Abstract
We show that a fuzzy uniformity D is uniquely determined by its family of α-level uniformities ( D α: α ϵ (0, 1)). On the other hand, if a family ( D ( α): α ϵ (0, 1)) of uniformities on a set X is given and the family satisfies certain conditions, then there exists a unique fuzzy uniformity D on X whose family of α-level uniformities is the given family.
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