Completing preferences by means of analogical proportions

Abstract

We suppose that all we know about the preferences of an agent, is given by a (small) collection of relative preferences between choices represented by their evaluations on a set of criteria. Taking lesson from the success of the use of analogical proportions for predicting the class of a new item from a set of classified examples, we explore the possibility of using analogical proportions for completing a set of relative preferences. Such an approach is also motivated by a striking similarity between the formal structure of the axiomatic characterization of weighted averages and the logical definition of an analogical proportion. This paper discusses how to apply an analogical proportion-based approach to the learning of relative preferences, assuming that the preferences are representable by a weighted average, and how to validate experimental results. The approach is illustrated by examples.