Choquet Integral Versus Weighted Sum in Multicriteria Decision Contexts

In this paper, we address the problem of comparing the performances of two popular aggregation operators, the weighted sum and the Choquet integral, for selecting the best alternative among a set of alternatives, all evaluated according to different criteria. While the weighted sum is simple to use and very popular, the Choquet integral is still hard to use in practice but leads theoretically to better results in terms of concordance with the preferences of a decision maker. However, given the efforts needed to set the parameters of the Choquet integral, it is important to measure, for a given decision problem, if it is really worth defining the Choquet integral or if a simple weighted sum could have been used to determine the best alternative. We will compute the probability that a recommendation to a decision maker could only been obtained with the Choquet integral and not with a weighted sum. When the number of criteria increases, the results show that this probability tends to one. However, a high value of probability can only be attained for particular data sets.