Abstract. In this paper first, we introduce three fuzzy approximation operators denoted C∗, C, C∗ on an arbitrary set X, and then we use these operators to associate various topologies to a given finite state machine. Also, we obtain some basic properties of these topological spaces. Finally, for a given fuzzy finite state automata M = (Q, :E, μ), these results allows us to obtain (fuzzy) topology on Q, in terms of the source and successors Kuratowski closure operators on Q.
