Neuro-symbolic artificial intelligence has garnered considerable attention amid increasing industry demands for high-performance neural networks that are interpretable and adaptable to previously unknown problem domains with minimal reconfiguration. However, implementing neuro-symbolic hardware is challenging due to the complexity in symbolic knowledge representation and calculation. We experimentally demonstrated a memristor-based neuro-fuzzy hardware based on TiN/TaOx/HfOx/TiN chips that is superior to its silicon-based counterpart in terms of throughput and energy efficiency by using array topological structure for knowledge representation and physical laws for computing. Intrinsic memristor variability is fully exploited to increase robustness in knowledge representation. A hybrid in situ training strategy is proposed for error minimizing in training. The hardware adapts easier to a previously unknown environment, achieving ~6.6 times faster convergence and ~6 times lower error than deep learning. The hardware energy efficiency is over two orders of magnitude greater than field-programmable gate arrays. This research greatly extends the capability of memristor-based neuromorphic computing systems in artificial intelligence.