Fuzzy Sets and Systems最新文献

英文中文

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 : 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

Quasi-deterministic fuzzy automata: Isomorphisms and fuzzy deterministic automata minimization 准确定性模糊自动机：同构与模糊确定性自动机最小化

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

Fuzzy Sets and Systems

Pub Date : 2025-11-16 DOI: 10.1016/j.fss.2025.109677

José R. González de Mendívil , Zorana Jančić , Aitor González de Mendívil Grau , Ivana Micić , Stefan Stanimirović

Minimization of fuzzy deterministic finite automata (FDfAs) is a challenging problem due to two main reasons. First, the graded nature of transitions and state memberships makes traditional minimization techniques difficult to apply. Second, a minimal FDfA is not necessarily unique, as multiple equivalent FDfAs of the same size may exist. In this paper, we focus on finding a polynomial-time minimization method that constructs a minimal FDfA for a given FDfA. Our approach is based on establishing isomorphisms between well-known polynomial-time constructions, providing a mathematical foundation for the proposed method. Specifically, we introduce the notion of quasi-deterministic fuzzy finite automata (QDFfAs) and explore their isomorphism properties with the Myhill-Nerode automaton of a fuzzy language. We show that the determinization via factorization of a QDFfA preserves strong isomorphism with the generalized Myhill-Nerode automaton of the recognized fuzzy language. This insight enables the development of an efficient minimization method by leveraging the interpretable backward replica of an FDfA.

由于两个主要原因，模糊确定性有限自动机（fdfa）的最小化是一个具有挑战性的问题。首先，转换和状态成员的分级性质使得传统的最小化技术难以应用。其次，最小的对外直接投资并不一定是唯一的，因为可能存在多个相同规模的等效对外直接投资。在本文中，我们着重于寻找一种多项式时间最小化方法，该方法对给定的FDfA构造最小FDfA。我们的方法基于建立已知多项式时间结构之间的同构，为提出的方法提供了数学基础。具体来说，我们引入了准确定性模糊有限自动机（QDFfAs）的概念，并探讨了它们与模糊语言的Myhill-Nerode自动机的同构性质。我们证明了通过因子分解的QDFfA的确定与识别的模糊语言的广义Myhill-Nerode自动机保持强同构。通过利用FDfA的可解释向后副本，这种洞察力使开发有效的最小化方法成为可能。

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引用次数: 0

Adaptive fuzzy wavelet network control for nonlinear cooperative load transportation systems 非线性协同负荷系统的自适应模糊小波网络控制

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

Fuzzy Sets and Systems

Pub Date : 2025-11-16 DOI: 10.1016/j.fss.2025.109681

Matin Fadavi , Majdeddin Najafi , Farid Sheikholeslam

In this paper, the impact of nonlinear components is studied for cooperative load transportation systems with any number of quadrotors and a single slung load suspended by ropes. The main goal is to control and estimate constraints caused by the nonlinear term of the load transportation system. A novel distributed control strategy is proposed for cooperative systems based on adaptive fuzzy wavelet networks (AFWNs). Distributed AFWNs are employed to compensate for nonlinear effects. Another result is the expansion of the system’s attraction region for the initial state values. Also, by employing an integral term in the control law, the formation error of the agents converges to zero. These expansions allow the system to significantly improve its robustness to disturbances. The simulation results illustrate that the proposed method can keep the agents in desired formation and guide the load in right direction.

本文研究了具有任意数量的四旋翼飞行器和单个绳索悬吊载荷的协同载荷传输系统的非线性分量的影响。其主要目标是控制和估计由负荷输送系统的非线性项引起的约束。提出了一种基于自适应模糊小波网络的协作系统分布式控制策略。采用分布式AFWNs来补偿非线性效应。另一个结果是系统对初始状态值的吸引区域的扩展。同时，通过在控制律中引入积分项，使智能体的形成误差收敛于零。这些扩展允许系统显著提高其对干扰的鲁棒性。仿真结果表明，该方法能使智能体保持在理想的队形中，并能引导负载向正确的方向移动。

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 : 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

Modular indistinguishability: The aggregation problem 模不可区分性：聚合问题

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

Fuzzy Sets and Systems

Pub Date : 2025-11-14 DOI: 10.1016/j.fss.2025.109679

M.D.M. Bibiloni-Femenias , O. Valero

In the literature there are two different approaches that extend the classical crisp notion of equivalence relation to the fuzzy framework. On the one hand, one can find the notion of indistinguishability operator and a few of its generalizations. These can be understood as a kind of measurement of the degree of similarity or indistinguishability between objects. On the other hand, fuzzy (quasi-)metrics measure such a degree with respect to a parameter. The study of both types of the aforesaid notions has been carried out independently without any connection between them. As a consequence, the notion of modular indistinguishability operator has been introduced recently. Such a notion unifies under the same framework both aforesaid similarity concepts. In this paper, we explore the aggregation problem for modular indistinguishability operators and for several generalizations. Hence we introduce the notions of modular fuzzy pre-order, modular fuzzy partial order and modular equality and we characterize the functions that are able to fuse all these different types of modular similarities. The aforementioned characterizations are stated in terms of triangular triplets or related notions, monotony and dominance. In contrast to the non-modular case, the class of those functions that merge modular fuzzy pre-orders (modular fuzzy partial orders) is shown to match the class of modular indistinguishability operators (modular equalities). Furthermore, the relationships between the non-modular aggregation problem, the modular one and the fuzzy metric aggregation problem are explored and the differences between them are clarified by means of appropriate examples.

在文献中，有两种不同的方法将经典的清晰的等价关系概念扩展到模糊框架。一方面，我们可以找到不可分辨算子的概念和它的一些推广。这些可以被理解为一种测量物体之间的相似程度或不可区分程度。另一方面，模糊（准）度量度量相对于参数的这种程度。对上述两种概念的研究都是独立进行的，两者之间没有任何联系。因此，最近引入了模不可分辨算子的概念。这种概念将上述两个相似概念统一在同一框架下。本文研究了模不可分辨算子的聚集问题和若干推广问题。因此，我们引入了模模糊预阶、模模糊偏阶和模等式的概念，并刻画了能够融合所有这些不同类型的模相似的函数。上述特征是根据三角三联体或相关概念，单调和优势来陈述的。与非模情况相反，那些合并模模糊预阶的函数类（模模糊偏阶）被证明与模不可区分算子类（模等式）匹配。进一步探讨了非模聚集问题、模聚集问题和模糊度量聚集问题之间的关系，并通过适当的实例说明了它们之间的区别。

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引用次数: 0

The choquet–Stieltjes integral with dual set-Functions: a unified theory and applications 对偶集函数的choquet-Stieltjes积分：统一理论及应用

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

Fuzzy Sets and Systems

Pub Date : 2025-11-14 DOI: 10.1016/j.fss.2025.109678

Jih-Jeng Huang , Chin-Yi Chen

We introduce a unified framework extending the classical Choquet integral by incorporating Stieltjes-type accumulation functions and dual set-functions. This construction, termed the dual Choquet–Stieltjes (DCS) integral, broadens non-additive integral theory, allowing simultaneous treatment of threshold-dependent behaviors and asymmetric interactions. We prove fundamental properties including well-definedness, monotonicity, and comonotonic additivity under precisely specified conditions. We establish convergence theorems (monotone convergence, Fatou’s lemma, dominated convergence) with complete proofs, and demonstrate applications in decision-making. Our framework generalizes existing extensions under a single, coherent approach that maintains theoretical properties while enhancing modeling flexibility. Through parameter recovery studies, we demonstrate the theoretical soundness of our approach and identify scenarios where the full DCS framework is necessary to capture complex interdependencies and threshold effects.

通过引入stieltje型累积函数和对偶集函数，对经典Choquet积分进行了扩展，提出了一个统一的框架。这种结构被称为对偶Choquet-Stieltjes （DCS）积分，拓宽了非加性积分理论，允许同时处理阈值依赖行为和不对称相互作用。在精确规定的条件下，我们证明了一些基本性质，包括自定义性、单调性和共单调可加性。建立了收敛定理（单调收敛、法图引理、支配收敛）并给出了完整的证明，并证明了在决策中的应用。我们的框架在一个单一的、连贯的方法下概括了现有的扩展，在保持理论属性的同时增强了建模的灵活性。通过参数恢复研究，我们证明了我们的方法在理论上的合理性，并确定了完整的DCS框架对于捕获复杂的相互依赖性和阈值效应是必要的场景。

引用次数: 0

On the non-uniqueness of representation of (U, N)-implications 关于（U， N）表示的非唯一性——启示

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

Fuzzy Sets and Systems

Pub Date : 2025-11-13 DOI: 10.1016/j.fss.2025.109680

Raquel Fernandez-Peralta , Andrea Mesiarová-Zemánková

Fuzzy implication functions constitute fundamental operators in fuzzy logic systems, extending classical conditionals to manage uncertainty in logical inference. Among the extensive families of these operators, generalizations of the classical material implication have received considerable theoretical attention, particularly (S, N)-implications constructed from t-conorms and fuzzy negations, and their further generalizations to (U, N)-implications using disjunctive uninorms. Prior work has established characterization theorems for these families under the assumption that the fuzzy negation N is continuous, ensuring uniqueness of representation. In this paper, we disprove this last fact for (U, N)-implications and we show that they do not necessarily possess a unique representation, even if the fuzzy negation is continuous. Further, we provide a comprehensive study of uniqueness conditions for both uninorms with continuous and non-continuous underlying functions. Our results offer important theoretical insights into the structural properties of these operators.

模糊蕴涵函数是模糊逻辑系统中的基本运算符，是对经典条件的扩展，用于管理逻辑推理中的不确定性。在这些算子的广泛族中，经典物质蕴涵的推广已经得到了相当大的理论关注，特别是由t-适形和模糊否定构造的（S， N）蕴涵，以及它们使用析取一致子进一步推广到（U， N）蕴涵。先前的工作已经在模糊否定N连续的假设下建立了这些族的表征定理，保证了表示的唯一性。在本文中，我们对（U， N）-蕴涵证明了这最后一个事实，并表明它们不一定具有唯一表示，即使模糊否定是连续的。进一步，我们全面地研究了具有连续和非连续底层函数的一致子的唯一性条件。我们的结果为这些算子的结构特性提供了重要的理论见解。

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 : 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 : 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

Feature subset selection using fuzzy scale entropy-Based uncertainty measures for multi-scale fuzzy relation decision systems 基于模糊尺度熵不确定性测度的多尺度模糊关系决策系统特征子集选择

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.2025.109665

Jiaying Wang , Zhehuang Huang , Zhifeng Weng , Jinjin Li

As a typical multi-granularity data analysis model, multi-scale decision systems have received widespread attention from researchers in recent years. However, most multi-scale models struggle to handle continuous data and fail to accurately characterize the differences between samples in complex scenes. Moreover, there is a lack of investigation on fuzzy multi-scale uncertainty measures, as well as their application in dimension reduction. Motivated by these issues, we put forth a new multi-scale fuzzy relation decision system and investigate the uncertainty measures for fuzzy relation families at different scales. To this end, δ-fuzzy similarity relationship is presented to characterize the correlation of target objects. Fuzzy scale entropy is then proposed to reflect the distinguishing ability of fuzzy relation families with different scales. Some variants of the uncertainty measure, such as joint fuzzy scale entropy, conditional fuzzy scale entropy, and mutual fuzzy scale entropy, are then presented to reveal the relationship between the distinguishing ability of feature subsets. Finally, a knowledge reduction algorithm for multi-scale fuzzy relation decision systems is developed from the perspective of maintaining the distinguishing ability. Extensive experiments on 16 public datasets exhibit that our model can effectively reduce redundant features from different scales, and demonstrates competitive classification performance compared with four state-of-the-art dimension reduction algorithms.

多尺度决策系统作为一种典型的多粒度数据分析模型，近年来受到了研究者的广泛关注。然而，大多数多尺度模型难以处理连续数据，并且无法准确表征复杂场景中样本之间的差异。此外，对模糊多尺度不确定性测度及其在降维中的应用研究较少。针对这些问题，提出了一种新的多尺度模糊关系决策系统，并研究了不同尺度模糊关系族的不确定性度量。为此，提出了δ-模糊相似关系来表征目标对象之间的相关性。然后提出模糊尺度熵来反映不同尺度模糊关系族的区分能力。在此基础上，提出了联合模糊尺度熵、条件模糊尺度熵和互模糊尺度熵等不确定性测度的变体，以揭示特征子集识别能力之间的关系。最后，从保持识别能力的角度出发，提出了一种多尺度模糊关系决策系统的知识约简算法。在16个公共数据集上进行的大量实验表明，我们的模型可以有效地减少不同尺度的冗余特征，并且与四种最先进的降维算法相比，显示出具有竞争力的分类性能。

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