Abstract
This doctoral thesis brings forward a novel approach to quantiles for multivariate random variables, which gives rise to quantile functions mapping into specific complete lattices of sets. This allows to generalize the univariate case with respect to both the calculus and the application perspective. More specifically, a set-valued Value at Risk as well as stochastic orders are introduced in a natural manner. Moreover, a first algorithm to compute the empirical version of these new quantiles is developed. The application of these new concepts to the multiple-criteria decision making problem has shown to be very effective.