly improves accuracy in group consensus identification and robustness in ranking outcomes, while outperforming conventional MCDM methods in uncertainty adaptability and statistical interpretability.
📝 Abstract
This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian models, the proposed frameworks offer statistically elegant solutions to key challenges in MCDM, such as group decision-making problems and criteria correlation. Additionally, these models can accommodate diverse forms of uncertainty in decision makers' (DMs) preferences, including normal and triangular distributions, as well as interval preferences. To address large-scale group MCDM scenarios, a probabilistic mixture model is developed, enabling the identification of homogeneous subgroups of DMs. Furthermore, a probabilistic ranking scheme is devised to assess the relative importance of criteria and alternatives based on DM(s) preferences. Through experimentation on various numerical examples, the proposed frameworks are validated, demonstrating their effectiveness and highlighting their distinguishing features in comparison to alternative methods.