Fuzzy ultrametrics on the set of probability measures

We introduce a fuzzy ultrametric on the set of probability measures with compact support defined on a fuzzy metric space. The construction is a counterpart, in the realm of fuzzy ultrametric spaces, of the construction due to Vink and Rutten of an ultrametric on the set of probability measures with compact supports on an ultrametric space.It is proved that the set of probability measures with finite supports is dense in the natural topology generated by the defined fuzzy ultrametric.