This paper is dedicated to a robust ordinal method for learning the preferences of a decision maker between subsets. The decision model, derived from Fishburn and LaValle (1996) and whose parameters we learn, is general enough to be compatible with any strict weak order on subsets, thanks to the consideration of possible interactions between elements. Moreover, we accept not to predict some preferences if the available preference data are not compatible with a reliable prediction. A predicted preference is considered reliable if all the simplest models (Occam's razor) explaining the preference data agree on it. Following the robust ordinal regression methodology, our predictions are based on an uncertainty set encompassing the possible values of the model parameters. We define a robust ordinal dominance relation between subsets and we design a procedure to determine whether this dominance relation holds. Numerical tests are provided on synthetic and real-world data to evaluate the richness and reliability of the preference predictions made.

翻译：本文致力于研究一种稳健的序数方法，用于学习决策者在子集之间的偏好。决策模型源自Fishburn和LaValle（1996）的研究，其参数通过本文方法学习，该模型由于考虑了元素间的可能交互作用，足以兼容任意严格弱序下的子集偏好。此外，若现有偏好数据与可靠预测不兼容，我们允许放弃部分偏好预测。当所有能解释偏好数据的最简单模型（奥卡姆剃刀原则）达成一致时，该预测被视为可靠。遵循稳健序数回归方法论，我们的预测基于涵盖模型参数可能取值的集合。我们定义了子集间的稳健序数支配关系，并设计了判定该支配关系是否成立的计算流程。基于合成数据与实际数据的数值实验验证了所提偏好预测的丰富性与可靠性。