UTA-poly and UTA-splines: Additive value functions with polynomial marginals

Olivier Sobrie, Nicolas Gillis, Vincent Mousseau and Marc Pirlot

European Journal of Operational Research, 2018, vol. 264, issue 2, 405-418

Abstract: 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.

Keywords: Multiple criteria decision analysis; Additive value function model; Preference learning; Ordinal regression; Semidefinite programming (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:264:y:2018:i:2:p:405-418

DOI: 10.1016/j.ejor.2017.03.021

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