A robust hierarchical nominal multicriteria classification method based on similarity and dissimilarity

Cat-SD (Categorization by Similarity-Dissimilarity) is a multiple criteria decision aiding method for dealing with nominal classification problems (predefined and non-ordered categories). Actions are assessed according to multiple criteria and assigned to one or more categories. A set of reference actions is used to define each category. The assignment of an action to a given category depends on the comparison of the action to each reference set according to likeness thresholds. Distinct sets of criteria weights, interaction coefficients, and likeness thresholds can be defined per category. When applying Cat-SD to complex decision problems, may be useful to consider a hierarchy of criteria to give a more intelligible vision of the performances of the considered actions. We propose to apply Multiple Criteria Hierarchy Process to Cat-SD to take into account criteria structured in a hierarchical way. On the basis of the known deck of cards method, we also consider an imprecise elicitation of parameters permitting to consider interactions and antagonistic effects between criteria. The elicitation procedure we are proposing can be applied to any Electre method. With the purpose of exploring the assignments obtained by Cat-SD considering possible sets of parameters, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA). The SMAA methodology allows to draw statistical conclusions on the classification of the actions. The proposed method, SMAA-hCat-SD, helps the decision maker to check the effects of the variation of parameters on the classification at different levels of the hierarchy. We propose also a procedure, based on the concept of loss function, to get a deterministic classification fulfilling some requirements given by the decision maker and taking into account the hierarchy of criteria and the probabilistic assignments obtained through SMAA. Also this procedure can be applied to any classification Electre method. The application of the new proposal is shown through an example.