dc.description.abstract | We propose an axiomatization of the Choquet integral model for the
general case of a heterogeneous product set X = X1 Xn. Previous
characterizations of the Choquet integral have been given for
the particular cases X = Y n and X = Rn. However, this makes
the results inapplicable to problems in many fields of decision theory,
such as multicriteria decision analysis (MCDA), state-dependent
utility (SD-DUU), and social choice. For example, in multicriteria decision
analysis the elements of X are interpreted as alternatives, characterized
by criteria taking values from the sets Xi. Obviously, the
identicalness or even commensurateness of criteria cannot be assumed
a priori. Despite this theoretical gap, the Choquet integral model is
quite popular in the MCDA community and is widely used in applied
and theoretical works. In fact, the absence of a sufficiently general
axiomatic treatment of the Choquet integral has been recognized several
times in the decision-theoretic literature. In our work we aim to
provide missing results { we construct the axiomatization based on
a novel axiomatic system and study its uniqueness properties. Also,
we extend our construction to various particular cases of the Choquet
integral and analyse the constraints of the earlier characterizations.
Finally, we discuss in detail the implications of our results for the
applications of the Choquet integral as a model of decision making. | en_US |