Neuro-fuzzy system with learning tolerant to imprecision

In this paper, a new learning method tolerant to imprecision is introduced and used in neuro-fuzzy modeling. This method can be called ε-insensitive learning, where in order to fit the fuzzy model to real data, a weighted ε-insensitive loss function is used. The proposed method makes it possible to exclude an intrinsic inconsistency of neuro-fuzzy modeling, where zero-tolerance learning is used to obtain a fuzzy model tolerant to imprecision. The ε-insensitive learning leads to a model with the minimal Vapnik-Chervonenkis dimension (complexity), which results in improving generalization ability of this system and its robustness to outliers. Finally, numerical examples are given to demonstrate the validity of the introduced method.