Deriving multistage FNN models from Takagi and Sugeno´s fuzzy systems

Two multistage fuzzy neural network (FNN) models are derived from Takagi and Sugeno´s fuzzy systems by arranging single-stage reasoning units (stages) in an incremental and aggregation manner. The dimensionality problem is overcome since the number of rules is reduced to a linear function of the number of inputs. The network structure in each stage is based on Jang´s (1993) adaptive network based fuzzy inference system model. By applying the least squares estimate and backpropagation algorithms to the training process, the proposed models can learn multistage fuzzy rules from stipulated data pairs. Simulation results show that the proposed multistage FNN models are superior to its single-stage counterpart in the resource used, convergence speed and generalization ability