Accuracy-Interpretability Trade-Off for Precise Fuzzy Modeling using simple indices. Application to Industrial Plants1

Abstract In general, the techniques of fuzzy modeling are oriented to obtaining rule based systems with high accuracy but rarely interpretable in accordance with the fuzzy logic principles. Both concepts are in conflict and it is necessary to achieve a good trade-off between the two aspects. Here, an index to measure interpretability in fuzzy rule based systems, which has been proposed by the authors to improve accuracy-interpretability trade-off in previous work, is used for complex industrial problems, such as biotechnological processes in a wastewater treatment plant. This interpretability index is based on the aggregation of simple indices of complexity and similarity. Using generic neuro-fuzzy systems, a post-processing rule selection based on a genetic approach is done, considering the error as an index for accuracy and the aggregate index based on similarity for interpretability. In this work, this methodology is applied to an industrial plant to model two different processes: the biomass and substrate concentrations of a wastewater treatment plant. Both are modeled using different neuro fuzzy systems, FasArt and NefProx, and improved on the basis of the accuracy-interpretability trade-off. The results show that the approach permits fuzzy models to be obtained with a better balance between accuracy and interpretability, while also improving the simplicity of the model.