An extension of PROMETHEE to divisive hierarchical multicriteria clustering

Abstract

We consider an extension of PROMETHEE II for multicriteria ordered clustering. The method is based on a divisive hierarchical clustering algorithm. A new property of the net flow score is proved and then used to divide existing clusters. The method is illustrated on two applications: the ranking of management masters by the financial times and the human development index.

Assessing partially ordered clustering in a multicriteria comparative context

“…Working in a such comparative context is usual for researchers from the multiple criteria decision aid (MCDA) community, but interest in clustering remains limited. While MCC algorithms are very often extensions of classical PR algorithms (such as K -means and some hierarchical algorithms [16,18,19,20,36]), cluster validation tools are lacking.…”

“…In fact, research in MCC often proposes totally ordered clustering [17,20,21,22]. This constraint may not be adapted to the natural structure of the data, which may present quite distinct clusters but without any preferential relationship between them, as mentioned above for clusters A and B in Figure 1.…”

“…supplementary material). These methods were "naturally" extended for clustering purposes in MCC algorithms that generate partitions of totally ordered clusters [17,20,21,22]. In these MCC methods, this strong order constraint takes precedence over the compactness and separability properties of clusters.…”

A Dichotomous Approach to Reduce Rank Reversal Occurrences in PROMETHEE II Rankings

“…In this section, we present an alternative method to obtain a pre-order on the basis of a preference matrix. This is based on a hierarchical clustering procedure using a dichotomous process that has been proposed recently by De Smet [6]. The idea is to separate the n alternatives into two subgroups that are ordered.…”

“…On the contrary, we will rather investigate if it is possible to manage rank reversal. Therefore, we consider a new ranking method based on a property of the Promethee's net flow scores [6] with the aim to reduce rank reversal occurrences.…”