Fuzzy Sets and Systems最新文献

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Fixed-time adaptive fuzzy event-triggered fault-tolerant containment control for nonlinear multi-agent systems 非线性多智能体系统的定时自适应模糊事件触发容错控制

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-18 DOI: 10.1016/j.fss.2025.109732

Guanglei Zhao , Xianyu Liu

This work studies the fixed-time event-triggered fault-tolerant containment control problem for nonlinear multi-agent system (MAS) with actuator faults. First, by leveraging fuzzy logic system to approximate unknown nonlinear dynamics, a state observer is designed to estimate unmeasurable state variables. Second, to handle the actuator fault, a novel projection operator compensation mechanism is developed. Furthermore, a fixed-time nonlinear filter design is given to solve the explosion problem and dynamic event-triggering mechanism is proposed to save system resources. Then, combined with dynamic surface control and fuzzy control techniques, fixed-time adaptive fault-tolerant containment control strategy is proposed with rigorous stability analysis, and all followers are able to converge to the convex hull constructed by leaders. In contrast with existing approaches, the main superiority of the proposed containment control strategy is that the projection operator can handle actuator faults more efficiently, multiple parameters of nonlinear filter enhance system flexibility and dynamic threshold in triggering conditions helps to reduce triggering frequency. Finally, simulation results confirm that the proposed method ensures fixed-time convergence of the containment errors.

研究了具有执行器故障的非线性多智能体系统的固定时间事件触发容错控制问题。首先，利用模糊逻辑系统逼近未知的非线性动力学，设计状态观测器来估计不可测状态变量。其次，针对执行机构故障，提出了一种新的投影算子补偿机制。为解决爆炸问题，提出了定时非线性滤波器设计，并提出了动态事件触发机制，节约了系统资源。然后，结合动态曲面控制和模糊控制技术，提出了具有严格稳定性分析的定时自适应容错遏制控制策略，使所有follower都能收敛到由leader构造的凸包；与现有控制方法相比，该控制策略的主要优点是投影算子能更有效地处理执行器故障，非线性滤波的多参数增强了系统的灵活性，触发条件下的动态阈值有助于降低触发频率。最后，仿真结果验证了该方法能保证容错误差的定时收敛性。

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引用次数: 0

Innovative Razumikhin method for finite-time projective synchronization in fractional delay-coupled fuzzy memristive neural networks with jump mismatches 具有跳跃失配的分数阶延迟耦合模糊记忆神经网络有限时间投影同步的创新Razumikhin方法

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-20 DOI: 10.1016/j.fss.2025.109742

Wenqi Zhang , Xiang Wu , Hai Zhang , Xiaofeng Ye , Jinde Cao

This paper investigates finite-time projective synchronization (FTP-S) of Caputo fractional multilayer coupled Takagi-Sugeno (T-S) fuzzy delayed memristive neural networks with jumping mismatches. First, a new model combining multilayer coupling and jumping mismatches is proposed to address hierarchical interactions and synaptic weight shifts. Then, a novel Razumikhin finite-time stability lemma for Caputo fractional delayed systems is proposed. Leveraging this lemma and an event-triggered mechanism based on T-S fuzzy rules, sufficient conditions for FTP-S and its settling time are derived. Finally, the absence of Zeno behavior is demonstrated. Notably, the proposed lemma overcomes limitations of existing methods and applies broadly to other fractional delayed systems. Numerical simulations validate the effectiveness of the theory and control strategy.

研究了具有跳跃失配的Caputo分数阶多层耦合Takagi-Sugeno模糊延迟记忆神经网络的有限时间投影同步（FTP-S）。首先，提出了一种结合多层耦合和跳跃错配的新模型，以解决层次相互作用和突触权移的问题。然后，给出了Caputo分数阶时滞系统的Razumikhin有限时间稳定性引理。利用这一引理和基于T-S模糊规则的事件触发机制，导出了FTP-S及其建立时间的充分条件。最后，证明了芝诺行为的不存在。值得注意的是，所提出的引理克服了现有方法的局限性，并广泛地应用于其他分数阶延迟系统。数值仿真验证了理论和控制策略的有效性。

引用次数: 0

RF-WFCCL: A random forest-driven weighted fuzzy concept cognitive learning 随机森林驱动的加权模糊概念认知学习

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-15 DOI: 10.1016/j.fss.2025.109724

Weihua Xu, Chongze Zhang

Weighted Fuzzy Concept Cognitive Learning (WFCCL) improves concept learning by assigning different weights to attributes. However, existing weighting methods mainly rely on fuzzy entropy and fail to effectively handle the noise, uncertainty, and complexity commonly present in real-world data. Moreover, the key threshold λ for generating Advanced Weighted Fuzzy Concepts (AWFC) has not been thoroughly investigated, which may limit the depth of knowledge discovery and the applicability of the model. To address these issues, this paper proposes a Random Forest-Driven Weighted Fuzzy Concept Cognitive Learning (RF-WFCCL) method. The proposed approach leverages random forests to compute attribute importance, thereby making weight allocation more reflective of data characteristics and reducing the influence of noise and uncertainty. In addition, an adaptive optimization algorithm is designed to automatically determine the approximately optimal threshold

\hat{λ} (i)

for generating AWFC, enhancing the accuracy and applicability of concept cognition. Unlike traditional methods, our model not only improves the adaptability of weight allocation but also introduces a data-driven threshold optimization strategy to facilitate knowledge discovery. Finally, extensive experiments on 12 datasets using 12 classification algorithms demonstrate the feasibility and superiority of the proposed method.

加权模糊概念认知学习（WFCCL）通过赋予属性不同的权重来改进概念学习。然而，现有的加权方法主要依赖于模糊熵，不能有效地处理现实数据中普遍存在的噪声、不确定性和复杂性。此外，生成高级加权模糊概念（AWFC）的关键阈值λ还没有得到深入的研究，这可能会限制知识发现的深度和模型的适用性。为了解决这些问题，本文提出了随机森林驱动加权模糊概念认知学习（RF-WFCCL）方法。该方法利用随机森林计算属性重要性，从而使权重分配更能反映数据特征，减少噪声和不确定性的影响。此外，设计了自适应优化算法，自动确定AWFC生成的近似最优阈值λ^(i)，提高了概念认知的准确性和适用性。与传统方法不同，该模型不仅提高了权重分配的适应性，而且引入了数据驱动的阈值优化策略，便于知识发现。最后，在12个数据集上使用12种分类算法进行了大量实验，验证了该方法的可行性和优越性。

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引用次数: 0

Specificity measures based on fuzzy set inequality 基于模糊集不等式的特异性测度

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-19 DOI: 10.1016/j.fss.2025.109744

Nicolás Marín , Gustavo Rivas-Gervilla , Daniel Sánchez

Specificity is a measure that tells us to what extent a fuzzy set is a singleton. The variety of application domains of this measure requires different specific forms of calculating it. One way to control the semantic nuances in the way specificity is computed is to generate it from other well-known measures in the Fuzzy Set Theory that have a wide range of evaluation functions with different axiomatics. Following this strategy, in this work we study in depth the inequality measures based on their axiomatics, we establish a method to use them as generators of specificity measures, and we analyze the semantics and the desired properties of specificity measures obtained according to the axioms satisfied by the inequality measures used as generators. As we will see, relevant results have been obtained that relate different families of specificity and inequality measures.

特异性是一种度量，它告诉我们模糊集在多大程度上是单态的。该度量的各种应用领域需要不同的特定计算形式。控制专用性计算方式的语义细微差别的一种方法是从模糊集合理论中其他已知的具有不同公理的广泛评价函数的度量中生成专用性。根据这一策略，本文从不等式测度的公理出发，对其进行了深入的研究，建立了一种将不等式测度作为特定测度的生成器的方法，并根据作为生成器的不等式测度所满足的公理，分析了所得到的特定测度的语义和期望性质。正如我们将看到的，已经获得了与不同的特异性和不平等措施相关的相关结果。

引用次数: 0

Representation and construction of the classes Umin1 and Umax0 of uninorms on a bounded lattice 有界格上一致子的类Umin1和Umax0的表示和构造

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-11-15 DOI: 10.1016/j.fss.2025.109682

Hua-Peng Zhang , Yao Ouyang

After mining some inherent properties of the class

U_{\min}^{1}

of uninorms on a bounded lattice, we present structural representation theorems for uninorms in

U_{\min}^{1}

by distinguishing two cases. As an application of the representation theorems, we propose several construction methods for uninorms in

U_{\min}^{1}

. These results can be easily translated into their counterparts for uninorms in

U_{\max}^{0}

via the Duality Principle in poset theory.

在挖掘了有界格上一致子类Umin1的一些固有性质后，通过区分两种情况，给出了Umin1上一致子的结构表示定理。作为表示定理的一个应用，我们提出了在Umin1中构造一致子的几种方法。通过偏序集理论中的对偶原理，这些结果可以很容易地转化为Umax0中一致子的对应结果。

引用次数: 0

A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps 模糊Lipschitz地图的McShane-Whitney扩展的修订和扩展版本

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-17 DOI: 10.1016/j.fss.2025.109731

Eduardo Jiménez-Fernández , Jesús Rodríguez-López , Aurora Sánchez-Martín-Orozco , Enrique A. Sánchez-Pérez

In the paper [E. Jiménez-Fernández, J. Rodríguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space

(R, M_{ϕ, g}, *) .

However, while the function ϕ is only required to be increasing, some results of the paper implicitly assume that ϕ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires ϕ to be also left-continuous.

在论文中[d]。Jiménez-Fernández， J. Rodríguez-López， E. a . Sánchez-Pérez, Fuzzy Sets and Systems 406(2021),66-81]，给出了模糊度量空间间实值模糊Lipschitz映射的McShane-Whitney扩展定理。具体来说，上域空间被认为是一个所谓的欧几里得模糊度量空间（R, m φ,g,*）。然而，虽然函数φ只需要增加，但本文的一些结果隐含地假设φ是可逆的，即使这没有明确说明。我们在这里提出了另一种可能性，只要求φ也是左连续的。

引用次数: 0

The uncertainty importance measure analysis for fuzzy structural systems based on possibilistic variance 基于可能性方差的模糊结构系统不确定性重要性测度分析

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-16 DOI: 10.1016/j.fss.2025.109743

Guijie Li , Yang Zhan , Huimin Xue

To effectively characterize the effects of fuzzy uncertainties on structural systems, this study introduces a novel importance measure termed Possibilistic Variance-based Importance Measure (PVB-IM). By leveraging the High Dimensional Model Representation (HDMR) of the function, we extend the decomposition equation for fuzzy structural systems to establish the PVB-IM. This approach enables the identification of effects of fuzzy variables on system response within fuzzy uncertainties, thereby facilitating the design and optimization for such structural systems. We present a fundamental computational algorithm for PVB-IM using Monte Carlo simulation and propose an efficient algorithm based on the State Dependent Parameter (SDP) method for addressing complex engineering challenges. Through numerical and engineering examples, we validate the applicability and rationale of the PVB-IM, and demonstrate the accuracy and efficiency of the SDP algorithm.

为了有效地表征模糊不确定性对结构系统的影响，本研究引入了一种新的重要性度量，称为基于可能性方差的重要性度量（PVB-IM）。利用函数的高维模型表示（HDMR），我们扩展了模糊结构系统的分解方程，建立了PVB-IM。该方法能够识别模糊变量对模糊不确定性下系统响应的影响，从而便于此类结构系统的设计和优化。本文提出了一种基于蒙特卡罗模拟的PVB-IM的基本计算算法，并提出了一种基于状态相关参数（SDP）方法的有效算法来解决复杂的工程挑战。通过数值和工程实例验证了PVB-IM算法的适用性和合理性，并验证了SDP算法的准确性和高效性。

引用次数: 0

2-copulas and linear splines 2共轭和线性样条

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-20 DOI: 10.1016/j.fss.2025.109746

Fateme Kouchakinejad , Radko Mesiar , Andrea Stupňanová , Radomír Halaš

The notion of spline linearity for aggregation functions is recalled. We then focus on linear spline 2-copulas and various constructions of 2-copulas to investigate the impact of these constructions on spline linearity. Moreover, associative copulas that are linear splines are discussed. Some other methods that yield linear spline copulas are also presented and illustrated.

回顾了聚集函数的样条线性的概念。然后，我们将重点放在线性样条2-连和各种2-连的结构上，以研究这些结构对样条线性的影响。此外，还讨论了一类线性样条的结合能。本文还介绍并说明了其它几种生成线性样条联的方法。

引用次数: 0

Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence 欧几里得距离和Kullback-Leibler散度诱导的邻域模型

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-22 DOI: 10.1016/j.fss.2025.109745

Ignacio Montes

Robust statistics aims to develop methods that ensure the obtained results remain stable regardless of the quality of the data. A natural approach to enhancing the robustness of a probabilistic model is to consider a neighbourhood around a probability measure with a given radius. These models require two tools: a function for comparing probability measures and the radius measuring the level of imprecision or robustness to be added to the model. With these tools, a neighbourhood or distortion model is defined as the closed ball centred at the probability measure. Many well-known robust models, such as the ϵ-contamination, pari-mutuel model, or constant odds ratio, can be incorporated into the broader framework of neighbourhood models. Additionally, distances between probability measures, such as the total variation or the Kolmogorov distances, determine a neighbourhood model. This paper delves into the neighbourhood models induced by the Euclidean distance applied to the probability mass functions and the Kullback-Leibler divergence. For investigating these models from the perspective of imprecise probability theory, we make use of common optimisation tools with restrictions. We conclude this study providing a comparison study among different neighbourhood models.

稳健统计旨在开发方法，以确保所获得的结果保持稳定，无论数据质量如何。增强概率模型鲁棒性的一种自然方法是在给定半径的概率测度周围考虑一个邻域。这些模型需要两种工具：用于比较概率测量的函数和用于测量不精确或健壮程度的半径，以添加到模型中。使用这些工具，邻域或失真模型被定义为以概率度量为中心的封闭球。许多众所周知的健壮模型，如ϵ-contamination、pari-mutuel模型或恒定比值比，都可以纳入更广泛的邻域模型框架中。此外，概率测度之间的距离，如总变异或Kolmogorov距离，决定了邻域模型。本文研究了应用于概率质量函数和Kullback-Leibler散度的欧几里得距离诱导的邻域模型。为了从不精确概率论的角度研究这些模型，我们使用了带有限制的常见优化工具。最后，我们对不同的邻里模式进行了比较研究。

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引用次数: 0

A transition-state-based zeroing neurodynamics method for solving non-fully/fully LR fuzzy Sylvester matrix equation 求解非全/全LR模糊Sylvester矩阵方程的过渡状态归零神经动力学方法

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2026-04-15 Epub Date: 2025-12-05 DOI: 10.1016/j.fss.2025.109715

Lei Jia , Weibao Xiong , Yiwei Li

Considering that traditional methods encounter theoretical infeasibility and computational complexity when solving fuzzy Sylvester matrix equations, by leveraging the advantages of zeroing neurodynamics approach for calculation problems, this paper proposes a transition-state-based zeroing neurodynamic (TSBZN) method to address non-fully/fully LR fuzzy Sylvester matrix equation (i.e., NLFSM and FLFSM equations). Based on the element-wise forms of the NLFSM and FLFSM equations which are mainly derived from LR fuzzy numbers and relative operations, two TSBZN models are constructed by defining the mass matrix. At the same time, a novel transition-state-based activation function (TSBAF) is designed and applied to enhance the performance of TSBZN models. In the TSBAF, a transition state parameter is introduced and divides the convergence process into two phases: a traveling phase and a reaching phase. The traveling phase ensures that the TSBZN models are continuously attracted to the transition state and rapidly converges to it, while the reaching phase guarantees stability and precise control. Consequently, the TSBZN models activated by the TSBAF possess superior fixed-time convergence with stricter upper bound on settling time, ensuring that the exact solutions of the NLFSM and FLFSM equations can be obtained within a fixed time. The global stability and fixed-time convergence of these two TSBZN models are theoretically proven, with predefined-time convergence further guaranteed by a corollary. Serial numerical experiments validate the accuracy, efficiency, and superiority of the TSBZN models, and an image denoising application also shows their practical value.

针对传统方法求解模糊Sylvester矩阵方程存在理论不可行性和计算复杂性的问题，利用归零神经动力学方法求解计算问题的优势，提出了一种基于过渡状态的归零神经动力学（TSBZN）方法求解非全/全LR模糊Sylvester矩阵方程（即NLFSM和FLFSM方程）。基于主要由LR模糊数和相关运算导出的NLFSM和FLFSM方程的元素形式，通过定义质量矩阵，构建了两个TSBZN模型。同时，设计并应用了一种新的基于过渡状态的激活函数（TSBAF）来提高TSBZN模型的性能。在TSBAF中引入过渡状态参数，将收敛过程分为两个阶段：行进阶段和到达阶段。行进相位保证了TSBZN模型不断被吸引到过渡状态并快速收敛，到达相位保证了稳定性和精确控制。因此，TSBAF激活的TSBZN模型具有较强的定时收敛性和较严格的沉降时间上界，保证了NLFSM和FLFSM方程在固定时间内的精确解。从理论上证明了这两种TSBZN模型的全局稳定性和定时收敛性，并通过一个推论进一步保证了模型的定时收敛性。一系列数值实验验证了TSBZN模型的精度、效率和优越性，并在图像去噪应用中显示了其实用价值。

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