Fuzzy Knowledge and Recurrent Neural Networks: A Dynamical Systems Perspective

Hybrid neuro-fuzzy systems – the combination of artificial neural networks with fuzzy logic – are becoming increasingly popular. However, neuro-fuzzy systems need to be extended for applications which require context (e.g., speech, handwriting, control). Some of these applications can be modeled in the form of finite-state automata. This chapter presents a synthesis method for mapping fuzzy finite-state automata (FFAs) into recurrent neural networks. The synthesis method requires FFAs to undergo a transformation prior to being mapped into recurrent networks. Their neurons have a slightly enriched functionality in order to accommodate a fuzzy representation of FFA states. This allows fuzzy parameters of FFAs to be directly represented as parameters of the neural network. We present a proof the stability of fuzzy finite-state dynamics of constructed neural networks and through simulations give empirical validation of the proofs.