Fuzzy Sets and Systems最新文献

英文中文

Learning-enabled event-triggered fuzzy adaptive control of multiagent systems with prescribed performance: A chaos-based privacy-preserving method 具有规定性能的多代理系统的学习型事件触发模糊自适应控制：基于混沌的隐私保护方法

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-12 DOI: 10.1016/j.fss.2024.109171

Siyu Guo, Yingnan Pan, Zhechen Zhu

This paper considers the prescribed performance fuzzy adaptive tracking control problem of multiagent systems under a chaos-based privacy-preserving mechanism and a learning-enabled event-triggered mechanism. Initially, a chaos-based mask function is constructed, which is related to the chaotic states in the Lorentz system. The utilization of chaos adds unpredictability and full randomness to the mask function, which greatly reduces the risk of privacy leakage. Additionally, two value functions are designed as inputs of the fully connected neural network, and the fully connected neural network is used to predict the parameter value in the event-triggered mechanism, which effectively enhances the flexibility of the proposed learning-enabled event-triggered mechanism. Furthermore, in the process of controller design, by employing an error transformed function, the system errors are stabilized within the prescribed performance boundaries. Finally, a simulation example is provided to validate the effectiveness of the proposed control scheme.

本文考虑了基于混沌的隐私保护机制和学习型事件触发机制下多代理系统的规定性能模糊自适应跟踪控制问题。首先，本文构建了一个基于混沌的掩码函数，它与洛伦兹系统中的混沌状态有关。混沌的利用增加了掩码函数的不可预测性和完全随机性，从而大大降低了隐私泄露的风险。此外，还设计了两个值函数作为全连接神经网络的输入，并利用全连接神经网络预测事件触发机制中的参数值，这有效增强了所提出的学习型事件触发机制的灵活性。此外，在控制器设计过程中，通过采用误差变换函数，可将系统误差稳定在规定的性能边界内。最后，还提供了一个仿真实例来验证所提控制方案的有效性。

引用次数: 0

Subdifferential of fuzzy n-cell number-valued functions and its applications in optimization problems 模糊 n 单元数值函数的子差分及其在优化问题中的应用

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-12 DOI: 10.1016/j.fss.2024.109189

Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou

We give the concept of subdifferentiability for a fuzzy n-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.

我们给出了模糊 n 单元数值函数的次微分性概念。然后，我们根据新定义阐述了与次微分性相关的一些定理。最后，我们介绍了优化问题的一些应用，包括拉格朗日对偶问题和复合最小化问题。

引用次数: 0

Dynamic event-triggered fault-tolerant control for nonaffine systems with asymmetric error constraint 具有非对称误差约束的非石蜡系统的动态事件触发容错控制

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-08 DOI: 10.1016/j.fss.2024.109180

Yang Wu, Lianjun Hu, Qi Chen, Yong Zhang, Libing Wu

This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.

本文重点研究了状态不可测、误差约束不对称的非线性系统的动态事件触发容错控制（FTC）问题。首先，设计了一个自适应故障补偿观测器来计算非石蜡系统的不可测状态。然后，构建了一种动态事件触发策略（DETS）来调整控制信号，使其在传输过程中更加灵活。接着，设计了一种新的误差相关转换函数（EDCF）来限制跟踪误差，从而确保所设计的 Lyapunov 函数始终为正定值，并将对称约束边界扩展到非对称约束边界。通过 Lyapunov 稳定性分析，证明了闭环系统的跟踪性能和稳定性。最后，通过仿真实验验证了该方法的可用性。

引用次数: 0

Geometric properties of ternary fuzzy relations 三元模糊关系的几何特性

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-08 DOI: 10.1016/j.fss.2024.109188

Bin Pang , Xiu-Yun Wu , Bernard De Baets

Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.

近年来，三元模糊关系，尤其是模糊间性关系越来越受到关注。其中一个重要原因是，三元模糊关系的公理性质似乎非常适合捕捉抽象的 "间性 "概念的几何特征。在本文中，我们介绍了三元模糊关系的几个新性质，包括 Peano 性质、Pasch 性质和沙漏性质，它们都可以被定性为几何性质。我们研究了它们之间的相互关系，以及它们与各种模糊间性关系的联系。此外，在研究帕施性质和沙漏性质的过程中，我们从模糊凸结构理论的坚实理论基础中得到启发，引入了三元模糊关系的凸性质。

引用次数: 0

Quantile dependence: A generalization of upper and lower tail dependence 量子依赖性：上尾和下尾依赖性的一般化

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-07 DOI: 10.1016/j.fss.2024.109165

Ali Dastbaravarde, Ali Dolati

A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.

一种常用的关联测量方法是尾部依赖系数，它可以测量二元分布尾部的依赖强度。在本文中，我们引入了量级依赖性的概念，它扩展了尾部依赖性的概念，可用于测量两个随机变量的特定量级在分布域的特定区域内的依赖性。我们分析了所提出的量化依赖系数的特点，并提供了各种实例来证明我们的发现。

引用次数: 0

Asymmetric interval numbers: A new approach to modeling uncertainty 非对称区间数：不确定性建模的新方法

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-07 DOI: 10.1016/j.fss.2024.109169

Wojciech Sałabun

This paper introduces Asymmetric Interval Numbers

(A I N s)

, a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity.

A I N s

incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for

A I N s

, discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for

A I N s

. Several illustrative examples demonstrate the practical application of

A I N s

. Although challenges remain, such as exploring performance with different distributions and reducing overestimation,

A I N s

present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of

A I N s

, paving the way for further research and application in diverse scientific and industrial contexts.

本文介绍了非对称区间数 (AIN)，这是一种新型区间数，它结合了经典区间数的直接识别特性和模糊集的先进不确定性建模能力，同时又保持了简洁性。AIN 包含区间内的期望值，与经典区间数相比，能更准确地表示数据的不确定性。我们定义了 AIN 的基本算术运算，讨论了它们的特性，并提供了证明。此外，我们还提出了基本二元和一元运算的对称性和不对称性定理，从而加强了 AIN 的数学框架。几个示例展示了 AIN 的实际应用。尽管仍存在一些挑战，如探索不同分布的性能和减少高估，但 AINs 是区间运算中一个很有前途的进步。本研究强调了 AINs 的实践和理论意义，为进一步研究 AINs 并将其应用于各种科学和工业领域铺平了道路。

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引用次数: 0

Approximate reasoning based on the preference implication 基于偏好暗示的近似推理

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-07 DOI: 10.1016/j.fss.2024.109187

József Dombi , Tamás Jónás

In fuzzy logic, most of the implication operators are based on generalizations of the classical, material implication. That is, these implications are defined as the disjunction of the negated value of the first argument and the value of the second argument, while the underlying disjunction operators are associative triangular conorms. In our study, we concentrate on how a class of implication operators, called the preference implication operators, can be used in approximate reasoning. Using this implication operator family, we present a novel, Modus Ponens-like approximate reasoning method, in which we have two premises: (1) a statement and (2) a preference implication with an antecedent of this statement. Here, we show how the continuous logical value of the consequent of the preference implication can be derived from the continuous logical values of the premises. We point out that this novel approximate reasoning method is strongly connected with the so-called aggregative operator, which is a representable uninorm. Next, we also present a threshold value-based generalization of the Modus Ponens syllogism and demonstrate that the Modus Tollens syllogism can be generalized in the same way. Lastly, we provide an illustrative example.

在模糊逻辑中，大多数蕴涵运算符都是基于对经典的物质蕴涵的概括。也就是说，这些蕴涵被定义为第一个参数的否定值和第二个参数的值的析取，而基本的析取算子是关联三角形康式。在我们的研究中，我们将重点关注如何在近似推理中使用一类蕴涵算子，即偏好蕴涵算子。利用这个蕴涵算子族，我们提出了一种新颖的、类似于模态庞恩的近似推理方法，其中我们有两个前提：（1）一个语句和（2）一个带有该语句前因的偏好蕴涵。在这里，我们展示了如何从前提的连续逻辑值推导出偏好蕴涵的后果的连续逻辑值。我们指出，这种新颖的近似推理方法与所谓的聚合算子密切相关，而聚合算子是一种可表示的非规范。接下来，我们还介绍了基于阈值的莫度庞恩式三段论概括，并证明莫度托伦斯式三段论也可以用同样的方法概括。最后，我们提供了一个示例。

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引用次数: 0

Some notes on the coincidence of the Choquet integral and the pan-integral 关于乔奎特积分和泛积分重合的一些说明

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-05 DOI: 10.1016/j.fss.2024.109178

Tong Kang , Radko Mesiar , Yao Ouyang , Jun Li

In this note, we provide an example to show the weak (M)-property is really weaker than the (M)-property for some finite monotone measure defined on infinite space, and hence answer an open problem which was proposed in the paper (Li et al. (2023) [9]). We prove that if a monotone measure μ is autocontinuous, then the weak (M)-property and the (M)-property of μ are equivalent. We propose the concept of (C-P)-property of monotone measures and show a set of sufficient and necessary conditions that the Choquet integral coincides with the pan-integral. We further study the relationships between the Choquet integral and the pan-integral in the setting of the ordered pairs of monotone measures, and obtain some interesting properties.

在本注中，我们举例说明对于定义在无限空间上的某个有限单调度量，弱（M）属性确实比（M）属性弱，从而回答了论文（李等（2023）[9]）中提出的一个开放问题。我们证明，如果单调度量 μ 是自连续的，那么弱 (M)- 属性和 μ 的 (M)- 属性是等价的。我们提出了单调度量的(C-P)-属性概念，并证明了一组乔奎特积分与泛积分重合的充分必要条件。我们进一步研究了在单调度量的有序对的背景下，Choquet积分和泛积分之间的关系，并得到了一些有趣的性质。

引用次数: 0

General multifractal dimensions of measures 测量的一般多分形维度

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-05 DOI: 10.1016/j.fss.2024.109177

Bilel Selmi

The main aim of this paper is to present a comprehensive exploration of general multifractal dimensions of Borel probability measures, with a specific emphasis on the diverse methodologies available for their estimation or computation. We prove that these general dimensions enable us to compare a probability measure ϑ with the general multifractal Hausdorff or packing measure. Also, we aim to measure the degree of regularity or singularity of ϑ, and we examine the correlations between various approaches to defining the general multifractal exact dimension of Borel probability measures, using fractal analysis of the essential supports of these measures as the foundation.

本文的主要目的是全面探讨Borel概率度量的一般多分形维度，并特别强调了估算或计算这些维度的各种方法。我们证明，这些一般维度使我们能够比较概率度量ϑ与一般多分形Hausdorff或打包度量。此外，我们还旨在测量ϑ的规则性或奇异性程度，并以这些度量的基本支撑的分形分析为基础，研究了定义博尔概率度量的一般多分形精确维度的各种方法之间的关联。

引用次数: 0

Subsethood measures based on cardinality of type-2 fuzzy sets 基于第 2 类模糊集心率的次优度量

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems

Pub Date : 2024-11-04 DOI: 10.1016/j.fss.2024.109174

Carmen Torres-Blanc , Jesus Martinez-Mateo , Susana Cubillo , Luis Magdalena , Francisco Javier Talavera , Jorge Elorza

In this work we present a novel axiomatic framework for subsethood measures in type-2 fuzzy sets. It differs from previous approaches in two key ways. First, the degree of membership is not simply a fuzzy set as considered in other papers, but rather a label of the variable Truth, more in line with Zadeh's original idea. Secondly, the concept of subsethood is approached in terms of its relationship with cardinality. Additionally, illustrative examples of such measures are provided.

在这项研究中，我们提出了一个新颖的公理框架，用于研究 2 型模糊集合中的子实体度量。它在两个关键方面不同于以往的方法。首先，成员度并不像其他论文所考虑的那样只是一个模糊集，而是变量 Truth 的一个标签，这更符合 Zadeh 最初的想法。其次，子实体的概念是根据其与万有引力的关系来处理的。此外，还提供了此类度量的示例。

引用次数: 0

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