Abstract
Hierarchical fuzzy neural networks can use less rules to model nonlinear system with high accuracy. But the normal training method for hierarchical fuzzy neural networks is very complex. In this paper we modify the backpropagation approach and employ a time-varying learning rate that is determined from input-output data and model structure. Stable learning algorithms for the premise and the consequence parts of the fuzzy rules are proposed. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds. The new algorithms are very simple, we can train each sub-block of the hierarchical fuzzy neural networks independently.