Predicting Preferences by Means of Analogical Proportions

It is assumed that preferences between two items, described in terms of criteria values belonging to a finite scale, are known for a limited number of pairs of items, which constitutes a case base. The problem is then to predict the preference between the items of a new pair. A new approach based on analogical proportions is presented. Analogical proportions are statements of the form “a is to b as c is to d”. If the change between item-1 and item-2 is the same as the change between item-3 and item-4, and a similar statement holds for item’-1, item’-2, item’-3, item’-4, then one may plausibly assume that the preference between item-1 and item’-1 is to the preference between item-2 and item’-2 as the preference between item-3 and item’-3 is to the preference between item-4 and item’-4. This offers a basis for a plausible prediction of the fourth preference if the three others are known. This approach fits well with the postulates underlying weighted averages. Two algorithms are proposed that look for triples of preferences appropriate for a prediction. The first one only exploits the given set of examples. The second one completes this set with new preferences deducible from this set under a monotony assumption. This completion is limited to the generation of preferences that are useful for the requested prediction. The predicted preferences should fit with the assumption that known preferences agree with a unique unknown weighted average. The reported experiments suggest the effectiveness of the proposed approach.