  We study three notions of directability of fuzzy automata akin to the D1-,
D2- and D3-directability of nondeterministic automata. Thus an input word $w$
of a fuzzy automaton is D1-directing if a fixed single state is reachable by
$w$ from all states, D2-directing if exactly the same states are reachable by
$w$ from every state, and D3-directing if there is a state reachable by $w$
from every state. We study the various sets of directing words of fuzzy
automata, prove that the directability properties are decidable, and show how
such results can be deduced from the theory of directable nondeterministic
automata. Moreover, we establish the closure properties of the different
classes of directable fuzzy automata under the class operations of forming
subautomata, homomorphic images and finite direct products.
