Stability of hierarchical fuzzy systems generated by Neuro-Fuzzy

Hierarchical implementation provides a way of retaining the interpretability of a fuzzy system when the number of inputs to the system is very high. Existing Neuro-Fuzzy systems capable of constructing fuzzy systems from training data do not address this issue and restrict to the generation of single layer fuzzy systems. This paper first defines a generic hierarchical fuzzy system that can be implemented exploiting the recursion supported by standard programming languages. Secondly it shows that hierarchical fuzzy systems can be generated from a specialised multi-layer perceptron neural network using a heuristic rule extraction algorithm. Finally, the paper provides a proof for the stability of hierarchical fuzzy systems and the verification using simulation examples.