Fuzzy Sets and Systems最新文献

英文中文

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 : 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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引用次数: 0

Beyond parity: A fuzzy life-cycle index of gender equality with legal–Practical implementation gaps 超越平等：具有法律实践执行差距的性别平等模糊生命周期指数

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

Fuzzy Sets and Systems

Pub Date : 2025-12-03 DOI: 10.1016/j.fss.2025.109717

Firas Kaabi

We introduce the Fuzzy Life-Cycle Gender Equality Index (FLGEI). It treats gender (in)equality as graded membership in a normative set of equal-opportunity life-cycle states. Indicators are aggregated with a non-additive Choquet integral to capture complementarities and limited substitutability across domains. FLGEI separates de jure rights (Women, Business and the Law) from de facto outcomes (household surveys, ILOSTAT, time-use) and defines their difference as an implementation gap. A delay-aversion axiom penalizes persistent late-stage shortfalls. Shapley values and interaction indices provide transparent domain-level attribution. We also describe how the index is identified and estimated, how uncertainty is quantified, and how it can be used in simple counterfactual simulations. A Tunisia-MENA pilot (2000-2024) shows that childcare access and safety constraints jointly limit labor equality even under strong legal frameworks. Relative to additive and crisp alternatives, FLGEI is more stable to small perturbations and improves budget-targeting performance.

引入模糊生命周期性别平等指数（FLGEI）。它将性别平等视为一套机会均等的生命周期状态的规范中的分级成员资格。指标与非加性Choquet积分聚合，以捕获互补性和有限的跨域可替代性。FLGEI将法律上的权利（妇女、商业和法律）与事实上的结果（住户调查、劳工统计局、时间利用）分开，并将其差异定义为执行差距。延迟厌恶公理惩罚持续的后期缺陷。Shapley值和交互指数提供了透明的领域级归属。我们还描述了如何识别和估计指数，如何量化不确定性，以及如何在简单的反事实模拟中使用它。突尼斯-中东和北非地区试点（2000-2024年）表明，即使在强有力的法律框架下，儿童保育机会和安全限制也共同限制了劳动平等。相对于添加剂和脆替代品，FLGEI对小扰动更稳定，并提高了预算目标性能。

引用次数: 0

Fixed-time stability of unknown stochastic nonlinear systems: A new approach with prescribed upper bound 未知随机非线性系统的定时稳定性：一种具有规定上界的新方法

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

Fuzzy Sets and Systems

Pub Date : 2025-12-01 DOI: 10.1016/j.fss.2025.109707

Yixuan Yuan , Liping Xie , Junsheng Zhao , Kanjian Zhang

The present study explores the issue of fixed-time control for nonlinear systems that are affected by stochastic perturbations. The issue of infinite gain is effectively addressed by employing a function defined by variable gain over time, and two novel theorems are established. In the first theorem, the scenario is analysed in which both the drift and diffusion terms in stochastic nonlinear systems are known, and this demonstrates that the system achieves fixed-time stability in probability. However, given the potential imperfections inherent in real-world systems, such as model uncertainties and external disturbances, the concept of practical mean-square fixed-time stability is further introduced in Theorem 2. Traditional approaches typically rely on parameter-dependent upper-bound functions to estimate the settling time, which lack flexibility and adaptability to varying system requirements. In contrast, the proposed fixed-time control strategy, which includes a prescribed upper-bound on the dwell time, provides greater flexibility. It enables users to specify the upper limit of the dwell time in accordance with practical requirements. Furthermore, the design of the state-feedback controller employs fuzzy logic systems to approximate the unknown drift and diffusion terms in stochastic nonlinear systems, and by integrating a time-varying gain function, it enables the arbitrary specification of the upper bound on the dwell time. To verify the validity of the prescribed control scheme, this paper presents two simulation case analyses. A comparison and analysis of the results with those obtained by alternative methods demonstrates the rationality and quality of the prescribed control mechanism.

本研究探讨了受随机扰动影响的非线性系统的定时控制问题。利用随时间变化的增益函数有效地解决了无限增益的问题，并建立了两个新的定理。在第一个定理中，分析了随机非线性系统中漂移项和扩散项都已知的情形，证明了系统在概率上达到定时稳定性。然而，考虑到现实世界系统中固有的潜在缺陷，例如模型不确定性和外部干扰，在定理2中进一步引入了实际均方固定时间稳定性的概念。传统的方法通常依赖于参数相关的上界函数来估计稳定时间，缺乏灵活性和对不同系统需求的适应性。相比之下，所提出的固定时间控制策略提供了更大的灵活性，该策略包括规定的停留时间上限。用户可根据实际需要指定停留时间上限。此外，状态反馈控制器的设计采用模糊逻辑系统来逼近随机非线性系统中的未知漂移和扩散项，并通过积分时变增益函数来实现停留时间上界的任意规定。为了验证所定控制方案的有效性，本文给出了两个仿真案例分析。与其他方法的结果进行了比较分析，证明了所规定控制机制的合理性和质量。

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引用次数: 0

General and left-continuous operators on lattice-based sums 格基和上的一般和左连续算子

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

Fuzzy Sets and Systems

Pub Date : 2025-11-30 DOI: 10.1016/j.fss.2025.109706

Roberto G. Aragón , Pascual Jara , Jesús Medina

Lattice-based sum provides a procedure to obtain posets and lattices from families of posets and lattices, respectively. Establishing sufficient conditions to ensure the lattice structure was the most significant challenge achieved in previous works. Next steps are to consider structures with general operators defined on the lattices of the family, introduce a sum of these operators on the obtained lattice-based sum and study the properties preserved by this new definition. We will prove that the natural definition preserve, in general, the monotonicity, associativity, commutativity, etc. This paper also introduces a new mechanism focused on preserving the left-continuity property of the operators defined on the lattices. This new approach also preserves the associativity and the infimum of non-empty subsets, and takes into account (infinite) complete lattices, unlike the previous works.

基于格的和提供了一种分别从序集族和格族中获得序集和格的方法。在之前的工作中，建立足够的条件来确保晶格结构是最重要的挑战。下一步是考虑在族的格上定义了一般算子的结构，在得到的基于格的和上引入这些算子的和，并研究这个新定义所保留的性质。我们将证明自然定义一般地保持单调性、结合性、交换性等。本文还介绍了一种新的机制，其重点是保持在格上定义的算子的左连续性。这种新方法还保留了非空子集的结合性和最小值，并考虑了（无限）完全格，这与以前的工作不同。

引用次数: 0

Interactive calculus: Theory and applications of A-linearly correlated bivariate fuzzy processes 交互演算：a -线性相关二元模糊过程的理论与应用

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

Fuzzy Sets and Systems

Pub Date : 2025-11-29 DOI: 10.1016/j.fss.2025.109699

L.C. Barros , M. Shahidi , E. Esmi , T. Allahviranloo

In this paper, we extend the concepts of differentiability and integrability to some classes of multivariable fuzzy functions, called A-linearly correlated bivariate fuzzy processes. We introduce key concepts such as the A-total and A-directional derivatives for A-linearly correlated bivariate fuzzy processes, along with a tangent plane interpretation and the A-Jacobian matrix. Their properties and relationships are also examined. Moreover, we present the second order Fréchet differentiability for A-linearly correlated bivariate fuzzy processes and define the A-Hessian matrix. Furthermore, we introduce the concept of the A-double integral and apply Fubini’s Theorem to A-linearly correlated bivariate fuzzy processes. We provide several examples demonstrating its practical applications.

本文将可微性和可积性的概念推广到一类多变量模糊函数，称为a -线性相关二元模糊过程。我们介绍了关键概念，如a -线性相关二元模糊过程的a -全导数和a -方向导数，以及切平面解释和a -雅可比矩阵。它们的性质和关系也被检查。此外，我们给出了a -线性相关二元模糊过程的二阶frachimet可微性，并定义了A-Hessian矩阵。进一步，我们引入了a -二重积分的概念，并将傅比尼定理应用于a -线性相关二元模糊过程。我们提供了几个例子来演示它的实际应用。

引用次数: 0

Fuzzy fractional delay integro-differential equation with the generalized Hukuhara ψ-Caputo fractional derivative 广义Hukuhara - caputo分数阶导数的模糊分数阶时滞积分微分方程

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

Fuzzy Sets and Systems

Pub Date : 2025-11-27 DOI: 10.1016/j.fss.2025.109701

Aziz El Ghazouani, M’hamed Elomari , Said Melliani

This paper establishes rigorous mathematical foundations for fuzzy fractional delay integro-differential equations (FFDIDEs) involving the generalized Hukuhara ψ-Caputo fractional derivative – a previously unexplored combination in the literature. We address the critical theoretical gap in analyzing systems that simultaneously incorporate fuzzy uncertainty, memory effects (time delays), and non-local dynamics (integral terms). Through an innovative synthesis of Banach’s fixed point theorem and a novel monotone iterative technique, we prove: (1) existence and uniqueness of solutions under Lipschitz conditions (Theorems 2 and 3), (2) constructive approximation via monotone sequences converging uniformly to the solution (Lemma 2), and (3) continuous dependence on initial conditions with explicit stability bounds (Theorem 4).

Our framework systematically handles both d-increasing and d-decreasing solution cases through a unified ψ-Caputo operational calculus. The theoretical advances are validated through computational experiments demonstrating

O (h^{1 + α})

convergence rates for α ∈ (0, 1), with MATLAB simulations providing quantitative analysis of triangular fuzzy solutions (Example 1, Figures 1– 6). Beyond its theoretical contributions, this work enables new applications in fuzzy control systems with delays, fractional-order neural networks with uncertainty, and other complex systems requiring simultaneous treatment of non-locality and vagueness. The results fundamentally extend the existing fuzzy fractional calculus literature by establishing the first comprehensive solution theory for this important class of equations.

本文建立了包含广义Hukuhara - caputo分数阶导数的模糊分数阶时滞积分微分方程（FFDIDEs）的严格数学基础。我们在分析同时包含模糊不确定性、记忆效应（时间延迟）和非局部动力学（积分项）的系统时解决了关键的理论差距。通过Banach不动点定理的创新合成和一种新的单调迭代技术，我们证明了：(1)Lipschitz条件下解的存在唯一性（定理2和3），(2)单调序列一致收敛于解的构造逼近（引理2），(3)具有显式稳定性界的连续依赖于初始条件（定理4）。我们的框架通过统一的ψ-Caputo运算，系统地处理了d增加解和d减少解的情况。通过计算实验验证了理论进展，证明了α ∈ （0,1）的O（h1+α）收敛率，MATLAB仿真提供了三角模糊解的定量分析（例1，图1 - 6）。除了其理论贡献之外，这项工作还可以在具有延迟的模糊控制系统，具有不确定性的分数阶神经网络以及其他需要同时处理非局域性和模糊性的复杂系统中实现新的应用。结果从根本上扩展了现有的模糊分数微积分文献，建立了这类重要方程的第一个综合解理论。

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引用次数: 0

Type-1 fuzzy functions for forecasting: A literature review and bibliometric analysis 一类模糊函数预测：文献回顾与计量分析

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

Fuzzy Sets and Systems

Pub Date : 2025-11-27 DOI: 10.1016/j.fss.2025.109697

Aysegul Yabaci Tak , Nihat Tak

Type-1 Fuzzy Functions (T1FFs) have emerged as a rule-free alternative to classical fuzzy inference systems for tackling forecasting problems, especially in the presence of uncertainty and nonlinearity. This study provides a comprehensive literature review and a bibliometric analysis of T1FFs in the context of forecasting. A dataset of 25 articles indexed in the Web of Science Core Collection was examined to assess research trends, author collaboration networks, influential publications, source journals, and key thematic areas. Our review identifies four main components in the design of T1FF-based models: input structure, clustering methods, forecasting models, and objective function optimization. Through citation and co-authorship network analysis, we highlight prominent researchers and collaborations within the field. Source journal analysis reveals publication hotspots, while co-word analysis identifies dominant themes such as “forecasting,” “robust regression,” and “metaheuristic optimization.” The results suggest growing academic interest and methodological diversification in the use of T1FFs, with Turkey leading international contributions. This study serves as a roadmap for researchers aiming to build or extend T1FF-based forecasting systems.

1型模糊函数（t1ff）已成为经典模糊推理系统的无规则替代方案，用于解决预测问题，特别是在存在不确定性和非线性的情况下。本研究提供了全面的文献综述和文献计量学分析在预测背景下的T1FFs。研究人员研究了Web of Science核心合集收录的25篇文章的数据集，以评估研究趋势、作者合作网络、有影响力的出版物、来源期刊和关键主题领域。我们的综述确定了基于t1ff模型设计的四个主要组成部分：输入结构、聚类方法、预测模型和目标函数优化。通过引文和合著者网络分析，我们突出了该领域的杰出研究人员和合作。源期刊分析揭示了出版热点，而共词分析确定了主导主题，如“预测”、“稳健回归”和“元启发式优化”。研究结果表明，在T1FFs的使用方面，学术兴趣和方法多样化日益增加，土耳其在国际上的贡献领先。这项研究为旨在建立或扩展基于t1ff的预测系统的研究人员提供了路线图。

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引用次数: 0

A note on Chebyshev approximation to an inconsistent system of max-min equations 不一致极大极小方程组的切比雪夫近似

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

Fuzzy Sets and Systems

Pub Date : 2025-11-26 DOI: 10.1016/j.fss.2025.109702

Pingke Li

The consistency of max-min equations is a crucial issue to be concerned when modelling with fuzzy relations in approximate reasoning. An inconsistent system of max-min equations may be perturbed slightly to restore the consistency. This paper tackles the inconsistency resolving problem by means of Chebyshev approximation, i.e., minimizing the maximum absolute deviation in both the coefficient matrix and right-hand side vector. It demonstrates that the minimum deviation level for consistency may be obtained by a polynomial-time direct search method. A Chebyshev approximation is constructed accordingly with the number of modified elements in the coefficient matrix as few as possible.

在近似推理中用模糊关系建模时，极大极小方程的一致性是一个非常重要的问题。一个不一致的极大极小方程系统可以稍加扰动以恢复其一致性。本文用切比雪夫近似解决了不一致问题，即系数矩阵和右侧向量的最大绝对偏差都最小化。结果表明，用多项式时间直接搜索法可以求出一致性的最小偏差水平。在系数矩阵中修改元素的数目尽可能少的情况下，构造了切比雪夫近似。

引用次数: 0

Incremental perspective for Bi-selection of instances and features by employing fuzzy rough set technique 采用模糊粗糙集技术进行实例和特征双选择的增量视角

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

Fuzzy Sets and Systems

Pub Date : 2025-11-25 DOI: 10.1016/j.fss.2025.109705

Jiahao Li , Yanhong She , Xiaoli He , Ting Qian , Wenli Zheng

Fuzzy rough set-based bi-selection, which performs instance and feature selection simultaneously, has become an important technique for data reduction. This paper proposes a novel bi-selection approach from an incremental learning perspective for the dynamic selection of instances and features upon the arrival of new data. To enhance the robustness of the proposed algorithm (called IBSFRS) across datasets of varying sizes, an elite instance strategy is incorporated into the incremental instance selection process. The numerical experiments are conducted on 14 commonly used datasets by simulating an incremental learning scenario where new instances arrive in batches. The results demonstrate that the IBSFRS algorithm exhibits significant advantages in classification accuracy while maintaining a high reduction rate. Furthermore, it exhibits superior performance in the effectiveness metric, successfully balancing the reduction rate with classification accuracy in incremental environment.

同时进行实例和特征选择的模糊粗糙集双选择已成为数据约简的重要技术。本文从增量学习的角度提出了一种新的双选择方法，用于在新数据到达时动态选择实例和特征。为了增强所提出算法（称为IBSFRS）在不同大小数据集上的鲁棒性，在增量实例选择过程中引入了精英实例策略。在14个常用的数据集上进行了数值实验，模拟了新实例分批到达的增量学习场景。结果表明，IBSFRS算法在保持高约简率的同时，在分类精度上具有显著优势。此外，该方法在有效性指标上表现出优异的性能，成功地平衡了增量环境下的分类正确率和减少率。

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Dually feature-weighted fuzzy SVM based on HSIC LASSO 基于HSIC LASSO的双特征加权模糊支持向量机

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

Fuzzy Sets and Systems

Pub Date : 2025-11-24 DOI: 10.1016/j.fss.2025.109703

Tinghua Wang, Zhiyong Lai, Xin Zhang

Support vector machine (SVM) is an algorithm developed based on statistical learning theory and has exhibited superior performance in many fields. Despite its success, SVM assumes that all training samples are equally important during training, making it sensitive to noise or outliers. To mitigate this problem, SVM was extended to fuzzy SVM (FSVM), which assigns a fuzzy membership to each training point, thereby allowing different training points contribute differently to the learning of the decision boundary. Although FSVM improves the classification performance to some degree, it still operates under the assumption that all features contribute equally. This overlooks the different importance of different features in the classification process, potentially leading to undesirable classification results. At present, most feature weighting methods rely on heuristic search strategies, which often yield locally optimal solutions and predominantly focus on the correlation between features and labels while neglecting the redundancy between features. To address these limitations, we propose a novel approach termed dually feature-weighted FSVM based on Hilbert-Schmidt independence criterion (HSIC) least absolute shrinkage and selection operator (LASSO) (DFWFSVM-HL for short). Specifically, the HSIC is firstly used to calculate the minimum redundancy maximum relevance (mRMR) feature weights, and the global optimal solution is efficiently obtained by solving a LASSO optimization problem. Subsequently, the fuzzy membership function is refined by incorporating these feature weights, modulating the contribution of different features to the fuzzy membership function by a feature-weighted Euclidean distance between the sample and its corresponding class center. This effectively reduces the impact of noise or outliers on classification. Additionally, a feature-weighted kernel function is constructed using the feature weights, reducing the influence of weak or irrelevant features on classification. Comprehensive experiments on benchmark datasets validate the effectiveness of the proposed DFWFSVM-HL model, demonstrating its superiority in terms of several classification performance metrics.

支持向量机（SVM）是一种基于统计学习理论发展起来的算法，在许多领域都表现出优异的性能。尽管它取得了成功，但SVM假设在训练过程中所有的训练样本都是同等重要的，这使得它对噪声或异常值很敏感。为了解决这一问题，将支持向量机扩展为模糊支持向量机（FSVM），为每个训练点分配模糊隶属度，从而允许不同的训练点对决策边界的学习做出不同的贡献。虽然FSVM在一定程度上提高了分类性能，但它仍然是在所有特征贡献相同的假设下运行的。这忽略了分类过程中不同特征的不同重要性，可能导致不理想的分类结果。目前，大多数特征加权方法依赖于启发式搜索策略，往往产生局部最优解，并且主要关注特征与标签之间的相关性，而忽略了特征之间的冗余性。为了解决这些限制，我们提出了一种新的方法，称为基于Hilbert-Schmidt独立准则（HSIC）最小绝对收缩和选择算子（LASSO）的双特征加权FSVM （DFWFSVM-HL）。具体而言，首先将HSIC用于计算最小冗余最大相关（mRMR）特征权重，并通过求解LASSO优化问题高效地获得全局最优解。随后，通过合并这些特征权重来改进模糊隶属函数，通过样本与其相应类中心之间的特征加权欧氏距离来调节不同特征对模糊隶属函数的贡献。这有效地减少了噪声或异常值对分类的影响。此外，利用特征权重构造特征加权核函数，减少弱特征或不相关特征对分类的影响。在基准数据集上的综合实验验证了所提出的DFWFSVM-HL模型的有效性，证明了其在多个分类性能指标上的优越性。

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