A multicriteria ordered clustering algorithm to determine precise or disjunctive partitions

We consider multicriteria clustering problems where the groups are ordered from the best to the worst. An approach relying on the principles of the k-means algorithm and disjunctive sorting based on evidence theory (DISSET) method is proposed for the detection of ordered clusters. The distinctive feature of this method is that it allows to obtain both precise and disjunctive partitions. In such situation, the actions can be assigned even to pair of groups (and not only to precise clusters). The decision maker is assumed to provide the following inputs: an evaluation table, the desired number of clusters and a valued preference model (obtained for instance by PROMETHEE method). The method is illustrated on two real examples: the Human Development Index (HDI-2013) and the Logistics Performance Index (LPI-2014).