Fuzzy neural network systems (FNNSs) can incorporate the merits of fuzzy logic systems (FLSs) and neural networks (NN). This paper designs a type of non-singleton FNNSs for forecasting issues. The proposed hybrid backpropagation (BP) algorithms and recursive least square (RLS) algorithms are used for optimizing the parameters of antecedents, input measurements, and consequents simultaneously. Two computer simulation examples based on the data of European Network on Intelligent Technology (EUNITE) and data of west Texas intermediate (WTI) crude oil price are used for testing. Convergence analysis shows that the hybrid optimized FNNSs have very high generalization ability.
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