Although rate–distortion (RD) performance has traditionally driven image compression research, practical applications increasingly require model-based and interpretable methods. Inspired by the recently proven theoretical equivalence between Gaussian Mixture Models (GMMs) and first-order Takagi–Sugeno–Kang (TSK) fuzzy systems, this study proposes FI-GTFIC, a fully interpretable grayscale image compression method. FI-GTFIC replaces conventional GMM-based statistical modeling with an equivalent first-order TSK fuzzy representation, allowing explicit rule-based fuzzy reasoning to explain pixel-wise encoding and reconstruction. Its fuzzy-rule antecedents are obtained through Fuzzy C-Means (FCM) clustering, while consequents are directly calculated without training. By treating rule weights as fuzzy rule priors, all rules become fully interpretable. Thus, FI-GTFIC combines GMMs’ local adaptability with TSK systems’ global approximation and uncertainty-handling abilities. Since only a few statistical parameters are encoded into the bitstream, it adds no bit overhead and achieves competitive reconstruction performance with full interpretability on grayscale images.

The pairwise similarity-based ensemble clustering methods have demonstrated considerable potential in recent years. However, existing methods still suffer from two major challenges: (1) they often fail to fully exploit the high-order consistency among pairwise samples embedded in multi-order adjacency matrices, (2) they neglect to explore the correlations between information in the label space and the feature space in a high-order tensor space. To address these challenges, we propose a novel ensemble clustering method termed ECM-LECAM. First, multi-order sample relationships are extracted separately from the label space and the feature space to construct corresponding sets of multi-order adjacency matrices. Then, a high-order pairwise consistency concept is introduced to mine highly reliable consistent information from the multi-order adjacency matrices, leading to the construction of high-order consistency matrices. Based on these matrices, an ensemble clustering framework is developed to learn enhanced consensus adjacency matrices for each space. Furthermore, graph tensor learning is employed to jointly model the enhanced consensus adjacency matrices, thereby exploring the correlations among different consensus adjacency matrices and facilitating information propagation and interaction. Finally, Laplacian rank constraints are imposed on the consensus adjacency matrices to directly obtain discrete cluster assignments. Extensive experiments on multiple datasets demonstrate that ECM-LECAM achieves competitive and often superior clustering performance compared with representative state-of-the-art ensemble clustering methods.

The generalization capability of a classifier, which reflects its adaptability to previously unseen datasets, is a crucial performance indicator. In the realm of Takagi-Sugeno-Kang (TSK) fuzzy classifiers, improving generalization capability remains a key research focus. However, existing classifiers mainly prioritize the assessment of the generalization capability rather than analyzing its implementation process. This study, focusing on the gradual change in generalization capability, introduces a hierarchical TSK fuzzy classifier featuring a simple training structure and flexible training method. Unlike the conventional approach that incorporates additional generalization terms, a pair of generalization factors is used to dynamically strengthen the generalization capability of the proposed classifier and capture its gradient smoothness. Considering both theoretical and implementation perspectives, the relationship between the proposed and classical loss functions is established, demonstrating that the predicted outputs of adjacent layers are positively correlated. This verification confirms that the proposed classifier exhibits enhanced generalization capability in both its training structure and training method. In experimental evaluations of the classifier performance on six UCI datasets, the number of training layers or the generalization capability is varied while keeping the other parameter constant. The results demonstrate that the proposed classifier achieves enhanced generalization performance with fewer training layers while maintaining strong interpretability.

Artificial intelligence has shown great promise in noninvasive recognition of vulnerable coronary plaques. However, practical data issues in multicenter studies, such as inconsistent data distribution and insufficient or missing data labels, could significantly affect the recognition accuracy. Unsupervised domain adaptation (UDA) can be introduced to address this challenge, but several limits still remain. First, many existing UDA models lack interpretability, hindering healthcare professionals' ability to interpret and trust the model's decision. Second, some methods use pseudolabel to enhance performance, but often overlook the quality assessment of these pseudolabels, potentially leading to negative knowledge transfer. To this end, based on the interpretable Takagi-Sugeno-Kang fuzzy system (TSK-FS), a novel domain adaptive method is proposed to improve model generalizability for vulnerable coronary plaques recognition in multicenter data. First of all, TSK-FS is employed to construct a shared fuzzy feature space for the source domain and the target domain, aiming to better align data distribution. To make full use of the information of unlabeled target domain data and further reduce the negative knowledge transfer, the enhanced pseudolabel learning mechanism is further introduced by combining the graph-based random walking and label filtering. Moreover, Multicenter data of 910 patients with suspected or diagnosed coronary artery disease were collected from three hospitals for experiments. Experimental results demonstrate that the proposed DA-TSK-PLR-FS achieves the promising generalizability across multicenter datasets

Imbalanced classification remains a fundamental challenge in machine learning, where the Area Under the ROC Curve (AUC) is widely used for threshold-independent ranking evaluation, especially in AUC maximization studies. Existing AUC maximization methods suffer from two critical limitations: they rely on single fixed kernels that fail to capture complex data structures, and they incur prohibitive computational costs due to pairwise constraint construction. To address these issues, we propose the Generalized AUC Maximization Core Vector Machine (GAM-CVM), a fast imbalanced classification framework integrating multi-kernel learning with core vector machine optimization. Multiple affinity graphs are constructed from complementary perspectives and fused via cross-diffusion into a unified kernel matrix that respects the intrinsic data manifold. This fused kernel is embedded into a generalized AUC objective with a flexible ranking margin. Given the fused kernel matrix, the optimization stage of GAM-CVM achieves asymptotic linear time complexity with respect to the number of sample pairs under a fixed approximation accuracy by reformulating the learning objective as a center-constrained minimum enclosing ball problem. Extensive experiments demonstrate that GAM-CVM achieves the best overall average ranking and significantly outperforms most competing methods while maintaining the lowest optimization-stage running time.

In this study, in order to exploit an interpretable fuzzy large model on clean dataset from large and/or complex noisy-labeled data and then generate its student model appropriately through knowledge distillation for its lightweight usability, an Interpretable fuzzy large TabNet-based model, called IFLTNM, based on the well-proven deep neural network TabNet and interpretable fuzzy rules is first proposed as a type of fuzzy large models. By means of both the well-established memorization effect and the proposed consequent additive decomposition, after interpretable antecedents are fixed, the consequent parameters of all fuzzy rules in the IFLTNM model are appropriately determined at early training stage for almost clean training subset from the whole noisy-labeled training set. After that, by regularizing the learning objective of the proposed knowledge distillation on almost clean training subset with an extra loss function on almost noisy-labeled training subset obtained after the IFLTNM's training, the proposed learning objective is optimized to have IFLTNM's student model s-IFLTNM consisting of the same number of fuzzy rules sharing the same interpretable antecedents as in IFLTNM yet having linear consequents. IFLTNM has its structural and training novelty in the sense of leveraging both the memorization effect and consequent additive decomposition to train a fuzzy large model and acquire almost noisy-labeled training samples, and s-IFLTNM is distilled from IFLTNM creatively through leveraging both almost clean and noisy-labeled training samples instead of only clean samples. Experimental results on real-world benchmark datasets demonstrate the effectiveness of IFLTNM over the state-of-the-art methods, e.g., achieving 84.94% average testing accuracy yet preserving interpretability for the covertype dataset even with 30% symmetric label noise, and the power of s- IFLTNM in the sense of both a significant reduction of computational burden and model complexity of less than 400 on the adopted datasets with only a marginal drop in performance.

Existing magnetic resonance imaging (MRI) of rectal cancer for staging prediction task encounters serious dilemmas including both insufficient image data caused by the patient’s privacy and security concerns, and no interpretability caused by black-box prediction behaviors of the adopted classifiers like deep neural networks. To alleviate the above dilemmas, this study develops a fully interpretable rectal cancer staging prediction method called RCSP-FIMG-TSK by improving fully interpretable Takagi-Sugeno-Kang (TSK) fuzzy system FIMG-TSK. Except for sharing the advantages like full interpretability and output stability of FIMG-TSK, RCSP-FIMG-TSK has the following characteristics: (1) Comprehensible feature extraction is performed on MR images for guaranteeing that all fuzzy rules are rooted at each of salient yet comprehensible feature; (2) To realize small sample learning (SSL) on MR images, the proposed method trains FIMG-TSK through the consideration of two additional regularization terms in the learning objective, which aims at providing more generalization of the corresponding Gaussian Mixture Model (GMM) on small data; (3) The learning objective of RCSP-FIMG-TSK can be optimized in an analytical yet optimal solution to the weight of each rule. Experimental results on small rectal cancer datasets demonstrate the effectiveness of RCSP-FIMG-TSK in terms of testing performance, computational complexity and full interpretability.

The one-class classification (OCC) problem has garnered considerable research attention owing to the inherent difficulty and high cost associated with acquiring abnormal samples in many application scenarios. Among the existing methodologies, support vector data description (SVDD) has emerged as a classical approach, spawning a wide array of variants. Despite its extensive development, several critical challenges persist. For instance, (i) existing SVDD-based methods exhibit limitations when addressing multimodal data, particularly when the dimensions of each modality differ; (ii) these methods are highly sensitive to the trade-off parameter; and (iii) many SVDD variants demonstrate inadequate performance in scenarios with a scarce number of abnormal samples. To overcome these issues, we propose a novel one-class classification framework termed distribution entropy regularized multimodal subspace SVDD (DEMS-SVDD). Our contributions are threefold. First, we design two novel regularization terms—the multimodal graph regularization and the sparse projection matrix regularization—which collectively exploit complementary information and preserve consistency across multimodal data even when abnormal samples are limited. Second, we introduce a new weighting scheme, derived from sample distribution and information entropy theories and denoted as distribution entropy-based weights, to assign adaptive importance to each sample. Third, our framework considers the uncertainty of classification, the amount of information contained, the importance of establishing hypersphere boundaries, as well as the sample distribution. The DEMS-SVDD is instantiated in two variants, namely linear and nonlinear, and extensive experiments on multiple real-world datasets demonstrate its superior performance and robustness compared with numerous existing algorithms.

This study explores how to develop a novel deep stacking Takagi-Sugeno-Kang (TSK) fuzzy classifier to efficiently realize interpretable classification for large-scale multiclass complex data contaminated with noisy labels. To this end, the nested stacking TSK fuzzy classifier NSARD-TSK and its additive-rule-decomposition and antinoisy-labeling based learning method are proposed to embody their completely distinctive design methodology. 1) Each quasihigher order TSK (QHO-TSK) fuzzy subclassifier of NSARD-TSK is built in deep stacking way for several interpretable zero-order TSK fuzzy subclassifiers to roughly behave like a higher order TSK classifier, such that both strong uncertainty-handling capability and generalization are provided. 2) The parameters in all the fuzzy rules of each QHO-TSK fuzzy subclassifier except the last one are transformatively trained to have their desired and undesired parts such that the resultant fuzzy rules with desired parameters for clean data are acquired in early training and simultaneously difficult-to-classify data containing noisy labeling data are fixed. 3) Each successive QHO-TSK fuzzy subclassifier is stacked on difficult-to-classify data from the previous subclassifier so as to form NSARD-TSK's nested stacking structure with enhanced generalization capability. In particular, the last QHO-TSK fuzzy subclassifier adopts the proposed antinoisy-labeling squared loss function as its unique learning objective with a theoretical guarantee for suppressing noisy labels. 4) NSARD-TSK linearly aggregates all the subclassifiers to further improve its final classification performance without affecting NSARD-TSK's interpretability. Experiments on 12 benchmarking datasets with and without noisy labels validate NSARD-TSK's efficiency over the comparative methods in terms of average testing performance and model complexity.

Traditional single-center learning algorithms often face significant limitations in handling heterogeneous data integration, including insufficient generalization ability, weak privacy protection, and difficulties adapting to multicenter scenarios. To address these challenges, multicenter learning has emerged as a critical technological framework. Although our previously proposed MKTC-R0T algorithm partially addressed the integration and modeling of multicenter data through the knowledge transfer calibration strategy, it still exhibits notable shortcomings in terms of knowledge fusion stability, model interpretability and generalization, as well as the utilization of complementary information across centers. To overcome these limitations, we propose a knowledge calibration fusion and label space graph regularization-based multicenter Takagi-Sugeno-Kang (TSK) fuzzy system (KCF-LSG-MTSK). Specifically, we introduce an enhanced knowledge calibration and fusion strategy to effectively integrate heterogeneous information between the base center (BC) and auxiliary center (AC). We also propose a novel label space graph regularization scheme that constructs both intracenter and intercenter graph structures, leveraging data consistency and complementarity to enhance the quality of knowledge sharing. Furthermore, building upon first-order TSK fuzzy system optimization, our approach incorporates a projected maximum mean discrepancy transfer term to effectively reduce data distribution discrepancies between the BC and AC. Experimental results on thirteen benchmark datasets demonstrate that KCF-LSG-MTSK achieves an average accuracy of 88.7%, significantly outperforming State-of-the-Art single-center and multicenter methods, thereby validating the superiority of our approach in heterogeneous data integration, knowledge transfer, and interpretable classification.

As a typical means for semi-supervised learning, label propagation (LP) generally aims at predicting unlabeled samples by a tiny percentage of labeled samples. After briefly reviewing the existing LP methods based on the manifold assumption, this study summarizes three phenomenal-level issues in all these methods, including an explicit or implicit calculation of matrix inversion, strong dependency on K-nearest neighbor graph, and insufficient affinity learning. To address these issues, a novel LP method called Fast Doubly Reconstructed Affinity Propagation (FDRAP) for semi-supervised data classification is accordingly proposed by resorting to fast doubly reconstruction of the affinity graph. FDRAP starts with two unique ideas: (1) By characterizing the pairwise typicality of each nodal pair through the strength of each node therein, the given affinity graph is reconstructed to reflect the tendency of each nodal pair in representing two respective clusters. (2) By estimating the label propagation probability of each nodal pair through the difference from its disaffinity to the own disaffinity of each sample therein, each disaffinity originating from the reconstructed affinity graph is again reconstructed with such probability for much stronger separability of the final propagation matrix. And accordingly, its simple label propagation for each unlabeled sample is accomplished only through the summation of the reconstructed disaffinity multiplied by the label vector. The striking results on several test cases indicate that FDRAP has competitive classification accuracy and outlier detection, fast running speed and strong scalability.

Fuzzy ensemble clustering methods that rely on the fuzzy coassociation (FCA) matrix often focus predominantly on optimizing the FCA matrix itself, while insufficiently addressing the critical role of fuzzy connective matrices. This limitation results in three shortcomings: 1) the absence of localized connectivity among samples within fuzzy connective matrices, 2) the neglect of varying reliability across clusters during relational propagation, and 3) the underutilization of complementary structural information inherent in multiple fuzzy connective matrices. To overcome these challenges, this study introduces a novel fuzzy ensemble clustering method, termed fuzzy ensemble clustering method with learned enhanced fuzzy connective matrices (FECM-LEFCM), which systematically enhances the representational capacity of fuzzy connective matrices through three innovative mechanisms. At the sample level, an adaptive neighborhood learning mechanism is proposed to establish localized connections among samples. At the cluster level, a dynamic reliability assessment mechanism is developed to assign weights to clusters based on their quality. At the base clustering level, multiple fuzzy connective matrices are integrated into a third-order tensor to facilitate information exchange and leverage structural complementarity. Furthermore, by incorporating a Laplacian rank constraint into the enhanced fuzzy connective matrices, FECM-LEFCM directly constructs an FCA matrix containing the exact ground-truth cluster number connected components, eliminating the need for postprocessing to obtain the final clustering result. Experimental evaluations demonstrate the superior performance of FECM-LEFCM compared to State-of-the-Art methods.

Existing Deep Unsupervised Domain Adaptation (UDA) methods primarily rely on aligning black-box feature distributions, which often leads to semantic drift and lacks transparency regarding where the alignment occurs. To address these limitations, we propose an Interpretable Residual TSK UDA Network. First, we introduce a Residual TSK Fuzzy Layer that serves as a structural foundation for alignment. We treat the learnable fuzzy rules as semantic anchors that partition the high-dimensional feature space into interpretable fuzzy sub-regions while preserving feature discriminability via a residual connection. Second, leveraging this structured representation, we propose Rule-Class Conditional Alignment. Unlike global alignment strategies, our Rule-Anchored Semantic Alignment treats fuzzy rules as shared coordinate bases to enforce fine-grained consistency between source and target domains, effectively mitigating negative transfer caused by noisy pseudo-labels. We integrate these components into a dual-classifier mutual learning framework to refine decision boundaries. Extensive experiments on VisDA-2017, Office-Home, and ImageCLEF-DA benchmarks demonstrate that our method achieves state-of-the-art performance and offers intuitive visualizations of the adaptation process through rule activation dynamics.

Interpretable fuzzy-rule-based classification is frequently in great demand for many application scenarios. However, its generalization ability may be hindered by factors such as excessive fuzzy rule parameters and distribution shift. This study aims to improve an interpretable first-order Takagi-Sugeno-Kang (TSK) fuzzy classifier by developing a novel methodology based on adversarial task augmentation, which has recently been an efficient means for enhancing the generalization ability of a classifier. The proposed methodology is designed on the basis of both the conclusive claims in cognitive research and the unique perspective that a fuzzy rule, as a piece of knowledge, bridges input and output data spaces. Accordingly, an innovative concept of adversarial knowledge augmentation (KA2) is proposed, and then the KA2-based interpretable first-order TSK fuzzy classifier (TSK2A2) is developed. TSK2A2 has the following features: (1) Without any direct use of data-related tasks, it augments a virtual data distribution with a small number of interpretable augmented fuzzy rules by means of KA2; (2) Throughout the training of TSK2A2, to have adversarial generation of each augmented fuzzy rule, an AND-NOT operator is introduced to randomly negate certain conditions for its IF-part generation. All the particularly-designed parameters based on the generated IF-parts are applied to the corresponding THEN-parts; (3) TSK2A2 employs fast analytical training for all THEN-parts. Theoretical analysis and/or experimental results on the adopted datasets indicate that TSK2A2 achieves enhanced generalization performance while retaining desirable interpretability and training efficiency.

This study attempts to develop a novel cognitive-biased knowledge adversarial learning method for an interpretable Takagi-Sugeno-Kang (TSK) fuzzy classifier to enhance its generalization capability. Based on the cognitive bias that humans occasionally tend to understand "and" in a rule as a union rather than an intersection for the rule's interpretability, the concept of the cognitively "and" -biased adversarial TSK fuzzy classifier based on the cognitively "and" -biased adversarial attacks is proposed, and accordingly, the cognitively "and" -biased adversarial training method called CAT for the proposed classifier is derived to earn enhanced generalization capability. This study has three distinct merits: 1) the cognitively "and" -biased adversarial attacks on the fuzzy operators in fuzzy rules are invented as a novel means of adversarial attacks to mimic the human cognitive bias appearing in the rule's interpretability; 2) after training the proposed TSK fuzzy classifier with CAT, the resultant fuzzy rules reflect the cognitively biased behaviors in the sense of the transformation level from "and" to "or" operations for the first time by the randomly generated uninorm rather than frequently used fuzzy "and" operators; and 3) CAT has its theoretical guarantee of enhanced generalization and overfitting-avoidance capabilities. Extensive experimental results demonstrate that CAT has satisfactory classification performance and good interpretability.

Long-term time series forecasting (LTSF) faces significant challenges on small datasets due to overfitting, inconsistent training progress across model layers, and lack of interpretability. To address these issues, we propose Component-wise Independent Adaptive Learning and Local Optimization (CIALLO), a novel parallel forecasting framework that decomposes time series into reversible components — trend, waveform, and amplitude — allowing for independent modeling and targeted training. Highlights benefits of modularization: flexible sub-model selection, independent pre-training, clearer convergence analysis, and higher training efficiency. Emphasizes structural interpretability via decomposition and component-wise optimization rather than post-hoc attention.Experiments on benchmark Electricity Transformer Temperature (ETT) datasets and Traffic truncated dataset demonstrate that CIALLO achieves comparable or competitive performance with state-of-the-art models, particularly on long-term horizons and under limited data conditions. Ablations on designed modules show that lightweight sub-models and independent component training improve optimization stability, while guided gradient has minimal impact on final performance. Decomposition ablations indicate that detrending dominates while amplitude is beneficial only when scaling is reliable. Ablation on the amplitude adjustment reveals a stable U-shaped behavior, with moderate values giving the most balanced correction. Component-wise contributions and early-stopping behavior are analyzed, revealing inconsistent training progress across components.Training-time analysis also shows faster overall convergence compared to baselines. The error contribution across samples, representative prediction cases and the parameters of the designed sub-models are visualized and analyzed.Finally, the overall results are summarized and their implications for future model design and interpretability are discussed.

Multiview fuzzy clustering has attracted increasing attention owing to its strong clustering performance and inherent ability to effectively model uncertainty. However, most existing methods rely on the unrealistic assumption that all views are fully observed, which rarely holds in practice. Although several methods have been proposed to address incomplete multiview data, they typically focus only on extracting shared information across views while overlooking view-specific information. Moreover, they often tend to neglect missing views imputation, a key mechanism for handling incomplete data. Furthermore, by separating representation learning from clustering, many existing frameworks yield representations that are not necessarily optimal for clustering, thus compromising robustness. To address these limitations and based on fuzzy clustering, a novel enhanced one-step incomplete multiview clustering method (IMVFCM_DRL) is proposed in this article. First, to effectively handle incomplete multiview data, we construct a new representation learning framework that explicitly integrates missing-view imputation. Second, to fully exploit the multiview information, a dual-information learning strategy is introduced to jointly capture both common and view-specific information. Finally, a unified one-step fuzzy clustering framework with weighted structure preservation is developed, ensuring that representation learning and fuzzy clustering are jointly optimized. The experiments conducted on various multiview datasets demonstrate the effectiveness of IMVFCM_DRL.

This study attempts to propose a novel stacking classifier S-FA2M, based on fuzzy Apriori method (FAM) with adversarial knowledge assistance, so as to improve FAM by reducing its computational complexity, enhancing its generalization capability, and concurrently mitigating its challenge of determining support and confidence thresholds. S-FA2M features in four aspects: (1) Its knowledge adversarial training method, specifically tailored for FAM indeed enhances the generalization capability of each FAM sub-classifier by employing two appropriate adversarial attacks, namely cognitively confidence-debiased adversarial attack and averaging support-confidence adversarial attack; (2) S-FA2M employs a novel strategy, called input interrupted with outputs, to realize the stacking ensemble of FAM sub-classifiers based on their feature subsets. This strategy avoids the introduction of incomprehensible intermediate features into the corresponding fuzzy association rule mining, thereby maintaining the high interpretability of the mined rules and accelerating the rule mining procedure; (3) S-FA2M adopts a weighting aggregation strategy to combine all FAM sub-classifiers that share the same support and confidence thresholds, thus alleviating the difficulty of determining these thresholds; and (4) S-FA2M has its theoretical support for the above improvements for FAM. As a result, S-FA2M battles all of FAM’s three drawbacks in a trade-off way. S-FA2M can be constructed in three steps. Firstly, S-FA2M successively stacks several FAM sub-classifiers on their feature subsets by using input interrupted with outputs. Secondly, S-FA2M employs cognitively confidence-debiased adversarial attack and averaging support-confidence adversarial attack to simultaneously attack each FAM sub-classifier. Thirdly, S-FA2M quickly aggregates each attacked FAM sub-classifier by one-step calculation. Extensive comparison experiments on fourteen benchmarking datasets, statistical analysis, ablation study, and parameter sensitivity analysis empirically demonstrate the effectiveness of S-FA2M.

While the existing type I or II first-order Takagi-Sugeno-Kang (TSK) fuzzy classifiers generally take an additive type I or II first-order rule space followed by a nonadditive defuzzification without or with type-reduction, this study enriches their family by opening a reverse thinking about a nonadditive type I or II first-order rule space, followed by a simple additive defuzzification with the avoidance of explicit type-reduction calculation. Toward this end, the novel Types I & II Partition-based first-order TSK Fuzzy Classifiers (TIP-FC and TIIP-FC) and their training methods are developed for first-order linearity of consequent of each rule on all the fuzzy partitions themselves or their simple variants rather than each original feature, thereby having their distinct values in the sense of enhanced interpretability, smaller output variance, and/or denoising capability. Extensive experimental results on the adopted benchmark datasets indicate that both TIP-FC and TIIP-FC are at least comparable to and even superior to the comparative methods in terms of interpretability, classification performance, and/or denoising capability.

Distant metastasis (DM) as a major cause of treatment failure of nasopharyngeal cancer (NPC) actually occurs with a considerably gradual development in the early stage. Therefore, an ideal DM prediction model should be an efficient and interpretable model and simultaneously reflect/simulate this characteristic during its training. Towards such a goal, this study proposes a hierarchical Takagi-Sugeno-Kang (TSK) fuzzy classifier (H-TSKFC) to assure both enhanced classification performance and diversified generation of interpretable fuzzy rules therein through full-partial-rule-transmission fusion for simulating gradual development of DM. Profiting from full-partial-rule-transmission fusion between sub-classifiers, H-TSKFC was endowed with the following benefits. Firstly, a novel stacking mechanism without any use of residuals between sub-classifiers enhances its generalization capability. Secondly, the generation of interpretable fuzzy rules from the second TSK fuzzy sub-classifier provides a diversified way. That is, its useful rules fusion transmitted fully or partially from previous sub-classifier guarantees considerable consistency between sub-classifiers, while its remaining rules reflect gradual difference between them. In this way, the H-TSKFC’s structure naturally mimics the gradual development of DM. Finally, each sub-classifier therein can be trained sequentially and quickly with an analytical solution to accomplish an individual prediction on the original inputs and outputs. Experimental results indeed demonstrate that H-TSKFC possesses linguistic interpretability, along with considerable classification and generalization performance.