It has been shown that neural networks are able to infer regular crisp grammars from positive and negative examples. The fuzzy grammatical inference (FGI) problem however has received considerably less attention. In this paper we show that a suitable two-layer neural network model is able to infer fuzzy regular grammars from a set of fuzzy examples belonging to a fuzzy language. Once the network has been trained, we develop methods to extract a deterministic representation of the fuzzy automaton encoded in the network that recognizes the training set.