Fuzzy uniformly continuous functions

In [1] the authors introduce a definition of fuzzy continuity that enabler; to claim that a real function is bounded on a compact set if and only if it is fuzzy continuous. However, some other properties, natural for continuous functions, are not more valid for fuzzy continuous ones. An example of such property is the intermediate value principle. We show that if we use the methods from [1] to define fuzzy uniform continuity, we salvage this principle.