TSK models are a very powerful tool for function approximation problems given a dataset of input/output data. Given a global error function to approximate, there are several methodologies for training (adjust the parameters and find the optimal structure) the TSK model. Nevertheless, this strategy implies that the interpretability of the rules comprising the neuro-fuzzy TSK system as linearizations of the nonlinear subjacent system can be lost. Several recent works have addressed this problem with partial success, sometimes performing a tradeoff between global accuracy and local models interpretability. In this paper we propose an accurate modified TSK neuro-fuzzy model for function approximation that solves the cited problem, and that furthermore allows us to interprete the output of the rules as the Taylor Series Expansion of the system output around the rule centres.
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