Towards multicriteria clustering: An extension of the k-means algorithm

The research within the multicriteria classification field is mainly focused on the assignment of actions to pre-defined classes. Nevertheless the building of multicriteria categories remains a theoretical question still not studied in detail. To tackle this problem, we propose an extension of the well-known k-means algorithm to the multicriteria framework. This extension relies on the definition of a multicriteria distance based on the preference structure defined by the decision maker. Thus, two alternatives will be similar if they are preferred, indifferent and incomparable to more or less the same actions. Armed with this multicriteria distance, we will be able to partition the set of alternatives into classes that are meaningful from a multicriteria perspective. Finally, the examples of the country risk problem and the diagnosis of firms will be treated to illustrate the applicability of this method.