UTA-poly and UTA-splines: additive value functions with polynomial marginals
This work addresses the challenge for decision makers in multiple criteria decision analysis by providing a more flexible elicitation method, though it appears incremental as it builds on existing UTA disaggregation procedures.
The paper tackles the problem of determining marginal value functions in additive utility models by proposing to infer polynomials and splines instead of piecewise linear functions, using semidefinite programming instead of linear programming, and presents experimental results to illustrate the method.
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.