New results on convergence in distribution of fuzzy random variables

We study some properties of convergence in distribution of fuzzy random variables in the metric d(p), more precisely, if this type of convergence is preserved when we apply some functions between the space of fuzzy sets and other metric spaces. In particular, we show that this convergence is preserved when we take the closed convex hull, the maximum, the minimum, the product and the quotient. Moreover, it is preserved when we apply some functionals, such as the value or the ambiguity. Finally, we show some results regarding convergence in distribution with respect to the metric d(infinity).