On the closedness of imprecise probability models under aggregation

Given a number of imprecise probability models, we aim at aggregating them into a joint one using an aggregation rule such as the conjunction, disjunction, convex mixture, Pareto, conjunction-disjunction or maximal consistent subsets rules. We focus on the problem of analysing if these operators are closed, in the sense that the output belongs to the same family as the inputs. Specifically, we analyse this problem for the family of comparative probabilities, 2-monotone capacities, probability intervals, belief functions, p-boxes and minitive measures.