Interpretable machine learning: Convolutional neural networks with RBF fuzzy logic classification rules

A convolutional neural network (CNN) learning structure is proposed, with added interpretability-oriented layers, in the form of Fuzzy Logic-based rules. This is achieved by creating a classification layer based on a Neural-Fuzzy classifier, and integrating it into the overall learning mechanism within the deep learning structure. Using this new structure, one could extract linguistic Fuzzy Logic-based rules from the deep learning structure directly, which enhances the interpretability of the overall system. The classification layer is realised via a Radial Basis Function (RBF) Neural-Network, that is a direct equivalent of a class of Fuzzy Logic-based systems. In this work, the development of the RBF neural-fuzzy system and its integration into the deep-learning CNN is presented. The proposed hybrid CNN RBF-NF structure can from a fundamental building block, towards building more complex deep-learning structures with Fuzzy Logic-based interpretability. Using simulation results on a benchmark data-driven modelling and classification problem (labelled handwriting digits, MNIST 70000 samples) we show that the proposed learning structure maintains a good level of forecasting/prediction accuracy (> 96% on unseen data) compared to state-of-the-art CNN deep learning structures, while providing linguistic interpretability to the classification layer.