  The learning of predictive models for data-driven decision support has been a
prevalent topic in many fields. However, construction of models that would
capture interactions among input variables is a challenging task. In this
paper, we present a new preference learning approach for multiple criteria
sorting with potentially interacting criteria. It employs an additive
piecewise-linear value function as the basic preference model, which is
augmented with components for handling the interactions. To construct such a
model from a given set of assignment examples concerning reference
alternatives, we develop a convex quadratic programming model. Since its
complexity does not depend on the number of training samples, the proposed
approach is capable for dealing with data-intensive tasks. To improve the
generalization of the constructed model on new instances and to overcome the
problem of over-fitting, we employ the regularization techniques. We also
propose a few novel methods for classifying non-reference alternatives in order
to enhance the applicability of our approach to different datasets. The
practical usefulness of the proposed method is demonstrated on a problem of
parametric evaluation of research units, whereas its predictive performance is
studied on several monotone learning datasets. The experimental results
indicate that our approach compares favourably with the classical UTADIS method
and the Choquet integral-based sorting model.
