In this study, we propose a hierarchical two-view Takagi–Sugeno–Kang (TSK) fuzzy classifier based on a supervised adversarial mechanism (ADVML-FC) designed to address the limitations of traditional single- and two-view fuzzy classifiers, such as data underutilization, challenges in feature fusion, and poor generalization. The proposed model leverages the output of one view as perturbation information to challenge the other view, thereby promoting information exchange and fusion between the two views. Unlike conventional approaches that rely on random noise perturbations, the model uses signals derived from the opposing view outputs and dynamically adjusts the attack success rate (ρ) to prevent overfitting and enhance generalization. The model simplifies the objective function design and integrates the least-squares method to efficiently estimate the consequent parameters of fuzzy rules, thereby substantially reducing computational complexity. Moreover, the model retains a zero-order TSK fuzzy rule structure and integrates fuzzy C-means clustering with Gaussian membership functions to ensure semantic interpretability. Experimental results demonstrate that ADVML-FC achieves superior performance in terms of average training accuracy, average testing accuracy, F1-score, Kappa, and Matthews correlation coefficient across nine two-view datasets. The proposed model not only delivers exceptional classification performance in terms of interpretability, highlighting its strong potential for broad applicability.

Within-frequency coupling (WFC) and cross-frequency coupling (CFC) in brain networks reflect neural synchronization within the same frequency band and cross-band oscillatory interactions, respectively. Their synergy provides a comprehensive understanding of neural mechanisms underlying cognitive states such as emotion. However, existing multi-channel EEG studies often analyze WFC or CFC separately, failing to fully leverage their complementary properties. This study proposes a dual-branch graph neural network (DB-GNN) to jointly identify within- and cross-frequency coupled brain networks. Firstly, DB-GNN leverages its unique dual-branch learning architecture to efficiently mine global collaborative information and local cross-frequency and within-frequency coupling information. Secondly, to more fully perceive the global information of cross-frequency and within-frequency coupling, the global perception branch of DB-GNN adopts a Transformer architecture. To prevent overfitting of the Transformer architecture, this study integrates prior within- and cross-frequency coupling information into the Transformer inference process, thereby enhancing the generalization capability of DB-GNN. Finally, a multi-scale graph contrastive learning regularization term is introduced to constrain the global and local perception branches of DB-GNN at both graph-level and node-level, enhancing its joint perception ability and further improving its generalization performance. Experimental validation on the emotion recognition dataset shows that DB-GNN achieves a testing accuracy of 97.88% and an F1-score of 97.87%, reaching the state-of-the-art performance.

Radiation dermatitis (RD) represents the primary adverse outcome of ionizing radiation associated with chemotherapy in breast, head and neck, anal cancers and other medical conditions. For nasopharyngeal cancer (NPC) recognition, how to build an interpretable lightweight recognition model is a serious challenge. Traditional medical diagnostic models typically exhibit opaque decision-making processes with limited interpretability, and achieving high classification accuracy often necessitates increased model complexity. In order to address these limitations of traditional methods, the study proposes an innovative stacked hierarchical Takagi–Sugeno–Kang (TSK) fuzzy classifier for diagnosing the severity of RD in NPC patients. The classifier incorporates a low-rank rule feature structure and bidirectional approximation consequents, with each sub-classifier constructed from first-order TSK fuzzy systems. Its antecedent part employs a rule-feature matrix to characterize relationships between fuzzy rules and training features, where matrix decomposition techniques are applied to simplify rule-feature associations and generate representative discriminative rules. The consequent part integrates outputs from preceding sub-classifiers into the objective function, achieving approximation of both prior sub-classifier outputs and target outputs through independent training mechanisms. Finally, comparative experiments demonstrate that each sub-classifier in LRR-TSK requires only 3–15 fuzzy rules yet achieves an average accuracy exceeding 99.6%, highlighting its excellent performance. These improvements stem from the low-rank rule-feature matrix, which generates clear rules via matrix decomposition, and the bidirectional approximation method, which optimizes prediction accuracy, providing a transparent and efficient solution for handling complex medical data. However, the current training models still face the predicament that it is difficult to obtain the hyperparameter combinations of the models and the number of fuzzy rules is hard to determine. In future work, we aim to address these issues by integrating global optimization algorithms to achieve a global optimum solution, and extending the model into a multi-view joint learning framework to enhance diagnostic comprehensiveness.

Nasopharyngeal carcinoma (NPC) is a malignant tumor that originates from the back of the nasal canal from above the soft palate to the upper larynx. Because the nasopharyngeal location is deeply hidden, it is often difficult for a single imaging means to clarify its complex adjacency. In addition, there exist some differences and uncertainties in its clinical manifestations. Although two-view fuzzy classifiers can effectively tap into the nasopharyngeal location for hidden information and exhibit good classification performance, existing fuzzy reasoning for predicting whether or not a nasopharyngeal cancer often stems from the inability to reuse the one-sided rules. Therefore, a novel two-view mutual rectification and knowledge mergence Takagi-Sugeno-Kang fuzzy classifier (TVRM-TFC) is proposed here to address the challenge of using imaging means to fine-tune the organ tissues. Firstly, Kullback-Leibler divergence (KLIC) is used to select important features from various imaging sections (i.e., pieces of knowledge). Secondly, the interpretable zero-order Takagi-Sugeno-Kang (TSK) fuzzy classifier is used as the basic training unit to simultaneously obtain satisfactory accuracies and concise linguistic interpretability. Thirdly, from the perspective of both imaging means and the organ, this study fine-tunes the information required for decision-making between different imaging means, so that the complementary advantages of the different views may improve the decision-making information and thus increase decision accuracies. Finally, the perspective of imaging technology and the organ are merged to capture decision-making knowledge. These decision-making advantages from different views are organically integrated to compensate information and further optimize the decision-making information. The merits of the proposed classifier are demonstrated through comparative experimental analysis on CT and MRI data.

The first-order Takagi-Sugeno-Kang (TSK) fuzzy classifier with a fully combined fuzzy rule base (FuCo-FRB) is a potent and interpretable classifier for multiple input and multiple output (MIMO) tasks. However, FuCo-FRB possess an exponential increase in the number of fuzzy rules, and it poses challenges for efficient identification of the parameter matrix in MIMO tasks. A lightweight TSK fuzzy classifier (LW-TSK-FC) is proposed to achieve the balance of training efficiency and predictive performance especially on MIMO tasks. It has the following advantages: (1) An adaptive weighting method based on directly connected FRB enables the efficient generation of fuzzy rules, meanwhile retaining the distribution characteristic of FuCo-FRB to reduce information loss. (2) The consequent network of first-order TSK is optimized to a novel series structure by using matrix factorization. This new series structure increases the depth of consequent network and enable the implementation of kernel function and least learning machine (LLM), enhancing the calculation efficiency and predictive performance. (3) There are only weight parameters in consequent network of LW-TSK-FC and these parameters can be identified quantitatively by LLM, leading to a great training efficiency. The comparison experiments with other 14 power classifiers on 13 public UCI datasets shown comparable predictive performance and outstanding training and testing efficiency in both MISO and MIMO tasks. The experiments on a real-world clinical task demonstrated the significant capability of LW-TSK-FC on handling imbalanced small data, and can provide the semantic interpretability for reasoning process.

Brain networks are commonly used to identify cognitive neurobehavioral and brain conscious disorders. Most of the studies on state networks focus on the characterization and expression of resting-state brain networks, but there are few studies on dynamic brain networks. In fact, the analysis of dynamic brain networks can find more valuable information, because it can dynamically depict the dynamic characteristics of brain networks from the time dimension. However, too much consideration of the expression of dynamic networks will naturally hide many of its static characteristics. Therefore, this study proposes a tense-based multi-view fusion fuzzy learning model (TM-FL) to identify dynamic brain networks. TM-FL relearns the features of adjacent networks in high-dimensional space, mining the dynamic features between adjacent brain networks. Best of all, TM-FL can also capture resting information in the brain network at different times in the source space. The fuzzy TSK-based TM-FL also possesses the strong interpretability inherent in fuzzy systems. In this study, a fusion mechanism is designed to effectively integrate decision support under dynamic and static features, and enhance the classification and generalization performance of the proposed fuzzy classification model. For the proposed fusion fuzzy mechanism, Simon entropy is cleverly set as the regular term of the objective function, which not only constrains the decision weight, but also avoids the embarrassment of making mistakes in a leading decision. Experimental results show that TM-FL has good classification, generalization and interpretable capabilities in recognition of multi-channel epileptic electroencephalographic (EEG) signals.

Interpretable artificial intelligence (AI), also known as explainable AI, is indispensable in establishing trustable AI for bench-to-bedside translation, with substantial implications for human well-being. However, the majority of existing research in this area has centered on designing complex and sophisticated methods, regardless of their interpretability. Consequently, the main prerequisite for implementing trustworthy AI in medical domains has not been met. Scientists have developed various explanation methods for interpretable AI. Among these methods, fuzzy rules embedded in a fuzzy inference system (FIS) have emerged as a novel and powerful tool to bridge the communication gap between humans and advanced AI machines. However, there have been few reviews of the use of FISs in medical diagnosis. In addition, the application of fuzzy rules to different kinds of multimodal medical data has received insufficient attention, despite the potential use of fuzzy rules in designing appropriate methodologies for available datasets. This review provides a fundamental understanding of interpretability and fuzzy rules, conducts comparative analyses of the use of fuzzy rules and other explanation methods in handling three major types of multimodal data (i.e., sequence signals, medical images, and tabular data), and offers insights into appropriate fuzzy rule application scenarios and recommendations for future research.

Stacking-based takagi-sugeno-kang (TSK) fuzzy system ensemble has been successfully applied to imbalanced data classification. However, there still exist many challenges that need to be further addressed. For example, during stacking, augmenting output variables into the input feature space reduces the interpretability of antecedents of fuzzy rules. During sampling for balancing, discovering informative samples usually only relies on training samples, which may reduce generalizability. More importantly, there is no theory to support the reliability of stacking. To address the aforementioned challenges, in this study, we propose a deep reconciled and self-paced TSK fuzzy system ensemble framework termed D-RSP-TSKE for imbalanced data classification. Compared with the existing ensemble frameworks, its superiorities can be exhibited from the following three aspects. First, in the first layer, we use random undersampling to generate a class-balanced training set to train an initial zero-order TSK fuzzy classifier. Based on the TSK fuzzy classifier, then we define classifier-specific and testing-compatible sample sensitivity to discover informative (high-sensitive) samples and design a reconciled and self-paced sampling approach to balance the minority class for the training of the following layers. Second, to improve the interpretability of antecedents of fuzzy rules, we propose to transfer the output variables from antecedents to consequents through equivalent mathematical transformations while keeping the final output unchanged. These transferred output variables are interpreted as the dynamic fuzzy rule confidence. Third, furthermore, we engage in a comprehensive theoretical examination of our stacking-based ensemble to elucidate the underlying mechanisms that enable the stacking strategy to consistently deliver superior performance. We conduct tests and comparisons on 7 artificial datasets and 30 real-world datasets to evaluate D-RSP-TSKE. The experimental results demonstrate the effectiveness and interpretability of D-RSP-TSKE for imbalanced data classification.

Existing research reveals that the misclassification rate for imbalanced data depends heavily on the problematic areas due to the existence of small disjoints, class overlap, borderline, and rare data samples. In this study, by stacking zero-order Takagi-Sugeno-Kang (TSK) fuzzy subclassifiers on the minority class and its problematic areas in the deep ensemble, a novel deep-ensemble-level-based TSK fuzzy classifier (IDE-TSK-FC) for imbalanced data classification tasks is presented to achieve both promising classification performance and high interpretability of zero-order TSK fuzzy classifiers. Simultaneously, according to the stacked generalization principle, the proposed classifier lifts up oversampling from the data level to the deep ensemble level with a guarantee of enhanced generalization capability for class imbalance learning. In the structure of IDE-TSK-FC, the first interpretable zero-order TSK fuzzy subclassifier is built on the original training dataset. After that, several successive zero-order TSK fuzzy subclassifiers are stacked layer by layer on the newly identified problematic areas from the original training dataset plus the corresponding interpretable predictions obtained by the averaging strategy on all previous layers. IDE-TSK-FC simply takes the classical K -nearest neighboring algorithm at each layer to identify its problematic area that consists of the minority samples and its surrounding K majority neighbors. After randomly neglecting certain input features and randomly selecting the five Gaussian membership functions for all the chosen input features and the augmented feature in the premise of each fuzzy rule, each subclassifier can be quickly obtained by using the least learning machine to determine the consequent part of each fuzzy rule. The experimental results on both the public datasets and a real-world healthcare dataset demonstrate IDE-TSK-FC's superiority in class imbalanced learning.

In this paper, we propose a blockwise combination of interpretable Takagi-Sugeno-Kang (TSK) fuzzy classifiers to simultaneously achieve high accuracy and concise interpretability. As a special hierarchical fuzzy classifier, the proposed classifier is built in a stacked block-by-block way. Each base building block consists of multiple zero-order TSK fuzzy classifiers, which are simultaneously trained in an analytical manner by using negative correlation learning to enhance the generalization ability of the base building block. For utilizing the stacked generalization principle, a random projection of the outputs from the current base building block is presented to the next base building block together with the current training sample in order to enhance the generalization ability of our hierarchical fuzzy classifier. The purpose of such a special hierarchical structure is that all base building blocks can be trained in the same input-output space with the current training sample and the randomly projected output from the previous building block. In the input layer, the target output for the current training sample is used instead of the randomly projected output from the previous building block. Each TSK fuzzy classifier in base building blocks consists of interpretable TSK fuzzy rules, which are generated by randomly selecting input features and randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features. Merits of the proposed classifier are demonstrated through comparative studies on benchmark datasets.

Although Takagi-Sugeno-Kang (TSK) fuzzy classifier has been applied to a wide range of practical scenarios, how to enhance its classification accuracy and interpretability simultaneously is still a challenging task. In this paper, based on the powerful stacked generalization principle, a deep TSK fuzzy classifier (D-TSK-FC) is proposed to achieve the enhanced classification accuracy and triplely concise interpretability for fuzzy rules. D-TSK-FC consists of base-building units. Just like the existing popular deep learning, D-TSK-FC can be built in a layer-by-layer way. In terms of the stacked generalization principle, the training set plus random shifts obtained from random projections of prediction results of current base-building unit are presented as the input of the next base-building unit. The hidden layer in each base-building unit of D-TSK-FC is represented by triplely concise interpretable fuzzy rules in the sense of randomly selected features with the fixed five fuzzy partitions, random rule combinations, and the same input space kept in every base-building unit of D-TSK-FC. The output layer of each base-building unit can be learnt quickly by least learning machine (LLM). Besides, benefiting from LLM, D-TSK-FC's deep learning can be well scaled up for large datasets. Our extensive experimental results witness the power of the proposed deep TSK fuzzy classifier.