Copulas, lower probabilities and random sets : how and when to apply them?

A copula is an aggregation function, that can be used as a dependency model. Any multivariate distribution function can be characterized by its marginals and a copula. When introducing imprecision in the modelling of those distribution functions, different solutions are available to aggregate the univariate uncertainty representations into a multivariate one via the copula. We present some of those solutions, and discuss their respective inclusions for special cases : independence, necessity functions and pboxes.