  A deterministic finite automaton is directable if it has a directing word
which takes the automaton from every state to the same state. These notions
have been extended also to other kinds of automata. Thus, B.~Imreh and
M.~Steinby (1999) identified three natural types of directing words, called
D1-, D2- and D3-directing words, for nondeterministic finite automata (NFAs).
Here we adapt these notions for fuzzy finite automata (FFAs). The D3-directing
words obtained this way are precisely the directing words introduced by
V.~Karthikeyan and M. Rajasekar (2015). With any FFA F we associate an NFA Fnd
which has the same Di-directing words as F. Thus, if these definitions are
used, the theory of directable FFAs reduces to that of NFAs.
  We also introduce three new kinds of directing words of fuzzy automata that
we call DD1-, DD2- and DD3-directing words, respectively which depend more on
the fuzzy transition degrees between states. We establish some basic properties
of the sets $DDi(F)$ of DDi-directing words of any given FFA F. In particular,
it is shown that these languages are regular, and that DDi-directability is
decidable. For so-called normal FFAs the languages DDi(F) are shown to have
some special properties. Several relationships between the families of the
corresponding sets DDi(F) of DDi-directing words are presented. We also
determine the complete meet-semilattice of the various classes of
DDi-directable FFAs and normal FFAs and their intersections.
