To develop a fault diagnosis model that combines high performance with intrinsic interpretability, this paper proposes a Transformer-based knowledge-inheritance fuzzy neural network (TKI-FNN). Specifically, a pre-trained Transformer classifier is first employed to generate logit vectors (i.e., unnormalized probability distributions). Subsequently, the knowledge distillation module transforms these logit vectors into soft labels by adjusting the temperature parameter, thereby embedding inter-class similarity information. These soft labels not only contain target class information but also implicitly characterize latent relationships among different fault categories. Finally, the knowledge-inherited Takagi–Sugeno–Kang (TSK) module receives soft labels through its consequent part and performs interpretable fault diagnosis inference. The model is optimized using gradient descent based on a composite objective function consisting of cross-entropy loss and soft-label regularization. This novel knowledge-inheritance paradigm enables the proposed TKI-FNN to effectively mitigate overfitting and improve fault diagnosis performance through soft-label regularization, while preserving the semantic interpretability of the downstream TSK module. In a series of experiments involving real industrial processes, the proposed model demonstrates significant advantages in both fault diagnosis accuracy and interpretability.