  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.
