A new scaling MCDA procedure putting together pairwise comparison tables and the deck of cards method

Abstract: This paper deals with an improved version of the deck of the cards method to render the construction of the ratio and interval scales more `accurate'. The improvement comes from the fact that we can account for a richer and finer preference information provided by the decision-makers, which permits a more accurate modelling of the strength of preference between two consecutive levels of a scale. Instead of considering only the number of blank cards between consecutive positions in the ranking of objects such as criteria and scale levels, we consider also the number of blank cards between non consecutive positions in the ranking. This information is collected in a pairwise comparison table that it is not necessarily built with precise values. We can consider also missing information and imprecise information provided in the form of ranges. Since the information provided by the decision-makers is not necessarily consistent, we propose also some procedures to help the decision-maker to make consistent his evaluations in a co-constructive way interacting with an analyst and reflecting and revising her/his judgments. The method is illustrated through and example in which, generalizing the SWING method, interacting criteria are aggregated through the Choquet integral.