  Additive utility function models are widely used in multiple criteria
decision analysis. In such models, a numerical value is associated to each
alternative involved in the decision problem. It is computed by aggregating the
scores of the alternative on the different criteria of the decision problem.
The score of an alternative is determined by a marginal value function that
evolves monotonically as a function of the performance of the alternative on
this criterion. Determining the shape of the marginals is not easy for a
decision maker. It is easier for him/her to make statements such as
"alternative $a$ is preferred to $b$". In order to help the decision maker, UTA
disaggregation procedures use linear programming to approximate the marginals
by piecewise linear functions based only on such statements. In this paper, we
propose to infer polynomials and splines instead of piecewise linear functions
for the marginals. In this aim, we use semidefinite programming instead of
linear programming. We illustrate this new elicitation method and present some
experimental results.
