Abstract
It is often the case in the applications of MultiCriteria Decision Making that the values of alternatives are unknown on some attributes. An interesting situation arises when the attributes having missing values are actually not relevant and shall thus
be removed from the model. Given a model that
has been elicited on the complete set of attributes,
we are looking thus for a way – called restriction
operator – to automatically remove the missing attributes from this model. Axiomatic characterizations are proposed for three classes of models. For
general quantitative models, the restriction operator
is characterized by linearity, recursivity and decomposition on variables. The second class is the set of
monotone quantitative models satisfying normalization conditions. The linearity axiom is changed
to fit with these conditions. Adding recursivity and
symmetry, the restriction operator takes the form of
a normalized average. For the last class of models
– namely the Choquet integral, we obtain a simpler
expression. Finally, a very intuitive interpretation
is provided for this last model