A new hierarchical multiple criteria ordered clustering approach as a complementary tool for sorting and ranking problems

Multiple criteria ordered clustering is a problem that involves grouping the objects of decisions (actions) into a priori unknown ordered classes considering the preferences of a decision maker (DM). By exploring the relationship between multiple criteria sorting and multiple criteria ordered clustering, we take advantage of some ordinal classification approaches to propose a new approach. The set of totally ordered clusters fulfills a property of monotonicity with respect to dominance and an asymmetric preference relation; this is useful for suggesting a more consistent and robust rank of actions regarding the existence of possible “irrelevant alternatives”. The algorithm designed to operationalize our approach makes use of either a fuzzy outranking relation or a fuzzy preference relation. Imperfect knowledge (namely uncertainty and imprecision) of criteria performance levels and model parameter values can be modelled using interval numbers. Our approach and algorithm are illustrated through a simple interval extension of the well-known PROMETHEE method, which is applied to group countries according to human development criteria. The OECD country governments are also grouped according to their public sector performance but instead using a fuzzy outranking relation in an interval framework. In both examples, the results are very promising.