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Generalized fuzzy betweenness relations and their connection with fuzzy Čech closure spaces 广义模糊间性关系及其与模糊Čech闭包空间的联系
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-10-02 DOI: 10.1016/j.fss.2025.109610
Yi Shi , Chong Shen , Hui Yang
{"title":"Generalized fuzzy betweenness relations and their connection with fuzzy Čech closure spaces","authors":"Yi Shi ,&nbsp;Chong Shen ,&nbsp;Hui Yang","doi":"10.1016/j.fss.2025.109610","DOIUrl":"10.1016/j.fss.2025.109610","url":null,"abstract":"<div><div>By a fuzzy betweenness relation we mean that a fuzzy ternary relation satisfies symmetry, reflexivity, antisymmetry and transitivity. This paper investigates certain generalized fuzzy betweenness relations, with the aim of showing that they can provide a suitable framework to establish the connection with fuzzy Alexandrov topology via fuzzy Čech closure operators. To be more precise, we define fuzzy quasi-betweenness relations by dropping symmetry and antisymmetry of fuzzy betweenness relations. After capturing a feature of them as fuzzy neighborhood-like structures, we apply a categorical lens to the study of the relationship between fuzzy quasi-betweenness relations and total strong fuzzy Čech closure spaces. It turns out that there is a Galois correspondence between the category of fuzzy quasi-betweenness relations and that of total strong fuzzy Čech closure spaces. As a direct consequence, there is a Galois correspondence between the category of fuzzy quasi-betweenness relations and that of strong Alexandrov fuzzy topological spaces.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109610"},"PeriodicalIF":2.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chebyshev's inequality for Choquet integral revisited 对Choquet积分的Chebyshev不等式的重新考察
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-10-02 DOI: 10.1016/j.fss.2025.109608
Hamzeh Agahi
{"title":"Chebyshev's inequality for Choquet integral revisited","authors":"Hamzeh Agahi","doi":"10.1016/j.fss.2025.109608","DOIUrl":"10.1016/j.fss.2025.109608","url":null,"abstract":"<div><div>Recently, Wang <span><span>[43, Fuzzy Sets and Systems 457, (2023) 105–118]</span></span> claimed that Chebyshev's inequality for Choquet integral holds under comonotonicity or supermodularity. Our counter-example demonstrates that supermodularity alone cannot validate Chebyshev's inequality for Choquet integral without comonotonicity. We also establish a refined Chebyshev inequality for Choquet integral that provides tighter bounds. As an application in probability theory, we derive a strengthened variance inequality that achieves equality for Bernoulli distributions. Finally, we present an open problem for future research.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109608"},"PeriodicalIF":2.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the quantum circuit implementation of fuzzy reasoning 关于量子电路模糊推理的实现
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-10-02 DOI: 10.1016/j.fss.2025.109611
Songsong Dai
{"title":"On the quantum circuit implementation of fuzzy reasoning","authors":"Songsong Dai","doi":"10.1016/j.fss.2025.109611","DOIUrl":"10.1016/j.fss.2025.109611","url":null,"abstract":"<div><div>In this paper, quantum circuits for fuzzy relational inferences are synthesized. The compositional rule of inference (CRI) and Bandler-Kohout subproduct (BKS) methods are two widely used fuzzy relational inference (FRI) schemes. To be able to work on a quantum computer, we first modify the CRI and BKS methods. Then we construct the quantum circuits for the modified CRI and BKS methods. Finally, implementation of modified CRI method on the OriginQ quantum computing cloud platform is demonstrated.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109611"},"PeriodicalIF":2.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triangular norms on finite lattices 有限格上的三角范数
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-10-02 DOI: 10.1016/j.fss.2025.109609
Peng He, Xue-ping Wang
{"title":"Triangular norms on finite lattices","authors":"Peng He,&nbsp;Xue-ping Wang","doi":"10.1016/j.fss.2025.109609","DOIUrl":"10.1016/j.fss.2025.109609","url":null,"abstract":"<div><div>This article intends to characterize triangular norms on a finite lattice. We first give a method for generating a triangular norm on a complete atomistic lattice by atoms. Then we prove that every triangular norm on a non-Boolean atomistic lattice is not left-continuous and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> is the unique left-continuous triangular norm on an atomistic Boolean lattice. Furthermore, we show that each atomistic Boolean lattice can be represented by a family of triangular norms on an atomistic lattice with the same number of atoms. Finally, we construct a triangular norm on a finite lattice by restricting a triangular norm on an extended atomistic lattice of the finite lattice to the finite lattice.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109609"},"PeriodicalIF":2.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conservative decision-making with sets of probabilities: How to infer new choices from previous ones 具有概率集的保守决策：如何从先前的选择中推断出新的选择
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-10-02 DOI: 10.1016/j.fss.2025.109612
Arne Decadt, Alexander Erreygers, Jasper De Bock
{"title":"Conservative decision-making with sets of probabilities: How to infer new choices from previous ones","authors":"Arne Decadt,&nbsp;Alexander Erreygers,&nbsp;Jasper De Bock","doi":"10.1016/j.fss.2025.109612","DOIUrl":"10.1016/j.fss.2025.109612","url":null,"abstract":"<div><div>We study a generalized version of maximizing expected utility, called E-admissibility, to make decisions when the decision-maker's uncertainty is described by a set of probability mass functions. In particular, instead of specifying this set directly, we assume that we only have partial information about the decision-maker's preferences or choices, in the form of which options she rejects from some finite sets of options. We describe both the decision-making process and the available information using choice functions, and we provide an algorithm, based on linear programming, to compute the most conservative extension of a given choice assessment to a choice function that makes decisions based on E-admissibility. Next, we relate this E-admissible extension to the so-called coherent extension and show how the same techniques that are used to simplify the computation of this coherent extension can also be used to simplify that of the E-admissible one. In our experiments, we demonstrate that decision-making with the E-admissible extension is faster and more informative than with the coherent one, but also observe that the required computations are challenging once the parameters of the problem scale.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"523 ","pages":"Article 109612"},"PeriodicalIF":2.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145229949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhanced state-constrained adaptive fuzzy exact tracking control for nonlinear strict-feedback systems 非线性严格反馈系统的增强状态约束自适应模糊精确跟踪控制
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-09-30 DOI: 10.1016/j.fss.2025.109598
Qiang Zhang , Dakuo He , Xin Li , Hailong Liu , Xingling Shao
{"title":"Enhanced state-constrained adaptive fuzzy exact tracking control for nonlinear strict-feedback systems","authors":"Qiang Zhang ,&nbsp;Dakuo He ,&nbsp;Xin Li ,&nbsp;Hailong Liu ,&nbsp;Xingling Shao","doi":"10.1016/j.fss.2025.109598","DOIUrl":"10.1016/j.fss.2025.109598","url":null,"abstract":"<div><div>An adaptive fuzzy exact tracking control (ETC) is constructed of nonlinear strict-feedback systems with full-state constraints, mismatched external disturbances. Compared with barrier Lyapunov function based on exponential-type constraint, a novel arctan-type constraint is proposed for the first time, whose convergence boundary is consistent with the exponential-type constraint and the initial value has a wider range of applicability under the same parameters. Different from dynamic surface control method and command filter method to solve the “differential explosion” in the backstepping design, the differential of the virtual controller is formulated within a polynomial expression, and an estimation of its maximum value is determined. Subsequently, using this upper bound estimation information, an adaptive fuzzy ETC mechanism is constructed. Utilizing this approach, whenever the tracking error diverges from the origin, an associated control mechanism springs into action, guiding it to converge towards and slide along the origin, thereby ensuring exact tracking control. To demonstrate the salient features of this control mechanism, a nonlinear system and a single-link robotic system are employed in simulation studies.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109598"},"PeriodicalIF":2.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
L-algebras with additional conditions 附加条件的l -代数
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-09-30 DOI: 10.1016/j.fss.2025.109607
Zhejie Duan
{"title":"L-algebras with additional conditions","authors":"Zhejie Duan","doi":"10.1016/j.fss.2025.109607","DOIUrl":"10.1016/j.fss.2025.109607","url":null,"abstract":"<div><div>This paper delves into the properties of L-algebras, particularly those satisfying additional conditions like (K), (C), (D), and <span><math><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span>. We see that new condition <span><math><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span> is equivalent to (C). Then we introduce and investigate special L-algebras and provides a full representation of this structure. Furthermore, we define and investigate linear ideals in L-algebras, showing their relationship to prime ideals in L-algebras satisfying (K) and (D). We also explore the representability of L-algebras, presenting a necessary and sufficient condition for representability in terms of a specific inequality, when the L-algebra satisfies <span><math><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span>. Finally, we investigate ordinal sums of L-algebras, which allows for the construction of new L-algebras, including linearly ordered ones, and analyze its properties in relation to representability.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109607"},"PeriodicalIF":2.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
M-step random multiaccess protocol-based robust predictive control for Takagi-Sugeno fuzzy systems with persistent disturbances 基于m步随机多址协议的持续扰动Takagi-Sugeno模糊系统鲁棒预测控制
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-09-29 DOI: 10.1016/j.fss.2025.109605
Yuying Dong , Zhenrong Huang , Chenxi Gao , Yan Song
{"title":"M-step random multiaccess protocol-based robust predictive control for Takagi-Sugeno fuzzy systems with persistent disturbances","authors":"Yuying Dong ,&nbsp;Zhenrong Huang ,&nbsp;Chenxi Gao ,&nbsp;Yan Song","doi":"10.1016/j.fss.2025.109605","DOIUrl":"10.1016/j.fss.2025.109605","url":null,"abstract":"<div><div>This paper investigates the issue of <em>M</em>-step robust fuzzy model predictive control (RFMPC) for a category of nonlinear systems that are described using Takagi-Sugeno (T-S) fuzzy models, subject to communication network constraints and persistent bounded disturbances. To mitigate data collisions and improve data transmission reliability, a random multiaccess protocol (RMP) is integrated into the <em>M</em>-step RFMPC framework, resulting in the proposed <em>M</em>-step RMP-based RFMPC approach. Specifically, a unified representation is developed to model the interplay between T-S fuzzy nonlinearities and the RMP for nonlinear systems subject to persistent bounded disturbances. Optimization problems are formulated to determine the terminal constraint set and robust one-step sets for T-S fuzzy systems in an offline manner. Utilizing a scheduling signal-dependent quadratic function approach, a novel <em>M</em>-step RMP-based RFMPC algorithm is proposed, comprising both offline and online components. Sufficient conditions are established to ensure both the feasibility of the proposed algorithm and the mean-square input-to-state stability of the resulting closed-loop system. Finally, the effectiveness and applicability of the proposed <em>M</em>-step RMP-based RFMPC approach are demonstrated through two illustrative examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109605"},"PeriodicalIF":2.7,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fuzzy S-hypersystems over fuzzy semihypergroups 模糊半超群上的模糊s超系统
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-09-23 DOI: 10.1016/j.fss.2025.109604
Pingting Ma , Husheng Qiao
{"title":"Fuzzy S-hypersystems over fuzzy semihypergroups","authors":"Pingting Ma ,&nbsp;Husheng Qiao","doi":"10.1016/j.fss.2025.109604","DOIUrl":"10.1016/j.fss.2025.109604","url":null,"abstract":"<div><div>Let <em>S</em> be a fuzzy semihypergroup. We introduce the notions of fuzzy <em>S</em>-hypersystems over fuzzy semihypergroups and study their elementary properties. We improve fuzzy regular relations and fuzzy strongly regular relations. The fuzzy hyper versions of the fundamental normal homomorphism theorems are obtained, and product and coproduct of fuzzy <em>S</em>-hypersystems are discussed. In addition, we derive some results on crisp <em>S</em>-hypersystems and semihypergroup.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109604"},"PeriodicalIF":2.7,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fuzzy prescribed performance tracking control for stochastic Markovian jump nonlinear systems with unmodeled dynamics and actuator faults 具有未建模动力学和执行器故障的随机马尔可夫跳变非线性系统的模糊预定性能跟踪控制
IF 2.7 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-09-23 DOI: 10.1016/j.fss.2025.109606
Junchang Zhai , Huanqing Wang , Changzhong Wang
{"title":"Fuzzy prescribed performance tracking control for stochastic Markovian jump nonlinear systems with unmodeled dynamics and actuator faults","authors":"Junchang Zhai ,&nbsp;Huanqing Wang ,&nbsp;Changzhong Wang","doi":"10.1016/j.fss.2025.109606","DOIUrl":"10.1016/j.fss.2025.109606","url":null,"abstract":"<div><div>Adaptive fuzzy prescribed performance fault-tolerant tracking control for unmodeled stochastic Markovian jump nonlinear systems with actuator failures is studied in this article. As online approximators, fuzzy logic systems (FLSs) are utilized to approximate unknown nonlinear functions and unavailable Markovian switching nonlinearities. To keep the control performance, an ameliorated finite-time prescribed boundary function was incorporated into the controller design, such that the tracking error can be suppressed by the decay boundary function. And the settling time and the size of the prescribed performance set can be arbitrarily predefined according to actual needs. A dynamic signal is employed to tackle the design difficulty of unmodeled dynamics. In view of gain fault and bias fault, an adaptive estimation plan is introduced to estimate the unknown fault parameters online such that the actual controller can be appropriately designed. The formulated fault-tolerant tracking control tactic can keep the boundedness of all signals in spite of Markovian switching, unmodeled dynamics, stochastic disturbances and actuator faults. Finally, the simulations verify the feasibility of the proposed tactic.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109606"},"PeriodicalIF":2.7,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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