Fuzzy Sets and Systems最新文献

英文中文

Adaptive neural security control of fuzzy systems with sojourn-probability-Based multi-mode attacks 基于逗留概率的多模式攻击模糊系统的自适应神经安全控制

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

Fuzzy Sets and Systems

Pub Date : 2025-11-04 DOI: 10.1016/j.fss.2025.109653

Weiling Bao , Shoucheng Yuan , Dian Zhang , Jun Cheng , Dan Zhang , Yu Fu

This paper addresses the challenges of hybrid cyberattacks on fuzzy systems, focusing on observer-based security control strategies enhanced by adaptive neural networks. A generalized multi-mode denial-of-service (DoS) attack model is developed, utilizing a variable matrix to represent diverse attack ranges across multiple communication channels, with sojourn probabilities employed to describe attack stochasticity, thus offering an alternative to traditional Markov models. The study also investigates unknown deception attacks, incorporating an online weight-adjusting neural network to estimate and counteract the adverse effects of these malicious inputs. Furthermore, a dynamic mismatch model framework is introduced to accurately characterize the evolving discrepancies between actual and estimated DoS attack modes, addressing the limitations of prior fixed mismatch assumptions. The findings present a robust foundation for enhancing the resilience of fuzzy systems against hybrid cyberattacks, providing significant implications for future research in network security. On this basis, by using Lyapunov theory, sufficient criteria that guarantee the boundedness of the closed-loop fuzzy system are established. Finally, the effectiveness and the superiority of the designed control strategy are verified by the tunnel diode circuit model.

本文解决了模糊系统混合网络攻击的挑战，重点研究了自适应神经网络增强的基于观测器的安全控制策略。提出了一种广义的多模式拒绝服务（DoS）攻击模型，利用可变矩阵表示跨多个通信通道的不同攻击范围，并利用逗留概率描述攻击的随机性，从而为传统的马尔可夫模型提供了一种替代方案。该研究还调查了未知的欺骗攻击，结合了一个在线权重调整神经网络来估计和抵消这些恶意输入的不利影响。此外，引入了一个动态错配模型框架，以准确表征实际和估计的DoS攻击模式之间不断变化的差异，解决了先前固定错配假设的局限性。研究结果为增强模糊系统抵御混合网络攻击的弹性提供了坚实的基础，为未来的网络安全研究提供了重要意义。在此基础上，利用李雅普诺夫理论，建立了保证闭环模糊系统有界性的充分判据。最后，通过隧道二极管电路模型验证了所设计控制策略的有效性和优越性。

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引用次数: 0

Hierarchical stability and stabilization criteria for delayed T-S fuzzy systems via preassigned-delay-subinterval-based Lyapunov functional 基于预分配时滞子区间的Lyapunov泛函的时滞T-S模糊系统的层次稳定性和镇定准则

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

Fuzzy Sets and Systems

Pub Date : 2025-11-04 DOI: 10.1016/j.fss.2025.109661

Huichao Lin , Jiuxiang Dong , Ju H. Park

This paper considers the stability and stabilization issues of T-S fuzzy systems with time-varying delays. A preassigned-delay-subinterval-based Lyapunov functional is constructed to capture more effective delay information. This Lyapunov functional uses different matrix pairs in different time-varying delay subintervals, so that each delay subinterval has its own Lyapunov functional, which relaxes the constraint of traditional Lyapunov functional using the same matrix pair in each delay subinterval. By employing this approach, the functional not only provides a concise hierarchical form but also eliminates the need to manually design different Lyapunov functionals for various N. Additionally, by utilizing the characteristics of the preassigned delay subintervals, a delay-product-type matrix is introduced into the Lyapunov functional. This technique relaxes the positive definiteness constraint of the Lyapunov matrix. Based on this, a hierarchical stability and stabilization criterion is derived for the T-S fuzzy system with N preassigned delay subintervals. Finally, three examples are used to test the superiority of the obtained stability and stabilization criteria.

研究具有时变时滞的T-S模糊系统的稳定性和镇定问题。为了捕获更有效的延迟信息，构造了一个基于预分配延迟子区间的Lyapunov泛函。该Lyapunov泛函在不同的时变时滞子区间中使用不同的矩阵对，使得每个时滞子区间都有自己的Lyapunov泛函，从而放松了传统Lyapunov泛函在每个时滞子区间中使用相同矩阵对的约束。通过采用这种方法，该泛函不仅提供了简洁的层次形式，而且消除了为不同n手动设计不同Lyapunov泛函的需要。此外，通过利用预先分配的延迟子区间的特征，将延迟积型矩阵引入Lyapunov泛函。这种方法放宽了李雅普诺夫矩阵的正定性约束。在此基础上，导出了具有N个预分配时滞子区间的T-S模糊系统的层次稳定性和镇定判据。最后，用三个算例验证了所得到的稳定性和稳定化准则的优越性。

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引用次数: 0

Uncertainty modelling of the nonlinear Black-Scholes equation and decision-making using fuzzy logic 非线性Black-Scholes方程的不确定性建模与模糊决策

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

Fuzzy Sets and Systems

Pub Date : 2025-10-30 DOI: 10.1016/j.fss.2025.109663

Amal Aarab , Aicha Driouch

In the financial world, particularly in option pricing, the price of underlying assets is often difficult to predict due to interest rate and volatility variations. In order to provide more accurate predictions, the fuzzy approach proves to be an effective tool for modelling the uncertainty inherent in financial markets. In this work, we propose a numerical approach for pricing European options using fuzzy-parameter partial differential equation. We analyse the extended nonlinear Black-Scholes problem of Barles-Soner’s model, leading to the computation of a range of European option prices. We determine the value for the fair price using the center of gravity method, along with its corresponding

α -

level derived from an optimization problem to assess its plausibility. In addition, we quantify the vagueness of the fuzzy output by the 15–85 mid-percentile range, which provides a description of the spread around the defuzzified value. These results support prediction and decision-making purposes.

在金融领域，特别是在期权定价中，由于利率和波动率的变化，标的资产的价格往往难以预测。为了提供更准确的预测，模糊方法被证明是对金融市场固有不确定性建模的有效工具。本文提出了一种利用模糊参数偏微分方程求解欧式期权定价的数值方法。本文分析了Barles-Soner模型的扩展非线性Black-Scholes问题，该问题导致了欧式期权价格区间的计算。我们使用重心法确定公平价格的价值，以及从优化问题中得出的相应α -水平，以评估其合理性。此外，我们通过15-85个中间百分位数范围量化模糊输出的模糊性，该范围提供了对去模糊化值周围传播的描述。这些结果支持预测和决策目的。

引用次数: 0

On the equivalence classes induced by L-fuzzy rough approximation operators 关于L-fuzzy粗糙逼近算子诱导的等价类

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

Fuzzy Sets and Systems

Pub Date : 2025-10-30 DOI: 10.1016/j.fss.2025.109662

Chun Yong Wang , Lijuan Wan , Bo Zhang

This paper studies the equivalence classes induced by

L

-fuzzy rough approximation operators from the theoretical point of view, where

L

is a doubly residuated lattice with an involutive negation. We examine the relationship between

L

-fuzzy rough approximation operators and the equivalence classes they induce. We point out the conditions, where a pair of

L

-fuzzy sets forms an

L

-fuzzy rough set and the family of all

L

-fuzzy rough sets induces a complete lattice, respectively. In particular, some results in this paper can be generalized into the equivalence classes induced by

L

-fuzzy rough approximation operators, where

L

is a residuated lattice.

本文从理论的角度研究了L-模糊粗糙逼近算子诱导的等价类，其中L是一个对合否定的双残格。我们研究了l -模糊粗糙逼近算子和它们所引出的等价类之间的关系。我们分别指出了一对l -模糊集形成l -模糊粗糙集和所有l -模糊粗糙集族形成完全格的条件。特别地，本文的一些结果可以推广到由L-fuzzy粗糙逼近算子诱导的等价类，其中L是一个残格。

引用次数: 0

Symmetric fuzzy stochastic Volterra integral equations with retardation and their application to modeling the spread of infectious diseases 具有时滞的对称模糊随机Volterra积分方程及其在传染病传播建模中的应用

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

Fuzzy Sets and Systems

Pub Date : 2025-10-28 DOI: 10.1016/j.fss.2025.109660

Marek T. Malinowski

This paper contains a study on stochastic Volterra integral equations with fuzzy sets values and involved in constant retardation. Moreover, the form of the equation is symmetric in the sense that fuzzy stochastic integrals are placed on both sides of the equation. This causes the novelty of non-monotonicity of diameters of

α

-cuts of solution values. We show that the considered initial value problem formulated in terms of the symmetric fuzzy stochastic Volterra integral equation is well posed. In particular, we show that there exists a unique solution and that this solution depends continuously on the parameters of the equation. The results are achieved under the conditions of Lipschitz continuity of drift and diffusion coefficients and continuity of kernels. Moreover, four different fuzzy stochastic Volterra integral equations have been offered to model the spread of an infectious disease. This is an innovative value in the modeling of infectious diseases. The solutions of these equations have been approximated using the Euler–Maruyama method.

本文研究了具有模糊集值的常滞后随机Volterra积分方程。此外，方程的形式是对称的，因为在方程的两侧放置了模糊随机积分。这导致了解值α-切径的非单调性的新颖性。我们证明了用对称模糊随机Volterra积分方程表述的所考虑的初值问题是适定的。特别地，我们证明了存在一个唯一解，并且这个解连续地依赖于方程的参数。结果是在漂移系数和扩散系数的Lipschitz连续性和核的连续性条件下得到的。此外，还提出了四种不同的模糊随机Volterra积分方程来模拟传染病的传播。这是传染病建模的创新价值。用欧拉-丸山法对这些方程的解进行了近似。

引用次数: 0

A generalization of Stone duality of archimedean lattice effect algebras 阿基米德格效应代数的Stone对偶性的推广

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

Fuzzy Sets and Systems

Pub Date : 2025-10-27 DOI: 10.1016/j.fss.2025.109644

Xin Liu, Yongjian Xie, Mengyuan Zhang

Based on the sheaf representations of hyperarchimedean MV-algebras, we suggested the definition of a spectral presheaf on the context category of an Archimedean lattice effect algebra and proved that two Archimedean lattice effect algebras are isomorphic if and only if their spectral presheaves are isomorphic. The spectral presheaf representation of an Archimedean lattice effect algebra can be considered as a generalized Stone duality of the lattice effect algebra.

基于超阿基米德v -代数的束表示，在阿基米德格效应代数的上下范畴上给出了谱束的定义，并证明了两个阿基米德格效应代数当且仅当它们的谱束同构时是同构的。阿基米德晶格效应代数的谱预层表示可以看作是晶格效应代数的广义Stone对偶。

引用次数: 0

New types of ordinal sums of fuzzy Sheffer strokes and the induced pseudo (quasi)-overlap and grouping functions 模糊Sheffer笔划的新型有序和及其诱导的伪（拟）重叠和分组函数

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

Fuzzy Sets and Systems

Pub Date : 2025-10-27 DOI: 10.1016/j.fss.2025.109657

Ting-hai Zhang , Feng Qin , Wenhuang Li , Zhihong Yi

It is well-established that the Sheffer stroke can independently form a complete logical system, holding unique theoretical significance within classical logic. Recently, scholars have explored the structures and properties of the corresponding fuzzy Sheffer stroke (hereafter referred to as

FSS

) within the fuzzy logic framework. This paper introduces two novel types of ordinal sums of

FSS

s, which are defined based on whether the

x

-coordinate or

y

-coordinate of the function lies within the subintervals of the summands. We investigate several important properties of these sums and establish their equivalent characterizations. Furthermore, building upon these two classes of ordinal sum structures, we construct pseudo (quasi)-overlap and grouping functions (abbreviated as

P Q O F

and

P Q G F

), and present their associated properties. These constructions provide two effective methods for developing

P Q O F

and

P Q G F

, which have broad applications in fuzzy inference and multi-attribute decision-making.

谢弗冲程可以独立形成一个完整的逻辑体系，在经典逻辑中具有独特的理论意义。近年来，学者们在模糊逻辑框架下探索了相应的模糊Sheffer冲程（以下简称FSS）的结构和性质。本文介绍了两种新的fss有序和，它们是根据函数的x坐标或y坐标是否在求和的子区间内来定义的。我们研究了这些和的几个重要性质，并建立了它们的等价刻画。此外，在这两类有序和结构的基础上，我们构造了伪（拟）重叠和分组函数（简称PQOF和PQGF），并给出了它们的相关性质。这些结构为PQOF和PQGF的开发提供了两种有效的方法，在模糊推理和多属性决策中有着广泛的应用。

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引用次数: 0

Vector induced OWA operators 矢量诱导OWA算子

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

Fuzzy Sets and Systems

Pub Date : 2025-10-25 DOI: 10.1016/j.fss.2025.109656

M. Ferrero-Jaurrieta , Z. Takáč , A. Kamp , Ľ Horanská , H. Bustince

Information aggregation often requires ordering of data based on different criteria, leading to the introduction of functions like Ordered Weighted Averaging (OWA) and Induced Ordered Weighted Averaging (IOWA) operators. The sorting of vector information is not trivial, and so far no induced aggregation operators have been studied in the multivalued context. We introduce the Vector Induced Ordered Weighted Averaging (VIOWA) operators, a vector extension of IOWA designed for aggregating multivalued data. We define VIOWA operators based on admissible orders, using all admissible permutations, and we explore its formulation using the best admissible permutations based on the degree of totalness. Additionally, we analyze the basic properties of these methods and their interrelations. To demonstrate the effectiveness of VIOWA operators, we apply them to multivalued time series prediction, in order to aggregate several vector-valued model predictions. Experiments on five datasets show the usefulness of VIOWA operator-based aggregation, outperforming individual models and other classical aggregation methods, highlighting its potential in multivariate settings.

信息聚合通常需要根据不同的标准对数据进行排序，从而引入了有序加权平均（OWA）和诱导有序加权平均（IOWA）操作符等函数。向量信息的排序是一个非常重要的问题，目前还没有研究多值环境下的诱导聚合算子。我们引入了矢量诱导有序加权平均算子（VIOWA），这是IOWA的矢量扩展，用于聚合多值数据。我们使用所有可允许的排列来定义基于可允许阶的VIOWA算子，并使用基于整体度的最佳可允许排列来探索其表述。此外，我们还分析了这些方法的基本性质及其相互关系。为了证明VIOWA算子的有效性，我们将其应用于多值时间序列预测，以聚合多个向量值模型预测。在五个数据集上的实验表明，基于VIOWA算子的聚合方法的有效性优于单个模型和其他经典聚合方法，突出了其在多变量环境中的潜力。

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引用次数: 0

Extended dissimilarities and d-Choquet integral for fuzzy numbers 模糊数的扩展异度与d-Choquet积分

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

Fuzzy Sets and Systems

Pub Date : 2025-10-25 DOI: 10.1016/j.fss.2025.109652

Diego García-Zamora , Antonio Fco Roldán López De Hierro , Humberto Bustince

d

-Choquet integrals were introduced as a class of functions that generalize the classical Choquet integral by replacing the difference with a dissimilarity. This paper faces the problem of computing d-Choquet integrals when the information is imprecise/vague and, more specifically, when it is modeled as fuzzy numbers. We also study the main properties of such an extension and analyze how the features of the considered dissimilarity and fuzzy measure impact the extended

d

-Choquet integral.

d-Choquet积分是将经典的Choquet积分推广为用不相似度代替差值的一类函数。本文面临的问题是计算d-Choquet积分当信息是不精确的/模糊的，更具体地说，当它被建模为模糊数。我们还研究了这种扩展的主要性质，并分析了所考虑的不相似度和模糊测度的特征如何影响扩展的d-Choquet积分。

引用次数: 0

Distributed fuzzy adaptive optimal consensus framework for multiagent with imprecise topology via reinforcement learning in graph games 基于图博弈强化学习的不精确拓扑多智能体分布式模糊自适应最优共识框架

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

Fuzzy Sets and Systems

Pub Date : 2025-10-24 DOI: 10.1016/j.fss.2025.109659

Hai Wang , Junmin Li , Jianmin Jiao , Jiaxi Chen , Chao He

This paper proposes a novel distributed optimal consensus framework for unknown multi-agent systems under Takagi-Sugeno (T-S) fuzzy graphs, substantially relaxing connectivity requirements. Unlike existing methods needing connected subgraphs per fuzzy rule, our approach handles disconnected cases including isolated followers (linear quadratic control) and single-neighbor scenarios (zero-sum games), with consensus rigorously proved under fuzzy union connectivity. Subsequently, a novel two-stage online distributed optimal policy iteration (PI) algorithm is developed based on the graph game perspective under T-S fuzzy graphs without relying on system dynamics information. The first stage obtains stabilizing gains from arbitrary initial gains conditions, while the second stage employs classical PI to seamlessly derive the distributed optimal policies. Moreover, the framework is extended to design a two-stage online distributed optimal integral Q-learning method, overcoming its initialization stabilizing challenges in Q-learning-based distributed control. Finally, the superiority and effectiveness of the proposed algorithms are verified through a robot MASs simulation.

本文提出了一种基于T-S模糊图的未知多智能体系统分布式最优共识框架，大大放宽了连通性要求。不同于现有的方法需要每个模糊规则连接子图，我们的方法处理不连接的情况，包括孤立的追随者（线性二次控制）和单邻居场景（零和博弈），并在模糊联合连通性下严格证明了一致性。随后，基于T-S模糊图下的图博弈视角，提出了一种不依赖系统动力学信息的两阶段在线分布式最优策略迭代（PI）算法。第一阶段从任意初始增益条件中获得稳定增益，第二阶段采用经典PI无缝导出分布式最优策略。在此基础上，扩展了该框架，设计了一种两阶段在线分布式最优积分q -学习方法，克服了基于q -学习的分布式控制中的初始化稳定问题。最后，通过机器人质量仿真验证了所提算法的优越性和有效性。

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