On fuzzy uniformities induced by a fuzzy metric space

Different types of fuzzy uniformities have been introduced in the literature standing out the notions due to Hutton, Höhle and Lowen. The main purpose of this paper is to study several methods to endow a fuzzy metric space (X,M,⁎), in the sense of George and Veeramani, with a probabilistic uniformity and with a Hutton [0,1](-quasi)-uniformity. We will show the functorial behavior of these constructions as well as its relation with respect to Lowen's functors and Katsaras's functors, which establish a relationship between the categories of probabilistic uniformities and Hutton [0,1](-quasi)-uniformities with the category of classical uniformities respectively. Furthermore, we also study the fuzzy topologies associated with these fuzzy uniformities.