We propose a family of probabilistic ordinal regression methods for multiple criteria sorting. They employ an additive value function model to aggregate the performances on multiple criteria and the threshold-based procedure to derive the class assignments of alternatives. The Decision Makers (DMs) can provide certain and uncertain assignment examples concerning a subset of reference alternatives, expressing the confidence levels using linguistic descriptions. On the one hand, we introduce Bayesian Ordinal Regression to derive a posterior distribution over a set of all potential sorting models by defining a likelihood for the provided preference information and specifying a prior of the preference model. This distribution emphasizes the potential differences in the models’ abilities to reconstruct the DM’s classification examples and thus is robust to the DM’s potential cognitive biases in her judgments. We also develop a Markov Chain Monte Carlo algorithm to summarize the posterior distribution of the preference model. On the other hand, we adapt Subjective Stochastic Ordinal Regression to sorting problems. It builds a probability distribution over the space of all value functions and class thresholds compatible with the DM’s certain holistic judgments. The ambiguity in representing incomplete and potentially uncertain preference information by the assumed sorting model is quantified using class acceptability indices. We investigate the performance and robustness of the introduced approaches through an extensive experimental study involving real-world datasets. We also compare them against novel methods based on mathematical programming that handle potential inconsistencies in uncertain preferences in the traditional way by minimizing the misclassification error or the number of misclassified reference alternatives.

我们提出了一系列用于多标准排序的概率序数回归方法。他们采用附加值函数模型来汇总多个标准的性能，并使用基于阈值的程序来导出替代方案的类别分配。决策者 (DM) 可以提供有关参考替代子集的某些和不确定的分配示例，并使用语言描述来表达置信水平。一方面，我们引入贝叶斯序数回归，通过定义所提供的偏好信息的可能性并指定偏好模型的先验，来导出一组所有潜在排序模型的后验分布。这种分布强调了模型重建 DM 分类示例的能力的潜在差异，因此对于 DM 判断中潜在的认知偏差具有鲁棒性。我们还开发了马尔可夫链蒙特卡罗算法来总结偏好模型的后验分布。另一方面，我们采用主观随机序数回归来对问题进行排序。它在所有价值函数和类别阈值的空间上建立了与 DM 的某些整体判断兼容的概率分布。使用类别可接受性指数来量化假设的排序模型表示不完整和潜在不确定的偏好信息的模糊性。我们通过涉及真实世界数据集的广泛实验研究来研究所引入方法的性能和稳健性。我们还将它们与基于数学规划的新方法进行比较，这些方法通过最小化错误分类错误或错误分类参考替代品的数量，以传统方式处理不确定偏好中的潜在不一致。