Distance to bipolar information from morphological dilation

Abstract

In this paper we propose definitions of distances to bipolar information. This notion is important to find a solution that matches bipolar queries, to exhibit recommendations satisfying preferences of an agent while respecting her constraints, to find an agreement between several agents. All these situations require to be able to compare candidate solutions, via their distance to some bipolar information, and several evaluation measures are proposed as well. We base distances and their comparison on mathematical morphology operators, in particular dilations and skeleton by influence zones.