Abstract
In 1992, a new definition of a fuzzy topological space was given by introducing the concept of a gradation of openness. In this paper, a new definition of a fuzzy uniform (resp. proximity) space is given by introducing the concept of a gradation of uniformity (resp. proximity) on a non empty set X. How to construct a gradation of openness induced by a gradation of uniformity (resp. proximity) is explained. The connexions between gradations of proximity and gradations of uniformity are investigated.
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