Assessing interpretability of data-driven fuzzy models: Application in industrial regression problems

Machine Learning (ML) has attracted great interest in the modeling of systems using computational learning methods, being utilized in a wide range of advanced fields due to its ability and efficiency to process large amounts of data and to make predictions or decisions with a high degree of accuracy. However, with the increase in the complexity of the models, ML's methods have presented complex structures that are not always transparent to the users. In this sense, it is important to study how to counteract this trend and explore ways to increase the interpretability of these models, precisely where decision-making plays a central role. This work addresses this challenge by assessing the interpretability and explainability of fuzzy-based models. The structural and semantic factors that impact the interpretability of fuzzy systems are examined. Various metrics have been studied to address this topic, such as the Co-firing Based Comprehensibility Index (COFCI), Nauck Index, Similarity Index, and Membership Function Center Index. These metrics were assessed across different datasets on three fuzzy-based models: (i) a model designed with Fuzzy c-Means and Least Squares Method, (ii) Adaptive-Network-based Fuzzy Inference System (ANFIS), and (iii) Generalized Additive Model Zero-Order Takagi-Sugeno (GAM-ZOTS). The study conducted in this work culminates in a new comprehensive interpretability metric that covers different domains associated with interpretability in fuzzy-based models. When addressing interpretability, one of the challenges lies in balancing high accuracy with interpretability, as these two goals often conflict. In this context, experimental evaluations were performed in many scenarios using 4 datasets varying the model parameters in order to find a compromise between interpretability and accuracy.