Comparison of applications of multicriteria UTA methods

Among the many multicriteria methods by total aggregation the UTA method proposed by Jacquet-Lagrèze and Siskos has the advantage of allowing the estimation of a non-linear additive utility function. However this method comes up against a problem of multiple solutions for the calculated weights of the utility function. When it comes to evaluating and classifying projects which are not part of the reference set the classifications of those projects will then depend on the chosen function. This problem has already been discussed in the literature in the case where the utility function cannot be estimated without errors. However, few of the solutions advanced in that context can be applied to the case where the estimation is without errors. This problem of multiple solutions and of predictive quality of the UTA method is analysed in the present paper, using as an example of application the classification of road investments projects. First of all, the authors propose to use an optimal fractional experimental plan as reference set. Then, they study different possible variants of the method and propose a new one which, maximising the smallest differences between the utilities of the projects, allows a great reduction in the domain of possible solutions.