At present, there has been an increasing interest in neuron-fuzzy systems, the combinations of artificial neural networks with fuzzy logic. In this paper, a definition of fuzzy finite state automata (FFA) is introduced and fuzzy knowledge equivalence representations between neural networks, fuzzy systems and models of automata are discussed. Once the network has been trained, we develop a method to extract a representation of the FFA encoded in the recurrent neural network that recognizes the training rules. At present, there has been been an increased interest in neuron-fuzzy systems, the combinations of artificial neural networks with fuzzy logic. In this paper, a definition of fuzzy finite state automata (FFA) is introduced and fuzzy knowledge equivalence representations between neural networks, fuzzy systems and models of automata are discussed. we have a method to extract a representation of the recurrent neural network that recognizes the training rules.