Deep learning paradigm is arguably the fastest growing branch of machine learning and artificial intelligence (AI) at the moment [1,2]. Deep neural networks (DNNs) are entirely based on the artificial neural networks and probabilistic type of uncertainties [3]. They have demonstrated eye-catching successes on image classification [4,5], speech processing [6,7] and many other complex problems [8,9] that traditional machine learning approaches are struggling with.Despite of the impressive advances DNNs have achieved, the research communities and enterprises are increasingly demanding explainable AI [10,11]. Indeed, DNN-based AI algorithms nowadays are more frequently getting involved for making decisions in financial and safety-critical applications [12,13]. However, DNNs are the typical type of "black box" models with a very high level of complexity level that only computers can understand. It is reported that such "black box" models can provide a wrong outcome with high confidence by modifying just one pixel in the input images [14]. The lack of transparency and explainability can pose a significant obstacle, especially for highly regulated, high-risk/high-value industries. Therefore, there is a high demand in developing alternative architectures, learning and model structure paradigms that can provide offer [15]: (1) high levels of precision comparable or surpassing the level achieved by humans or/and by the state-of-the-art methods (including DNNs); (2) be highly transparent, interpretable, easy to explain and use for humans; (3) computationally efficient, fast to train and use; (4) computational resource and training data lean -able to be trained with a single or handful or examples per class, not requiring computer accelerators, such as GPU, HPC, etc.As one of the pillars of the computational intelligence, fuzzy rule-based (FRB) systems are a mathematical tool to describe the human reasoning and decision-making processes [11]. FRB systems take the form of zero-order,
Highly interpretable hierarchical deep rule-based classifierXiaowei Gu a, b, ⁎, 1