In multiagent systems (MASs), policy iteration (PI) and value iteration (VI) are two fundamental reinforcement learning paradigms for solving optimal cooperative control problems, exhibiting an inherent tradeoff between convergence speed and communication complexity. To clarify this tradeoff, this article reformulates the Bellman optimality equation for MASs from a bilevel optimization perspective and rigorously establishes its equivalence to the original problem. The resulting iterative solution consists of two coupled levels for the value function and control policy. By examining how value function initialization affects the existence of zero-residual solutions of Bellman equations, a unified iteration (UI) paradigm is derived. The resulting paradigm inherits the fast convergence of PI while retaining the low communication complexity of VI. The impact of suboptimal solutions on the convergence of iterative value functions and the effect on the admissibility of the iterative control policies are examined. To implement the UI paradigm in practice, a batch data-driven fuzzy identifier–actor–critic structure is proposed, and the closed-loop stability of the learning system is established. The effectiveness of the proposed method is demonstrated on a benchmark problem.
Irregularly sampled time series are ubiquitous in applications such as healthcare, climate science, and finance, where missing values and non-uniform intervals pose significant challenges for forecasting. Existing methods typically fill missing values via linear interpolation and treat imputed data as ground truth, ignoring the inherent ambiguity of these synthetic values. To address this, we propose FITMixer, a fuzzy-inspired imputation-aware framework. Specifically, a fuzzy-inspired uncertainty estimation module quantifies the ambiguity of imputed regions into a soft pattern assignment tensor via differential pattern detection and a learnable convolutional network. A feature fusion and dynamic modulation module then adaptively adjusts feature weights based on the estimated uncertainty, implementing a “fine-grained inference under low uncertainty and conservative fallback under high uncertainty” strategy. A TimeMixer encoder finally captures channel and temporal dependencies. Experiments on three real-world datasets demonstrate that FITMixer consistently outperforms ten baseline models across multiple forecasting horizons. Ablation studies validate the effectiveness of each core module, and sensitivity analysis confirms the model's robustness. The proposed fuzzy-inspired paradigm offers a new perspective for handling ambiguity in irregularly sampled time series forecasting.
Heterophily graphs are graphs in which connected nodes tend to possess dissimilar class labels or feature representations. Compared with homophily graphs, they are capable of capturing more complex and diverse relationships, making them widely applicable in domains such as e-commerce, finance, and bioinformatics. However, the inherent heterophily and structural diversity of heterophily graphs introduce significant uncertainty, posing challenges for effective representation and learning. To address these issues, this paper proposes a Heterophily Graph Fuzzy System (HeGFS) for modeling uncertain heterophily graphs. HeGFS aims to tackle the key problems of fuzzy set definition, fuzzy rule construction, and model optimization in heterophily graph learning. The major contributions of this work are as follows: 1) heterophily node fuzzy sets and fuzzy rules are introduced to extend classical graph fuzzy systems to heterophily structured data; 2) the overall architecture and end-to-end training strategy of HeGFS are designed; 3) a K-means-based heterophily node clustering algorithm and a collaborative learning mechanism based on a heterophily node consequent module are developed; and 4) extensive experiments demonstrate that HeGFS achieves superior performance in heterophily node classification while maintaining interpretability and robustness.
Random vector functional link (RVFL) networks have gained considerable attention as efficient randomized learning models due to their fast training and simple architecture. However, classical RVFL still suffers from three fundamental limitations: the reliance on the squared loss makes it highly vulnerable to noise and outliers; matrix inversion introduces substantial computational overhead; and the uniform treatment of all samples ignores the varying credibility present in real-world datasets. Existing extensions address these issues only partially, robust loss functions improve noise tolerance, and intuitionistic fuzzy (IF) schemes enhance credibility awareness, yet no framework integrates both perspectives within a unified formulation. In this work, we propose the intuitionistic fuzzy flexi guardian regularized RVFL (IF-XG-RVFL), a theoretically grounded framework that simultaneously addresses robustness, credibility modeling, and computational efficiency. The novelty of IF-XG-RVFL lies in the joint integration of 1) IF credibility scores, derived from both global and local uncertainty characteristics, and 2) a bounded, asymmetric, and smooth FleXi Guardian (XG) loss, which provides controlled asymmetry and robust error penalization. This dual integration yields a credibility-weighted and robust-loss RVFL formulation that remains smooth and fully differentiable. By leveraging this smoothness, the IF-XG-RVFL optimization problem is efficiently solved using a Nesterov accelerated gradient (NAG)-based algorithm, eliminating the need for matrix inversion and substantially reducing computational overhead. In addition, we provide a theoretical generalization error bound for the proposed IF-XG-RVFL framework using Rademacher complexity, establishing its learning guarantees. To the best of our knowledge, this is the first RVFL framework that simultaneously resolves the three key limitations of classical RVFL: robustness to noise, credibility-aware learning, and matrix-inversion-free scalability within a single unified model. Extensive experiments on UCI benchmark datasets and the BreakHis breast cancer histopathology dataset demonstrate that the proposed IF-XG-RVFL consistently outperforms several state-of-the-art randomized neural network variants in accuracy, stability, average rank, and statistical significance, as verified with the Friedman and Nemenyi tests. Furthermore, we conduct an additional evaluation on imbalanced KEEL datasets using the F1-score, where IF-XG-RVFL achieves the highest average F1-score and the best average rank among all compared methods. These results highlight the effectiveness of jointly modeling credibility and robust loss within a unified randomized neural framework.
This paper addresses the observer-based fuzzy load frequency control problem for interval type-2 fuzzy multi-area power systems against coordinated attacks. Due to strong tie-line coupling with limited communication of multi-area power systems, here we consider the cooperative effects of two typical cyber-attacks i.e., denial-of-service attacks and false data injection attacks. An extended fuzzy observer is constructed to simultaneously estimate system states and unknown false data injection attacks generated by external dynamic systems. To achieve load frequency regulation, an observer-based fuzzy controller is designed. Meanwhile, a switched system is established by integrating the dynamics of the observer, controller, and coordinated attacks. By constructing an attack signal dependent Lyapunov function, sufficient conditions are derived to ensure the exponential stability of the resulting switched system with $H_{\infty }$ disturbance attenuation performance. Moreover, leveraging the properties of membership functions, slack matrices are introduced to reduce the conservatism of the stability conditions. To further enhance the system's control and observation performance, a reinforcement learning-based optimization algorithm is innovatively adopted to online adjust the membership functions of both controller and observer. Finally, simulation results are provided to demonstrate the effectiveness of the proposed security control approach.
Multi-label classification addresses scenarios where an instance may be associated with multiple labels simultaneously. To effectively model the multi-label data, it is essential to consider the feature-label inference, label distribution and label correlation. To this end, a rule-transferred Takagi-Sugeno-Kang fuzzy system (RT-TSK-FS) is proposed for multi-label classification. First, a label separation mechanism is built to partition the label set into common and rare labels according to their distribution characteristics, which serves as the basis for rule transfer. Then, a rule-transferred Takagi-Sugeno-Kang fuzzy system is designed, consisting of a joint antecedent (If-Part) and a transfer-driven consequent (Then-Part). Furthermore, a multi-label loss function is constructed upon the proposed rule-transferred fuzzy system. By jointly exploiting label distribution information and rule-transferred inference, RT-TSK-FS effectively captures feature-label dependencies and models correlations between common and rare labels. Extensive experimental results demonstrate the effectiveness of the proposed method.
Accurate traffic prediction in dynamic environments remains challenging, especially when recent observations and interactions across time points must be considered simultaneously. Traditional approaches, such as statistical techniques or machine learning models, either struggle to capture these interactions or require extensive historical information and/or large amounts of data and training effort. In this paper, we introduce a framework based on temporal fuzzy capacities combined with Choquet-like integrals for time series prediction. The proposed approach models temporal dependencies by assigning importance not only to individual time points but also to their interactions, while naturally emphasizing more recent observations. We define temporal capacities with explicit constraints that preserve the chronological structure of the data and allow flexible modeling of recent effects. To evaluate the proposal, we compare multiple capacity formulations and fuzzy integrals across multiple real-world datasets. The results show that the proposed method consistently achieves competitive performance, with improvements in several scenarios when compared to classical approaches. Additionally, a computational complexity analysis is provided, showing that the proposed framework offers a practical trade-off between predictive performance and computational cost. These findings suggest that temporal fuzzy integrals provide a flexible and interpretable alternative for time series prediction in dynamic environments.
Semi-supervised multi-label feature selection faces significant challenges in identifying discriminative features due to insufficient labeled data. Thus, most existing methods perform graph-based label propagation or learn a latent continuous label space to recover supervisory information. However, these methods neglect the heterogeneity of sample reliability during graph construction and fail to capture the fine-grained positive and negative semantics embedded in recovered labels. These limitations may lead to suboptimal supervision quality for feature evaluation. To address these challenges, we propose a novel dual fuzzy modeling framework for semi-supervised multi-label feature selection. Specifically, in the feature space, a reliability-aware fuzzy graph is constructed to adaptively modulate the contribution of each sample to structure construction based on its credibility, thereby enhancing the robustness of label propagation. In the label space, a bipolar fuzzy semantic modeling strategy is developed to transform binary annotations into generalized label distributions, enabling simultaneous characterization of positive and negative membership degrees. These components, complemented by positive and negative label correlations, are integrated into a unified $\ell _{2,1}$-norm regularized framework for feature selection. Theoretical analysis provides insights into how the proposed framework can improve propagation stability and semantic separability, thereby enabling more reliable supervision recovery. Furthermore, extensive experiments on multiple benchmark datasets demonstrate the effectiveness of our proposal for selecting informative features with limited annotations.
Tracking-error excursions during load-bearing motions can compromise the posture stability and load transfer of humanoid lower-limb (HLL) robots. Robust and sliding-mode controllers attenuate disturbances, but they neither intrinsically enforce designer-specified time-varying error envelopes nor resolve coupled gain selection. For HLL dynamics, embedding a prescribed-performance specification (PPS) is not merely imposing an external bound: The nonlinear mapping reconstructs the mechanical dynamics and propagates physical uncertainty into transformation-induced uncertainty. This article develops a diffeomorphism-based prescribed-performance adaptive robust control (PPARC) framework around this reconstructed system. The PPS inequality is converted into an unconstrained servo-stabilization problem; an adaptive robust law compensates the induced uncertainty; and plausibility-aware fuzzy-set information is mapped by a $D$-operation into separate tracking- and effort-related objectives for Nash game-based coordinated gain optimization. The Nash game is thereby driven by the same Lyapunov-UUB characterization used to establish stability, rather than appended as empirical tuning. Lyapunov analysis proves uniform boundedness and uniform ultimate boundedness, guaranteeing PPS satisfaction with ultimately bounded transformed errors. Comparative simulations show that PPARC preserves the prescribed envelopes and reduces accumulated RMS tracking error by $32.8\%$ relative to SMC; gains obtained by Nash game-based coordinated gain optimization increase this reduction to $33.0\%$ while maintaining comparable control effort.
This paper investigates the global practical prescribed-time adaptive fuzzy tracking control problem for p-normal nonlinear systems with external disturbances based on monotonic performance tube constraints. A quasi-linear formulation is adopted to extract control terms, overcoming the design difficulty caused by the non-affine property of control inputs. Combined with adaptive fuzzy control, a novel dual-sigmoid membership function is adopted to approximate system unknown nonlinearities and external disturbances. A novel design scheme of monotonic tube boundary performance functions is proposed to realize performance constraints with asymmetric decay rates, which improves the flexibility and steady-state accuracy of the constraint mechanism. Moreover, an error self-tuning mechanism is devised to impose refined dynamic constraints on tracking errors in prescribed time, thereby ensuring global prescribed performance tracking regardless of initial conditions. Finally, rigorous Lyapunov analysis confirms that all closed-loop signals are globally uniformly ultimately bounded, while systems output converge to the steady-state residual set within the prescribed time. Simulation results demonstrate the validity and superiority of the developed scheme.
The work is motivated by a recently published formal proof establishing that the exploration of an tecedent–consequent structures is necessary for guaranteeing feasibility, reducing conservatism, and establishing optimality in Linear Matrix Inequalities (LMIs)-based Parallel Distributed Compensation (PDC) control design. Therefore, this paper presents a comparative effectiveness analysis of the original Takagi–Sugeno (TS) fuzzy model transformation and the recently proposed TS fuzzy model transition and input-space manipulation methods, all developed for the comprehensive exploration of antecedent–consequent structures. The investigation is further motivated by the fact that these recently proposed methods have so far been studied predominantly at a theoretical level, while comparative practical modeling and control-design insights remain limited. Therefore, the Translational Oscillator with a Rotational Actuator (TORA) benchmark system is employed as a representative case study. Although TORA is selected, the revealed tendencies originate from the underlying convex hull manipulation principles and are not specific to the TORA system itself. The analysis focuses on the manipulability of the convex hulls spanned by the consequent vertices of TS fuzzy models, including minimization or optimization of the number of vertices, manipulation of convex-hull tightness or looseness, parameter-dependent convex-hull tunability, and manipulation of the dimensionality of the TS fuzzy model input space, all of which directly influence the achievable antecedent–consequent structure. The most important conclusion of the paper is that the combined application of these approaches is very effective for systematically exploring the achievable control solutions to identify the controller that best satisfies the control-performance requirements.
Traditional TSK (Takagi-Sugeno-Kang) fuzzy systems suffer from three fundamental limitations: exponential rule growth from Cartesian product-based generation, cross dimensional interaction constraints imposed by T-norm aggregation, and limited expressiveness of linear consequents. To simultaneously address these shortcomings, this paper proposes MGE-DNTSK (Multi-Granularity Ellipsoidal Dual-Neural TSK), a novel neural fuzzy classification system comprising a hierarchical granulation layer and a dual-neural TSK (DNTSK) transformation layer. Unlike existing approaches that tackle these limitations in isolation, MGE-DNTSK unifies differentiable information granulation with neural rule generation within a single end-to-end framework. Specifically, the granulation layer constructs tilted hyper-ellipsoidal granules via low-rank Cholesky factorization across coarse, medium, and fine tiers, encoding inter-feature correlations into membership representations with linear parameter complexity. Building upon these representations, the DNTSK layer replaces Cartesian product-based rule generation and linear consequent functions with a shared neural antecedent incorporating adaptive pruning and independent neural consequents, thereby decoupling rule complexity from input dimensionality while enhancing local nonlinear expressiveness. The entire architecture is optimized through a three-stage cur riculum protocol. Experiments on 16 benchmark datasets show that MGE-DNTSK achieves leading performance across four evaluation metrics against 15 representative baselines, particularly on high-dimensional data, and a real-world industrial fault diagnosis case study further exhibits its practical effectiveness.
This paper quantifies asymmetry under imprecision by introducing a probabilistic interpretation for fuzzy numbers and a non-moment-based skewness coefficient derived from it. The coefficient adapts classical quantile-based skewness measures (Bowley, Kelley, Groeneveld–Meeden) to the α-cut representation of fuzzy numbers. Existing studies typically employ heuristic modifications of the classical Fisher-Pearson formula, therein sub stituting membership functions for probability densities without a rigorous semantic bridge between the two. Our coefficient, in contrast, is grounded in am explicit probabilistic interpretation, rendering it both mathematically meaningful and aligned with the semantics of fuzzy set theory. Our approach interprets a fuzzy number's left and right membership function components as cumulative and survival probability functions of associated random variables. This pro vides a probabilistic reading of its α-cuts as generalized quantiles representing intervals of values that are “at least (1 − α) probable”, thereby highlighting a duality between probability and possibility theory. As a quantile-based measure, the proposed coefficient offers invariance under scale and location transfor mations. Moreover, its point-based variant requires only a fixed number of quantile evaluations per computation, constant time in the α-discretization, compared with the linear cost of moment based alternatives. The coefficient comprises two complemen tary constituents: an “inner” measure quantifying the intrinsic skewness of the underlying probabilistic distributions, and an “outer” measure capturing the fuzzy number's overall profile asymmetry. We illustrate the measures within a fuzzy mean variance-skewness portfolio optimization framework on historical equity data, comparing their performance with two of the most highly cited original moment-based fuzzy skewness coefficients from the literature.
High-resolution land–ocean integrated digital elevation models (DEMs) are critical for navigation, coastal management, and marine engineering in strait environments. However, existing DEM products are too coarse, while bathymetric observations are sparse, heterogeneous, and unevenly distributed, making high-resolution reconstruction difficult. To address this problem, this study proposes a transfer learning-based Fuzzy Elevation-Aware Mixture of Experts (TFEA-MoE) framework for DEM super-resolution in the Taiwan Strait. The core methodological contribution is an elevation aware fuzzy expert routing mechanism, which uses learnable Gaussian membership functions to softly assign pixels to shallow, transition, and deep water experts. Embedded in a Bass Strait to Taiwan Strait transfer learning framework, this routing strategy enables smooth and physically interpretable residual correction under sparse ATL24 and shipborne supervision. Experimental results show that TFEA-MoE achieves the lowest errors among the compared methods under the evaluated protocols. Based on held-out sparse bathymetric observations, compared with the average performance of all baseline methods, TFEA-MoE reduces RMSE, MAE, Slope RMSE, and Slope MAE by 23.87%, 34.01%, 22.02%, and 21.48%, respectively. Ablation studies confirm the contributions of transfer learning and fuzzy expert routing, with fuzzy refinement reducing the four metrics by 12.36%, 34.89%, 12.26%, and 16.05%, respectively. Because these observation-level improvements may be partially influenced by spatial autocorrelation, spatially independent testing is used as the main evidence for target-domain generalization, with uncertainty and seam-continuity analyses supporting reconstruction stability. These results indicate that TFEA-MoE provides a promising and interpretable approach for DEM super-resolution under sparse and heterogeneous bathymetric observations.
The characterizing set-valued functions of uninorms, pseudo-uninorms and $n$-uninorms are extended for pseudo-$n$-uninorms and studied. While in the case of uninorms, pseudo-uninorms and $n$-uninorms, the graphs of characterizing set-valued functions cover all points of discontinuity and non-commutativity, this holds only partially in the case of pseudo-$n$-uninorms, which have non-symmetric characterizing set-valued functions.
This paper focuses on the finite-time stabilization of interval type-2 (IT2) fuzzy polynomial positive systems. For the purpose of stability analysis, an IT2 fuzzy co-positive Lyapunov function (FCLF) is designed, which inevitably generates a term with the derivative of the membership functions (MFs) of the IT2 FCLF. In dealing with this term, unlike most previous studies which only consider the boundary information of the derivative of the MFs of the IT2 FCLF, this paper also introduces the nature of the derivative of the MF. While the proposed IT2 FCLF gives more relaxed stabilization results, it also leads to more complicated non-convex problems. To solve this difficulty, the matrix decomposition technique is used to design the feedback control gains of IT2 fuzzy polynomial controllers. Moreover, if the information of the MFs is ignored, the results obtained will be very conservative. In order to reduce conservatism, an improved piecewise linear approximation method is proposed. It offers a novel perspective on approximating MFs, facilitating the incorporation of more valuable information, such as the approximation errors, into the stability conditions so that the relaxation of the stability analysis results can be enhanced. Finally, a simulation example verifies the effectiveness of the proposed strategy.
This paper investigates the attitude fault-tolerant control (FTC) problem for rigid spacecraft subject to actuator faults and input saturation. A Takagi-Sugeno (T-S) fuzzy rep resentation is constructed within a prescribed compact angular velocity region, which enables systematic observer and controller synthesis for the nonlinear attitude dynamics. To overcome the limitations of overly simplistic static fault models in representing diverse engineering failures, a generalized polynomial function approximation strategy is introduced. This formulation encompasses a wider spectrum of fault profiles and improves fault-reconstruction fidelity. Building upon this, an intermediate variable-based fuzzy fault observer is developed. This design relaxes the restrictive strictly positive real (SPR) condition commonly required in classical observer designs, providing greater flexibility in gain selection. Leveraging the observer's estimates, an adaptive FTC scheme is synthesized to compensate for actuator faults while respecting input saturation. The region dependent UUB of the closed-loop system is rigorously established via Lyapunov stability theory. Finally, simulations on a spacecraft benchmark model verify the effectiveness of the proposed fuzzy based FTC strategy.
In many fields, different types of data are often available for the same set of entities. Each type of data can be seen as a separate layer. Real-world datasets also often include uncertainty. When analyzed carefully, this multilayer data can reveal deeper insights, but only if imprecision is taken into account. While graph neural networks (GNNs) are effective at learning from structured data, they struggle to handle uncertainty and provide clear explanations. To address these challenges, we introduce a fuzzy graph covering-based graph neural network (FGC-GNN). Our framework models any multimodal data with uncertainty as a fuzzy graph, where edges represent uncertain relationships. We use graph covering in fuzzy graphs to implement a convolutional strategy that fuses attention to reduce redundancy, highlight important substructures, and maintain uncertainty during representation learning. This representation is used in a GNN to find meaningful patterns and improve both robustness and interpretability. This article presents tests onstandard biomedical datasets, showing that FGC-GNN improves performance across multiple datasets and fuzzy learning methods. We have performed a one-way analysis of variance (ANOVA) to reflect the significance of the study. Our model provides a transparent, efficient decision-support tool.
In sequential pattern mining (SPM), three-way SPM aims to reduce redundant patterns by classifying items into weak, medium, and strong groups, mining only patterns of medium and strong items with no strong items in pattern gaps. However, this approach requires users to categorize the items manually, producing discrete results with undetermined boundaries, and its rigid gap constraint overfilters valid patterns. To address this problem, based on item frequency and user interest, we mine fuzzy three-way nonoverlapping sequential patterns (FNPs) with flexible quantitative gap constraints, and propose an algorithm called FNP-Miner. FNP mining does not satisfy the anti-monotonicity property, and we overcome this limitation by deriving a fuzzy support upper bound and designing a pruning strategy to effectively reduce the number of candidate patterns. Furthermore, to enhance the efficiency of fuzzy support computation, the support of a pattern is calculated using the occurrence information of its subpatterns based on an inverted index structure. To evaluate the performance of FNP-Miner, we compare it with 13 competitive algorithms on eight benchmark datasets, and propose two indicators to measure the interest degree of patterns and gaps. The experimental results show that FNP-Miner finds patterns that are more preferred by the user, and achieves better performance than the compared algorithms.
The fault evolution of converter transformers exhibits complex dynamic characteristics characterized by the strong coupling between long-term thermochemical gradual variations and high-frequency electrical transient jumps. Existing methods relying on fixed time windows and symmetric information granulation fail to adapt to the asymmetric distributions of jump signals. This limitation leads to insufficient diagnostic reliability and possible violations of a predefined severity–type compatibility constraint. To address these challenges, this article proposes a fault diagnosis method for converter transformers based on asymmetric fuzzy granulation and physics-embedded cascaded stochastic configuration networks. First, an adaptive temporal fuzzy granulation (ATFG) module based on skewness statistics was constructed to achieve semantic-guided soft granular focused representation, which is theoretically proven to possess an optimal lower bound for interval error. Second, a multi-source variable-information granularity interactive attention (VGIA) mechanism was designed to deeply aggregate the spatiotemporal coupled features of multi-source faults. Finally, by vectorizing and cascading physical priors as inputs, a physical knowledge-embedded cascaded stochastic configuration network (PK-CSCN) was established to achieve physically structured and evidence-traceable classification of fault severities and types. Its global approximation capability over feature manifolds is theoretically proven. Experimental results on 14,983 measured converter-transformer samples demonstrate that, while achieving strict consistency with the predefined severity–type compatibility constraint, the proposed method achieves a classification accuracy of 96.70%, significantly outperforming existing mainstream models.
