FuzzyTL-uniform spaces

Abstract

The main purpose of this paper is to introduce a new structure that is a fuzzyTL-uniform space. We show that our structure generates a fuzzy topological space, precisely, a fuzzyT-locality space. Also, we deduce the concept of level uniformities of a fuzzyTL-uniformity. We connect the category of fuzzyTL-uniform spaces with the category of uniform spaces. We establish a necessary and sufficient condition, under which a fuzzyTL-uniformity is probabilistic pseudometrizable. Finally, we define a functor from the category of fuzzyTL-uniform spaces into the category of fuzzyT-locality spaces and we show that it preserves optimal lifts.