  The Choquet integral is a powerful aggregation operator which lists many
well-known models as its special cases. We look at these special cases and
provide their axiomatic analysis. In cases where an axiomatization has been
previously given in the literature, we connect the existing results with the
framework that we have developed. Next we turn to the question of learning,
which is especially important for the practical applications of the model. So
far, learning of the Choquet integral has been mostly confined to the learning
of the capacity. Such an approach requires making a powerful assumption that
all dimensions (e.g. criteria) are evaluated on the same scale, which is rarely
justified in practice. Too often categorical data is given arbitrary numerical
labels (e.g. AHP), and numerical data is considered cardinally and ordinally
commensurate, sometimes after a simple normalization. Such approaches clearly
lack scientific rigour, and yet they are commonly seen in all kinds of
applications. We discuss the pros and cons of making such an assumption and
look at the consequences which axiomatization uniqueness results have for the
learning problems. Finally, we review some of the applications of the Choquet
integral in decision analysis. Apart from MCDA, which is the main area of
interest for our results, we also discuss how the model can be interpreted in
the social choice context. We look in detail at the state-dependent utility,
and show how comonotonicity, central to the previous axiomatizations, actually
implies state-independency in the Choquet integral model. We also discuss the
conditions required to have a meaningful state-dependent utility representation
and show the novelty of our results compared to the previous methods of
building state-dependent models.
