Deck of Cards method for Hierarchical, Robust and Stochastic Ordinal Regression

Abstract: We consider the recently introduced application of the Deck of Cards Method (DCM) to ordinal regression proposing two extensions related to two main research trends in Multiple Criteria Decision Aiding, namely scaling and ordinal regression generalizations. On the one hand, procedures, different from DCM (e.g. AHP, BWM, MACBETH) to collect and elaborate Decision Maker's (DM's) preference information are considered to define an overall evaluation of reference alternatives. On the other hand, Robust Ordinal Regression and Stochastic Multicriteria Acceptability Analysis are used to offer the DM more detailed and realistic decision-support outcomes. More precisely, we take into account preference imprecision and indetermination through a set of admissible comprehensive evaluations of alternatives provided by the whole set of value functions compatible with DM's preference information rather than the univocal assessment obtained from a single value function. In addition, we also consider alternatives evaluated on a set of criteria hierarchically structured. The methodology we propose allows the DM to provide precise or imprecise information at different levels of the hierarchy of criteria. Like scaling procedures, the compatible value function we consider can be of a different nature, such as weighted sum, linear or general monotone value function, or Choquet integral. Consequently, the approach we propose is versatile and well-equipped to be adapted to DM's characteristics and requirements. The applicability of the proposed methodology is shown by a didactic example based on a large ongoing research project in which Italian regions are evaluated on criteria representing Circular Economy, Innovation-Driven Development and Smart Specialization Strategies.