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.

翻译：本文提出贝叶斯框架，用于处理多准则决策问题的多个方面，通过概率化解释多准则决策方法与挑战。利用贝叶斯模型的灵活性，所提出的框架为多准则决策中的关键难题（如群体决策问题与准则相关性）提供了统计上优雅的解决方案。此外，这些模型能够适应决策者偏好的多种不确定性形式，包括正态分布与三角分布，以及区间偏好。针对大规模群体多准则决策场景，开发了概率混合模型，能够识别决策者中的同质子群体。进一步，设计了一种概率排序方案，基于决策者偏好评估准则与备选方案的相对重要性。通过多个数值示例的实验验证，所提出的框架被证实有效，并凸显了其相较于其他方法的显著特征。