A robust hierarchical nominal classification method based on similarity and dissimilarity

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 for defining each category. The assignment of an action to a given category depends on the comparison of the action to the reference set according to a likeness threshold. Distinct sets of criteria weights, interaction coefficients, and likeness thresholds can be defined per category. When applying Cat-SD to complex decision problems, considering a hierarchy of criteria may help to decompose them. We propose to apply Multiple Criteria Hierarchy Process (MCHP) to Cat-SD. An adapted MCHP is proposed to take into account possible interaction effects between criteria structured in a hierarchical way. We also consider an imprecise elicitation of parameters. 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 to obtain a final classification fulfilling some requirements by taking into account the hierarchy of criteria and the probabilistic assignments obtained applying SMAA. The application of the proposed method is showed through an example.