In nonlinear systems, the system response frequently fluctuates with the discrepancy of variation trends over a certain horizon. In this situation, type-2 fuzzy neural networks can be limited in capturing trend features from the point prediction process due to the inherent value mapping, which may suffer from trend blindness. To address this problem, a trend-aware-based type-2 vector fuzzy neural network (TA-T2VFNN) is designed for modeling nonlinear systems. First, a quantization framework with a hybrid encoding strategy is designed to process both the magnitude and trend information of variables. In this strategy, the trend information with the rate and direction of change is represented by vectors instead of scalars, which aims to compensate for the accumulated error caused by insufficient input information. Second, a directional attention mechanism-based vector fuzzy rule is proposed to capture the trend relationship to mimic the local fluctuation patterns. Then, the vector operation is embedded into fuzzy rules for geometric inference, which can obtain the vector features with point and trend. Third, a collaborative feedback learning algorithm is developed to update the magnitude and direction parameters of TA-T2VFNN. Then, the modeling accuracy can be maintained by obtaining trusted output points and output trends. Finally, the effectiveness of TA-T2VFNN is verified by multiple practical applications.

Fuzzy rough feature selection (FRFS) effectively alleviates the curse of dimensionality by eliminating redundant and irrelevant features, thereby improving model generalization. However, most existing algorithms focus on minimizing classification uncertainty, even though lower uncertainty does not necessarily imply stronger class discrimination or improved classification performance. This challenges the common assumption that uncertainty alone sufficiently captures feature relevance in pattern classification tasks. To bridge this gap, we propose a Margin-Aware Fuzzy Rough Feature Selection (MAFRFS) framework that explicitly incorporates structural characteristics of class distributions, namely, within-class compactness and between-class separability, into the feature evaluation process. By integrating margin-based structural cues with fuzzy rough uncertainty modeling, MAFRFS effectively guides the selection toward more separable and discriminative feature subsets. Extensive experiments reported on 23 publicly available datasets demonstrate that MAFRFS is highly scalable and more effective than FRFS. Algorithms developed under MAFRFS consistently outperform some state-of-the-art feature selection algorithms.

Uncertainty modeling with different granularity structures is a research hotspot in granular computing. However, most granularity-related uncertainty measures lack effective means to represent and exploit the inherent granularity information in data, making it difficult for them to capture the distribution characteristics of samples and causing noise samples in high-aggregation regions to be misidentified. Meanwhile, they rarely involve noise-resistance mechanisms and struggle to accurately characterize the differences between samples in strongly disturbed environments, resulting in sensitivity to noise and insufficient robustness. Motivated by these issues, we investigate a novel granular-ball distinguishing measure that enhances noise-resistance on three levels: the algebraic perspective (dependency function), information theory (variable-precision entropy), and granular-ball computing (granulation mechanism). To this end, we define a relative-distance fuzzy similarity relation that fully considers local and global data distribution, thus effectively mitigating the influence of noise and outliers. A relative-distance granular-ball dependency function is then introduced by means of the relative-distance fuzzy similarity relation and fuzzy decision. Moreover, several granular-ball fuzzy entropy measures are presented, incorporating a variable-precision view to flexibly deal with noise and uncertainty. Finally, a granular-ball distinguishing measure is presented to comprehensively evaluate the distinguishing ability of candidate features. From the view of maintaining the classification ability, we further developed a heuristic feature selection algorithm with the distinguishing measure. Numerical experiments on 18 benchmark datasets demonstrate the effectiveness and robustness of the proposed model, as well as its superiority over six state-of-the-art comparative algorithms.

Imbalanced classification problems pose a significant challenge in machine learning, especially when the minority class contains critical information. In this context, Fuzzy Rule-Based Classification Systems (FRBCSs) have been widely used due to their interpretability and flexibility, but typically rely on sampling techniques to address class imbalance. FARCI, a fuzzy association rule-based classifier, is specifically designed for imbalanced datasets by introducing tailored modifications to the FARC-HD fuzzy classifier, improving performance without relying on data preprocessing. However, FARCI uses fixed membership function supports, which may limit its effectiveness in small disjuncts, and the application of the additive combination may introduce bias during inference. In this paper, we propose FARCI+, an enhanced version of FARCI that addresses these limitations through two key contributions: (1) it tunes the support of the membership functions using the 3-tuples fuzzy linguistic model to better represent minority class subregions, and (2) it incorporates generalizations of the Choquet integral in the inference stage to achieve more robust aggregation in imbalanced contexts. The effectiveness of FARCI+ is assessed through extensive experimentation on 66 binary imbalanced datasets from the KEEL repository. The results demonstrate that the combination of both components in FARCI+ significantly improves classification performance, particularly for datasets with high imbalance ratios, without affecting performance in moderately imbalanced datasets.

The accuracy of the kinematic information of a redundant robot directly influences the control performance of its end-effector. However, in practical applications, kinematic parameters may change. To address this challenge, this paper proposes a robust learning and fuzzy control (RLFC) model that possesses kinematic learning and simultaneous control capabilities, enabling the estimation of unknown kinematic parameters and achieving adaptive control for redundant robots. Specifically, the RLFC model comprises two components: an integral-enhanced recurrent neural dynamics (IERND) and a fuzzy-enhanced recurrent neural dynamics (FERND). The IERND is designed to enhance the noise tolerance in kinematic parameter learning. Based on the learned kinematic parameters, the FERND, which incorporates a fuzzy logic system for dynamically adjusting convergence parameters, achieves effective position and orientation tracking of the end-effector in the redundant robot. Theoretical analyses are provided to demonstrate the convergence of the RLFC model. Simulations and experiments validate the effectiveness of the RLFC model in parameter learning, noise tolerance, and kinematic control. The accompanying video can be accessed at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://youtu.be/DS6k7Cu19sU</uri>.

As the foundation of next-generation wireless networks, distributed learning (DL) is expected to be integrated into 6 G communication networks, profoundly advancing the transformation of intelligent connectivity. However, network-induced delays critically degrade the performance of DL algorithms in practical deployments. Beyond the communication limitation, many emerging applications involve antagonistic interactions among agents, introducing additional complexity. To overcome these challenges, we propose a decentralized distributed cooperation–competition learning (DCCL) algorithm based on neuro-fuzzy networks, designed for latency communication networks. The algorithm innovatively employs the signed graph to naturally encode the coupling coopetition relationships among agents, and incorporates the delay model into its design. It demonstrates superior adaptability for DL problems with bimodal coalitional adversarial interactions in latency-prone mission-critical services. Moreover, we extend the neuro-fuzzy network into a distributed version, and the resulting distributed neuro-fuzzy model inherently preserves the interpretability characteristic and superior learning capability. Based on structural balance theory and discrete Lyapunov stability theory, we rigorously prove the convergence of the DCCL algorithm and derive an explicit sufficient condition in the form of a maximum allowable latency tolerance. The proposed algorithm benefits privacy protection by transmitting only model parameters. Experiments are conducted to validate the performance of the DCCL algorithm on several datasets for regression and classification. Furthermore, we discuss the limitations of the DCCL algorithm, providing a balanced perspective for future research.