An affine fuzzy model with local and global interpretations

Universal approximation properties of Mamdani fuzzy model are well known. On the other hand, Takagi-Sugeno fuzzy model with affine consequent was thought to be a local approximator of the dynamics. However, it can also be tuned to be an universal approximator, but loosing its local interpretation. In this paper, an innovative affine global model with universal approximation capabilities which maintains local interpretation is introduced.This novel model can be considered a generalization of Takagi-Sugeno affine fuzzy model, and is based on decoupling the dynamic parameters of the system at the fuzzification step. We demonstrate how this new model can exactly match non-linear functions expressed either as product form or additive form.Finally, we apply all the above to model a multivariable tank, analyzing the modelling errors obtained, depending on the model used: Mamdani, Takagi-Sugeno or the affine one with decoupled dynamics.