The TaSe-NF model for function approximation problems: Approaching local and global modelling

Optimization of the local sub-models when using neuro-fuzzy systems to model input/output data can be spoiled during the global optimization process, therefore special care has to be taken to avoid this loss. Some approaches involving grid input space partitioning that optimize local sub-models whilst still obtaining a good global system performance have appeared. However, this is a more complex task for radial basis function networks, scatter-partitioning fuzzy systems and neuro-fuzzy models in general. This work presents a modified neuro-fuzzy model, known as the TaSe-NF model, which is a special case of a scatter-partitioned Takagi–Sugeno–Kang fuzzy system or normalized radial basis function neural network. The TaSe-NF model maintains the optimization properties of the local sub-models (fuzzy rules or RBF nodes) when the model is globally optimized thanks to the modified calculation of the final normalized activation of the rules, which provides an appropriate input space partitioning to achieve these objectives. To show the characteristics of the proposed model, a learning methodology for this model, which consists of a clustering algorithm especially suited to function approximation problems, a local search technique and a membership function merging approach, with the objective of improving the transparency, i.e. ease of interpretability, of the extracted fuzzy rule set is also proposed.