On the elicitation of criteria weights in PROMETHEE-based ranking methods for a mobile application

Today, almost everybody has a smartphone and applications have been developed to help users to take decisions (e.g. which hotel to choose, which museum to visit, etc). In order to improve the recommendations of the mobile application, it is crucial to elicit the preference structures of the user. As problems are often based on several criteria, multicriteria decision aiding methods are most adequate in these cases, and past works have proposed indirect eliciting approaches for multicriteria decision aiding methods. However, they often do not aim of reducing as much as possible the cognitive efforts required by the user. This is prerequisite of mobile applications as they are used by everybody. In this work, the weights to assign to the evaluation criteria in a PROMETHEE-based ranking approach are unknown, and therefore must be elicited indirectly either from a partial ranking provided by the user or from the selection of his/her most preferred alternative into a subset of reference alternatives. In the latter case, the cognitive effort required by the decision-maker is minimal. Starting from a linear optimisation model aimed at searching for the most discriminating vector of weights, three quadratic variants are proposed subsequently to overcome the issues arising from the linear model. An iterative quadratic optimisation model is proposed to fit the real setting in which the application should operate, where the eliciting procedure must be launched iteratively and converge over time to the vector of weights, which are the weights that the user implicitly assigns to the evaluation criteria. Finally, three experiments are performed to confirm the effectiveness and the differences between the proposed models.