  Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart
of elementary CA, which are 2-state CA, via the polynomial representation of
local rules. In this paper, we first develop a new fuzzification methodology
for $q$-state CA. It is based on the vector representation of $q$-state CA,
that is, the $q$-states are assigned to the standard basis vectors of the
$q$-dimensional real space and the local rule can be expressed by a tuple of
$q$ polynomials. Then, the $q$-state vector-valued fuzzy CA are defined by
expanding the set of the states to the convex hull of the standard basis
vectors in the $q$-dimensional real space. The vector representation of states
enables us to enumerate the number-conserving rules of 3-state vector-valued
fuzzy CA in a systematic way.
