Preference Learning from Interval Pairwise Data. A Distance-Based Approach

Preference learning has recently received a lot of attention within the machine learning field, concretely learning by pairwise comparisons is a well-established technique in this field. We focus on the problem of learning the overall preference weights of a set of alternatives from the (possibly conflicting) uncertain and imprecise information given by a group of experts into the form of interval pairwise comparison matrices. Because of the complexity of real world problems, incomplete information or knowledge and different patterns of the experts, interval data provide a flexible framework to account uncertainty and imprecision. In this context, we propose a two-stage method in a distance-based framework, where the impact of the data certainty degree is captured. First, it is obtained the group preference matrix that best reflects imprecise information given by the experts. Then, the crisp preference weights and the associated ranking of the alternatives are derived from the obtained group matrix. The proposed methodology is made operational by using an Interval Goal Programming formulation.