  Computability theorists have introduced multiple hierarchies to measure the
complexity of sets of natural numbers. The Kleene Hierarchy classifies sets
according to the first-order complexity of their defining formulas. The Ershov
Hierarchy classifies $\Delta^0_2$ sets with respect to the number of mistakes
that are needed to approximate them. Biacino and Gerla extended the Kleene
Hierarchy to the realm of fuzzy sets, whose membership functions range in a
complete lattice $L$ (e.g., the real interval $[0; 1]_\mathbb{R}$). In this
paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and
investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy
$n$-c.e. sets which form the finite levels of this hierarchy. Intuitively, a
fuzzy set is $n$-c.e. if its membership function can be approximated by
changing monotonicity at most $n-1$ times. We prove that the Fuzzy Ershov
Hierarchy does not collapse; that, in analogy with the classical case, each
fuzzy $n$-c.e. set can be represented as a Boolean combination of fuzzy c.e.
sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does
not exhaust the class of all $\Delta^0_2$ fuzzy sets.
