Are there fuzzy state machines?

Yes. FSMs are obtained by assigning membership grades as weights to the
states of a machine, weights on transitions between states, and then a
composition rule such as MAX/MIN or PLUS/TIMES (see [4]) to calculate new
grades of future states. Refer to the following article, or to Section
III of the Dubois and Prade′s 1980 textbook (see [16]).

   Gaines, Brian R., and Kohout, Ladislav J., "Logic of Automata",
   Int. J. Gen. Sys. 2(4):191-208, 1976.