Infinite fuzzy computations

We consider Büchi automata weighted over the fuzzy semiring F=([0,1],max,min,0,1). A Büchi theorem for the class of ω-recognizable series with coefficients in F, i.e., for behaviors of Büchi automata over F is established. Furthermore, we show that an infinitary language is Büchi recognizable iff its characteristic series is ω-recognizable.