Emerging deep fuzzy neuralnetwork-based fault diagnosis (FD)—integrating deep neural networks (DNNs) and fuzzy neural networks (FNNs) in sequential or parallel architectures—has demonstrated great potential in both high performance and model interpretability. However, in the cascade architecture, the membership functions of the FNN struggle to finely describe the complex fault features extracted by the DNN, leading to reduced FD performance. Meanwhile, the abstraction of fault features undermines the FNN's interpretability. In the parallel architecture, designing a reasonable strategy to fuse the heterogeneous features extracted by the DNN and FNN is nontrivial. To address these challenges, we propose a novel FD model called linguistically interpretable fuzzy neural network with knowledge distillation, which integrates DNN and FNN through the perspective of knowledge distillation, aiming for high performance while preserving FNN's intrinsic interpretability. The model extracts modality probability knowledge from a well-trained DNN teacher unit and feeds into the knowledge distillation unit to generate soft labels encapsulating modality similarity knowledge. These soft labels carry the teacher unit's core insights into FD and activate implicit information of negative modalities. Then, the knowledge-based Takagi–Sugeno–Kang unit uses the soft labels as consequent variables to perform linguistically interpretable rule reasoning from original features to fault modalities. The model is optimized by minimizing a composite loss comprising cross-entropy, soft label regularization, and L2 regularization, ensuring more knowledge is transferred to the distilled unit. Comprehensive evaluation across a series of industrial process cases validated the model's effectiveness in performance and interpretability.

Mainstream strategies for addressing imbalanced monitoring data distributions, such as data sampling and cost-sensitive learning methods, face multiple challenges, including data heterogeneity, uncertainty, biased attention toward normal or fault classes, and reduced discriminability of fault features. These issues collectively lead to a degradation in fault diagnosis (FD) performance. To overcome the aforementioned bottlenecks, this article proposes a unified FD framework, termed a granular computing.based deep neural network (GDNN), which is designed from the novel perspective of granular ball (GB) embedding. Within this framework, the input data are first transformed into suboptimal latent features through a generic deep neural network (DNN).based feature extraction component. Subsequently, an information granulation component reorganizes these features into class-specific local neighborhood structures in the form of GBs. Finally, a Softmax-based fully connected classifier performs FD. The GDNN framework supports end-to-end learning by minimizing a composite loss function consisting of the cross-entropy loss and the justifiable granularity (JG) loss. The main contribution of this work lies in a novel GB embedding mechanism that guides DNNs to focus on GB-based structures rather than isolated individual samples in imbalanced scenarios. Each class is represented by a GB that encapsulates its structural knowledge in the latent feature space, thereby ensuring consistent attention across classes and effectively mitigating severe overfitting. Experimental results on two industrial processes demonstrate that the proposed framework performs robustly across diverse imbalanced scenarios and adapts well to different DNN architectures, providing a novel perspective and a generalizable paradigm for imbalanced FD.

Federated Fuzzy C-Means (FCM) clustering methods have demonstrated success in standard federated learning (FL) environments, but model heterogeneity presents a significant challenge. This heterogeneity hampers communication content selection and makes traditional aggregation methods, such as federated averaging (FedAvg), insufficient for diverse client models. Additionally, handling non-IID data distributions and learning robust feature representations remain unresolved in some existing approaches. To tackle these issues, we propose FFCMD, a federated FCM clustering framework designed to address model heterogeneity while enhancing feature learning and accommodating non-IID data. FFCMD integrates an autoencoder (AE) with a fuzzy C-Means network (FCMN), augmented by mutual knowledge distillation (mKD), to improve data feature learning, communication, and aggregation under heterogeneous conditions. The AE incorporates a clustering-oriented penalty term to learn discriminative features, boosting performance on complex datasets. Rather than direct parameter aggregation, mKD updates the global model using local devices' soft assignments, naturally handling structural variations across client models. Moreover, FFCMD employs discrepancy-aware weighting mechanisms to dynamically align local and global category distributions during soft assignment embedding, effectively addressing the challenges posed by non-IID data. Extensive experiments on multiple public datasets show that FFCMD outperforms state-of-the-art methods, particularly in non-IID scenarios, and excels even in the presence of model heterogeneity.

Classification tasks involving tabular data often require a balance between exceptional performance and heightened interpretability. To address this challenge, we propose a linguistically interpretable deep fuzzy classification system called FFT-FFR-RBFC. The system employs a Fuzzy Feature Transformation (FFT) unit, formed by employing a stacked architecture of multiple Takagi-Sugeno-Kang (TSK) fuzzy models with non-linear conclusions, to distill high-level fuzzy features from the input data, a Rule-Based Fuzzy Classifier (RBFC) unit to perform classification using these features, while a Fuzzy Feature Reconstruction (FFR) unit in tandem with the FFT to enhance the system's linguistic interpretability by remapping the high-level features back to their original space. The proposed approach is optimized by minimizing a composite loss function that balances classification and reconstruction losses, ensuring a harmonious interplay between performance and interpretability. Comprehensive evaluation across 20 diverse datasets demonstrates that the system's is exceptionally promising, particularly for high-dimensional or large-scale tabular data classification tasks, achieving superior classification performance while maintaining a high degree of interpretability.