A Comparative Analysis between the Linear Aggregation Model and the Choquet Integral Considering the Number of Ordinances Attainable in the Context of Multicriteria Decision Support

A central problem in the area of Multicriteria Decision Support (MCDA) is to order a set of alternatives based on a set of criteria, by means of an aggregation function, which can be linear or non-linear. This paper analyzes the behavior of the classical linear model and the model based on the Choquet integral (case 2-additive) in relation to the number of ordinances achievable by each method, for the same decision matrix, and by means of a Monte Carlo simulation step, in which the parameters of the two models are randomly varied. The results show that the Choquet model (2-additive) allows to find a significantly larger number of ordering when compared to the linear one, especially when the number of alternatives and criteria grows. This means that the 2-additive shock integral allows modeling a larger set of decision-maker preferences when compared to the linear model.