Fuzzy Sets and Systems最新文献

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FNCEOD: Fuzzy neighborhood combination entropy-based outlier detection 基于模糊邻域组合熵的离群点检测

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

Fuzzy Sets and Systems

Pub Date : 2026-03-01 Epub Date: 2025-11-17 DOI: 10.1016/j.fss.2025.109683

Qian Hu , Jiapeng Bai , Jun Zhang , Yafei Song , Jusheng Mi

Outlier detection, as an important direction of data mining, aims to identify data objects that deviate from normal patterns and is widely used in fields such as financial fraud, network security, and medical diagnosis. Functioning as an essential tool in knowledge acquisition and data mining, granular computing provides a novel framework that emulates human cognitive patterns for resolving large-scale complex problems. However, traditional outlier detection methods based on granular computing are difficult to balance data diversity and fuzziness. Therefore, this article constructs an outlier detection model based on fuzzy neighborhood combination entropy using neighborhood fuzzy granules and combination entropy. Firstly, the fuzzy neighborhood combination entropy of the information system is defined, and the relative fuzzy neighborhood combination entropy of the object is defined by the change in neighborhood fuzzy entropy caused by the object. Secondly, the relative fuzzy cardinality of the object is defined by the difference degree between its fuzzy neighborhoods, and the anomaly factor of the object is measured by its relative fuzzy neighborhoods combination entropy and relative fuzzy cardinality. Then, an outlier detection model based on the combination entropy of fuzzy neighborhoods is constructed and the relevant algorithm is designed. Finally, the effectiveness and efficiency of the proposed method were verified through publicly available datasets.

异常值检测是数据挖掘的一个重要方向，旨在识别偏离正常模式的数据对象，广泛应用于金融欺诈、网络安全、医疗诊断等领域。作为知识获取和数据挖掘的重要工具，颗粒计算为解决大规模复杂问题提供了一种模拟人类认知模式的新框架。然而，传统的基于粒度计算的离群点检测方法难以平衡数据的多样性和模糊性。因此，本文利用邻域模糊颗粒和组合熵构建了基于模糊邻域组合熵的离群点检测模型。首先定义了信息系统的模糊邻域组合熵，通过对象引起的邻域模糊熵的变化来定义对象的相对模糊邻域组合熵。其次，通过模糊邻域之间的差异程度来定义目标的相对模糊基数，通过相对模糊邻域的组合熵和相对模糊基数来度量目标的异常因子；然后，构建了基于模糊邻域组合熵的离群点检测模型，并设计了相关算法。最后，通过公开的数据集验证了该方法的有效性和效率。

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引用次数: 0

Reinforcement learning-based stochastic structurally-sparse sliding mode control for IT-2 T-S fuzzy interconnected multi-area power system 基于强化学习的it - 2t -s模糊互联多区域电力系统随机结构稀疏滑模控制

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

Fuzzy Sets and Systems

Pub Date : 2026-03-01 Epub Date: 2025-11-11 DOI: 10.1016/j.fss.2025.109675

Shengda Tang , Zihan Chen , Hai Wang , Jun Cheng

This article develops a novel fuzzy stochastic structurally-sparse sliding mode control (FS⁴MC) scheme for the malicious attacks-injected interconnected multi-area power systems (IMAPSs). In response to the nonlinear characteristics of valve position deviation and the uncertain switching feature of the inter-area feedback communication network (FCN), an interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy IMAPS model with the Markov jump structurally-sparse FCN topology is established. Subsequently, FS⁴MC compensation strategy is developed for this model to counteract the impact of attack signals, ensuring the finite-time reachability of the ideal sliding surface and the stochastic stability of the IT-2 T-S fuzzy IMAPS with switching FCN topology. On the other hand, since the FS⁴MC scheme design relies on IMAPS dynamics, which is frequently unavailable, a data-centric algorithm is developed to compute this scheme without requiring either model information or an initially stabilizing policy pair. Finally, the case study on a three-area IMAPS demonstrates the effectiveness of the proposed method.

针对恶意攻击注入的互联多区域电力系统，提出了一种新的模糊随机结构稀疏滑模控制（FS4MC）方案。针对阀位偏差的非线性特性和区域间反馈通信网络（FCN）切换特性的不确定性，建立了具有马尔可夫跳变结构稀疏FCN拓扑结构的区间type-2 (IT-2) Takagi-Sugeno （T-S）模糊IMAPS模型。随后，针对该模型开发了FS4MC补偿策略，以抵消攻击信号的影响，保证了理想滑动面有限时间可达性和具有交换FCN拓扑的IT-2 T-S模糊IMAPS的随机稳定性。另一方面，由于FS4MC方案设计依赖于IMAPS动态，而IMAPS动态经常不可用，因此开发了一种以数据为中心的算法来计算该方案，而不需要模型信息或初始稳定策略对。最后，以三区域IMAPS为例，验证了该方法的有效性。

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引用次数: 0

Fractional-order ultra-local model-based direct adaptive fuzzy sliding mode control for mechatronic systems with mismatched disturbances and input nonlinearities 含失匹配干扰和输入非线性的机电系统分数阶超局部模型直接自适应模糊滑模控制

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

Fuzzy Sets and Systems

Pub Date : 2026-03-01 Epub Date: 2025-11-08 DOI: 10.1016/j.fss.2025.109674

Dingxin He , Haoping Wang , Yang Tian , Minxuan Zha , Radu-Emil Precup

Aiming at the trajectory tracking problem of the mechatronic systems in the presence of uncertainties, matched and mismatched disturbances, and input nonlinearities, a fractional-order ultra-local model-based direct adaptive fuzzy controller (FO-DAFC) is proposed in this paper. To reduce the difficulty of controller design, the fractional-order ultra-local model is constructed to reformulate the complex mechatronic system. Then, a global sliding surface is proposed to eliminates the reaching phase and ensures the global robustness. Furthermore, an ideal global sliding mode controller is designed to converge the tracking error. However, the unknown and unmeasured parameters are existed in the ideal controller. The fuzzy logic system is thus established to approximate the ideal control law. And the fuzzy weight adaptive law is designed by using gradient descent method. Correspondingly, the direct adaptive fuzzy controller is proposed. After that, the stability of the closed-loop system with the proposed FO-DAFC is analyzed through using Lyapunov theorem. Ultimately, the numerical simulation of 2-DOF robotic manipulator with different input nonlinearities and co-simulation of 4-DOF robotic manipulator compared with other controllers are completed. The obtained results demonstrate the effectiveness and superiority of the proposed controller.

针对存在不确定性、匹配和不匹配干扰以及输入非线性的机电系统轨迹跟踪问题，提出了一种基于分数阶超局部模型的直接自适应模糊控制器（FO-DAFC）。为了降低控制器设计的难度，建立了分数阶超局部模型，对复杂的机电系统进行了重构。然后，提出一个全局滑动面来消除到达相位，保证全局鲁棒性。在此基础上，设计了一种理想的全局滑模控制器来收敛跟踪误差。然而，在理想的控制器中存在未知和不可测参数。从而建立模糊逻辑系统来逼近理想控制律。采用梯度下降法设计了模糊权值自适应律。相应地，提出了直接自适应模糊控制器。然后，利用李雅普诺夫定理分析了采用所提出的FO-DAFC的闭环系统的稳定性。最后，完成了不同输入非线性条件下的2自由度机械臂的数值仿真以及4自由度机械臂与其他控制器的联合仿真。仿真结果验证了所提控制器的有效性和优越性。

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引用次数: 0

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 : 2026-03-01 Epub 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

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 : 2026-02-15 Epub 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

Global and approximate optimization for constrained max-min systems 约束最大最小系统的全局近似优化

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

Fuzzy Sets and Systems

Pub Date : 2026-02-15 Epub Date: 2025-10-22 DOI: 10.1016/j.fss.2025.109654

Weili Yang , Weipeng Liu , Cailu Wang

This paper focuses on the global optimization problem in max-min systems subject to non-negative affine equality constraints. By constructing the greatest lower bound, we establish a solvability criterion for the global optimization problem and derive a uniqueness criterion for globally optimal solutions. We construct the feasible max-plus projection set to determine the set of all globally optimal solutions. An algorithm is developed to verify the solvability of the global optimization problem and to find all globally optimal solutions. Furthermore, when the global optimization problem is unsolvable, we introduce approximate optimization to obtain the optimal feasible value by using the max-plus vector norm, and provide the set of all approximate optimal solutions. The effectiveness of the proposed method is demonstrated through illustrative examples.

研究非负仿射等式约束下的最大-最小系统的全局优化问题。通过构造最大下界，建立了全局优化问题的可解性判据，导出了全局最优解的唯一性判据。构造可行的极大加投影集来确定全局最优解的集合。提出了一种验证全局优化问题可解性和求全局最优解的算法。进一步，在全局优化问题不可解时，引入近似优化，利用最大加向量范数获得最优可行值，并给出所有近似最优解的集合。通过算例验证了该方法的有效性。

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 : 2026-02-15 Epub 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

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 : 2026-02-15 Epub 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

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 : 2026-02-15 Epub 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

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 : 2026-02-15 Epub 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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