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

• Published in: Omega (Oxford) Vol. 117; p. 102820
• Main Authors: Díaz, Raymundo, Fernández, Eduardo, Figueira, José-Rui, Navarro, Jorge, Solares, Efrain
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-06-2023
• Subjects: Clustering; Fuzzy preferences; Imperfect knowledge; Multi-criteria analysis; Clustering; Multi-criteria analysis; Imperfect knowledge; Fuzzy preferences
• ISSN: 0305-0483
• DOI: 10.1016/j.omega.2022.102820

•A new preference-oriented clustering method.•Clusters are totally ordered according to a strict preference relation.•It is useful to rank large sets of actions.•It helps to characterize classes in multi-criteria ordinal classification.•Imprecision and uncertainty handled by interval outranking approaches.
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.