Fuzzy Turing machines and fuzzy languages were introduced by Zadeh, Lee and Santos in nineteen seventies. Unfortunately, it appears that from computability point of view their model is too powerful --- its nondeterministic version accepts non--recursively enumerable fuzzy languages. Moreover, from the viewpoint of the modern fuzzy logic theory the model is too restrictive since it is defined only for a specific $t$-norm (G\"odel norm). Therefore we propose a generalization of the original model that is based on rigorous mathematical fundamentals of fuzzy logic. Its acceptance criterion is modified so that the resulting model obeys the Church--Turing Thesis.