Deducing fuzzy inference systems with different numbers of membership functions from a neuro-fuzzy inference system

The starting point for this contribution is an adapted neuro-fuzzy system of Huber/Berthold with a set of adapted membership functions (number and shape). The heuristically adapted number and shape of the membership functions may not be the best choice, especially when considering human understandability of the adapted rules. We transform a-posteriori the number of fuzzy terms and evaluate classification performance and understandability, considering the influence of the weighting of the neuro-fuzzy units as well. Inference for the new, transformed (deduced) system is done by an expanded max-min inference strategy. For this expanded inference the influence of the neuro-fuzzy membership functions to the predefined number of fuzzy terms have to be determined. Thus, we introduce so called degradation factors. The evaluation of our inventions is done by medical data.