  In this short note, we show by elementary computations that the notion of
non-Archimedean fuzzy normed (and 2-normed) spaces is void. Namely, there are
no strictly convex spaces at all --not even the zero-dimensional linear space.
  Before this, we also study the case of strictly convex non-Archimedean normed
spaces; in this setting we see that the only nonzero linear space (defined over
an arbitrary non-Archimedean field) that satisfies this property is the
one-dimensional linear space over $\mathbb{Z}/3\mathbb{Z}$.
  Consequently, the results that have been proven for this class of spaces,
like the Mazur-Ulam Theorem, are either trivial or empty statements.
