On multicriteria clustering

International audienceIn Multi-Criteria Decision Aid one may generally identify three main typologies of problems: choice, ranking and sorting. Closely related to the last is that of clustering which we formally define in this article along with presenting a classification of different types of clustering objectives. We propose a clustering approach that can be applied to any of these objectives by making use of preferential statements between pairs of alternatives and grouping alternatives that are indifferent to each other while also ensuring that the relations between these groups contain several properties that we define. As finding the optimal result to this grouping problem in an exact manner is exponential in complexity we propose a heuristic approach which first groups the alternatives based solely on the indifference situations between them and at a second stage shifts alternatives from one cluster to another in order to ensure that certain properties between these groups are kept