  In this paper, we define asymptotic dimension of fuzzy metric spaces in the
sense of George and Veeramini. We prove that asymptotic dimension is an
invariant in the coarse category of fuzzy metric spaces. We also show several
consequences of asymptotic dimension in the fuzzy setting which resemble the
consequences of asymptotic dimension in the metric setting. We finish with
calculating asymptotic dimension of a few fuzzy metric spaces.
