Pub Date : 2026-04-15Epub Date: 2025-12-20DOI: 10.1016/j.fss.2025.109730
Narayan Choudhary, Aastha Nirvana, S.P. Tiwari
This work focuses on the categorical study of L-fuzzy automata with a pair of L-fuzzy relations as morphisms, where L is a complete regular residuated and co-residuated lattice. Specifically, we introduce and study the categorical concepts such as product, monics, and their duals in this category, as well as further examine the monoidal structure. Moreover, we investigate the relationship between the category of L-fuzzy automata and the category of non-deterministic automata. We show the existence of isomorphisms between the category of L-fuzzy automata and the category of chains of non-deterministic automata.
{"title":"L-fuzzy automata based on complete regular residuated and co-residuated lattice: A categorical study","authors":"Narayan Choudhary, Aastha Nirvana, S.P. Tiwari","doi":"10.1016/j.fss.2025.109730","DOIUrl":"10.1016/j.fss.2025.109730","url":null,"abstract":"<div><div>This work focuses on the categorical study of <em>L</em>-fuzzy automata with a pair of <em>L</em>-fuzzy relations as morphisms, where <em>L</em> is a complete regular residuated and co-residuated lattice. Specifically, we introduce and study the categorical concepts such as product, monics, and their duals in this category, as well as further examine the monoidal structure. Moreover, we investigate the relationship between the category of <em>L</em>-fuzzy automata and the category of non-deterministic automata. We show the existence of isomorphisms between the category of <em>L</em>-fuzzy automata and the category of chains of non-deterministic automata.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109730"},"PeriodicalIF":2.7,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885516","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}
Pub Date : 2026-04-01Epub Date: 2025-11-27DOI: 10.1016/j.fss.2025.109701
Aziz El Ghazouani, M’hamed Elomari , Said Melliani
This paper establishes rigorous mathematical foundations for fuzzy fractional delay integro-differential equations (FFDIDEs) involving the generalized Hukuhara ψ-Caputo fractional derivative – a previously unexplored combination in the literature. We address the critical theoretical gap in analyzing systems that simultaneously incorporate fuzzy uncertainty, memory effects (time delays), and non-local dynamics (integral terms). Through an innovative synthesis of Banach’s fixed point theorem and a novel monotone iterative technique, we prove: (1) existence and uniqueness of solutions under Lipschitz conditions (Theorems 2 and 3), (2) constructive approximation via monotone sequences converging uniformly to the solution (Lemma 2), and (3) continuous dependence on initial conditions with explicit stability bounds (Theorem 4).
Our framework systematically handles both d-increasing and d-decreasing solution cases through a unified ψ-Caputo operational calculus. The theoretical advances are validated through computational experiments demonstrating convergence rates for α ∈ (0, 1), with MATLAB simulations providing quantitative analysis of triangular fuzzy solutions (Example 1, Figures 1– 6). Beyond its theoretical contributions, this work enables new applications in fuzzy control systems with delays, fractional-order neural networks with uncertainty, and other complex systems requiring simultaneous treatment of non-locality and vagueness. The results fundamentally extend the existing fuzzy fractional calculus literature by establishing the first comprehensive solution theory for this important class of equations.
{"title":"Fuzzy fractional delay integro-differential equation with the generalized Hukuhara ψ-Caputo fractional derivative","authors":"Aziz El Ghazouani, M’hamed Elomari , Said Melliani","doi":"10.1016/j.fss.2025.109701","DOIUrl":"10.1016/j.fss.2025.109701","url":null,"abstract":"<div><div>This paper establishes rigorous mathematical foundations for fuzzy fractional delay integro-differential equations (FFDIDEs) involving the generalized Hukuhara <em>ψ</em>-Caputo fractional derivative – a previously unexplored combination in the literature. We address the critical theoretical gap in analyzing systems that simultaneously incorporate fuzzy uncertainty, memory effects (time delays), and non-local dynamics (integral terms). Through an innovative synthesis of Banach’s fixed point theorem and a novel monotone iterative technique, we prove: (1) existence and uniqueness of solutions under Lipschitz conditions (Theorems 2 and 3), (2) constructive approximation via monotone sequences converging uniformly to the solution (Lemma 2), and (3) continuous dependence on initial conditions with explicit stability bounds (Theorem 4).</div><div>Our framework systematically handles both <em>d</em>-increasing and <em>d</em>-decreasing solution cases through a unified <em>ψ</em>-Caputo operational calculus. The theoretical advances are validated through computational experiments demonstrating <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>h</mi><mrow><mn>1</mn><mo>+</mo><mi>α</mi></mrow></msup><mo>)</mo></mrow></math></span> convergence rates for <em>α</em> ∈ (0, 1), with MATLAB simulations providing quantitative analysis of triangular fuzzy solutions (Example 1, Figures 1– 6). Beyond its theoretical contributions, this work enables new applications in fuzzy control systems with delays, fractional-order neural networks with uncertainty, and other complex systems requiring simultaneous treatment of non-locality and vagueness. The results fundamentally extend the existing fuzzy fractional calculus literature by establishing the first comprehensive solution theory for this important class of equations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109701"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685551","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}
Pub Date : 2026-04-01Epub Date: 2025-12-07DOI: 10.1016/j.fss.2025.109725
Yu Kong, Hua-Wen Liu
<div><div>In this paper, we mainly study the classes of uninorms whose neutral elements are middle-transitive and not in any non-trivial cycle, defined on bounded pseudo-ordered sets. Firstly, to generalize the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> of uninorms on bounded lattices, we introduce the definitions of the classes <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of uninorms on bounded pseudo-ordered sets. Secondly, we characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-subnorms and uninorms. We characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-superconorms and uninorms. In addition, we introduce the definitions of the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets, generalizing the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> on bounded lattices. We introduce the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets as the extensions of the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mi>r</mi></msubs
{"title":"Several classes of uninorms on bounded pseudo-ordered sets","authors":"Yu Kong, Hua-Wen Liu","doi":"10.1016/j.fss.2025.109725","DOIUrl":"10.1016/j.fss.2025.109725","url":null,"abstract":"<div><div>In this paper, we mainly study the classes of uninorms whose neutral elements are middle-transitive and not in any non-trivial cycle, defined on bounded pseudo-ordered sets. Firstly, to generalize the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> of uninorms on bounded lattices, we introduce the definitions of the classes <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of uninorms on bounded pseudo-ordered sets. Secondly, we characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-subnorms and uninorms. We characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-superconorms and uninorms. In addition, we introduce the definitions of the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets, generalizing the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> on bounded lattices. We introduce the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets as the extensions of the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mi>r</mi></msubs","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109725"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790850","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}
Pub Date : 2026-04-01Epub Date: 2025-11-24DOI: 10.1016/j.fss.2025.109703
Tinghua Wang, Zhiyong Lai, Xin Zhang
Support vector machine (SVM) is an algorithm developed based on statistical learning theory and has exhibited superior performance in many fields. Despite its success, SVM assumes that all training samples are equally important during training, making it sensitive to noise or outliers. To mitigate this problem, SVM was extended to fuzzy SVM (FSVM), which assigns a fuzzy membership to each training point, thereby allowing different training points contribute differently to the learning of the decision boundary. Although FSVM improves the classification performance to some degree, it still operates under the assumption that all features contribute equally. This overlooks the different importance of different features in the classification process, potentially leading to undesirable classification results. At present, most feature weighting methods rely on heuristic search strategies, which often yield locally optimal solutions and predominantly focus on the correlation between features and labels while neglecting the redundancy between features. To address these limitations, we propose a novel approach termed dually feature-weighted FSVM based on Hilbert-Schmidt independence criterion (HSIC) least absolute shrinkage and selection operator (LASSO) (DFWFSVM-HL for short). Specifically, the HSIC is firstly used to calculate the minimum redundancy maximum relevance (mRMR) feature weights, and the global optimal solution is efficiently obtained by solving a LASSO optimization problem. Subsequently, the fuzzy membership function is refined by incorporating these feature weights, modulating the contribution of different features to the fuzzy membership function by a feature-weighted Euclidean distance between the sample and its corresponding class center. This effectively reduces the impact of noise or outliers on classification. Additionally, a feature-weighted kernel function is constructed using the feature weights, reducing the influence of weak or irrelevant features on classification. Comprehensive experiments on benchmark datasets validate the effectiveness of the proposed DFWFSVM-HL model, demonstrating its superiority in terms of several classification performance metrics.
{"title":"Dually feature-weighted fuzzy SVM based on HSIC LASSO","authors":"Tinghua Wang, Zhiyong Lai, Xin Zhang","doi":"10.1016/j.fss.2025.109703","DOIUrl":"10.1016/j.fss.2025.109703","url":null,"abstract":"<div><div>Support vector machine (SVM) is an algorithm developed based on statistical learning theory and has exhibited superior performance in many fields. Despite its success, SVM assumes that all training samples are equally important during training, making it sensitive to noise or outliers. To mitigate this problem, SVM was extended to fuzzy SVM (FSVM), which assigns a fuzzy membership to each training point, thereby allowing different training points contribute differently to the learning of the decision boundary. Although FSVM improves the classification performance to some degree, it still operates under the assumption that all features contribute equally. This overlooks the different importance of different features in the classification process, potentially leading to undesirable classification results. At present, most feature weighting methods rely on heuristic search strategies, which often yield locally optimal solutions and predominantly focus on the correlation between features and labels while neglecting the redundancy between features. To address these limitations, we propose a novel approach termed dually feature-weighted FSVM based on Hilbert-Schmidt independence criterion (HSIC) least absolute shrinkage and selection operator (LASSO) (DFWFSVM-HL for short). Specifically, the HSIC is firstly used to calculate the minimum redundancy maximum relevance (mRMR) feature weights, and the global optimal solution is efficiently obtained by solving a LASSO optimization problem. Subsequently, the fuzzy membership function is refined by incorporating these feature weights, modulating the contribution of different features to the fuzzy membership function by a feature-weighted Euclidean distance between the sample and its corresponding class center. This effectively reduces the impact of noise or outliers on classification. Additionally, a feature-weighted kernel function is constructed using the feature weights, reducing the influence of weak or irrelevant features on classification. Comprehensive experiments on benchmark datasets validate the effectiveness of the proposed DFWFSVM-HL model, demonstrating its superiority in terms of several classification performance metrics.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109703"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645981","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}
Pub Date : 2026-04-01Epub Date: 2025-11-25DOI: 10.1016/j.fss.2025.109705
Jiahao Li , Yanhong She , Xiaoli He , Ting Qian , Wenli Zheng
Fuzzy rough set-based bi-selection, which performs instance and feature selection simultaneously, has become an important technique for data reduction. This paper proposes a novel bi-selection approach from an incremental learning perspective for the dynamic selection of instances and features upon the arrival of new data. To enhance the robustness of the proposed algorithm (called IBSFRS) across datasets of varying sizes, an elite instance strategy is incorporated into the incremental instance selection process. The numerical experiments are conducted on 14 commonly used datasets by simulating an incremental learning scenario where new instances arrive in batches. The results demonstrate that the IBSFRS algorithm exhibits significant advantages in classification accuracy while maintaining a high reduction rate. Furthermore, it exhibits superior performance in the effectiveness metric, successfully balancing the reduction rate with classification accuracy in incremental environment.
{"title":"Incremental perspective for Bi-selection of instances and features by employing fuzzy rough set technique","authors":"Jiahao Li , Yanhong She , Xiaoli He , Ting Qian , Wenli Zheng","doi":"10.1016/j.fss.2025.109705","DOIUrl":"10.1016/j.fss.2025.109705","url":null,"abstract":"<div><div>Fuzzy rough set-based bi-selection, which performs instance and feature selection simultaneously, has become an important technique for data reduction. This paper proposes a novel bi-selection approach from an incremental learning perspective for the dynamic selection of instances and features upon the arrival of new data. To enhance the robustness of the proposed algorithm (called IBSFRS) across datasets of varying sizes, an elite instance strategy is incorporated into the incremental instance selection process. The numerical experiments are conducted on 14 commonly used datasets by simulating an incremental learning scenario where new instances arrive in batches. The results demonstrate that the IBSFRS algorithm exhibits significant advantages in classification accuracy while maintaining a high reduction rate. Furthermore, it exhibits superior performance in the effectiveness metric, successfully balancing the reduction rate with classification accuracy in incremental environment.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109705"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737890","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}
Pub Date : 2026-04-01Epub Date: 2025-12-07DOI: 10.1016/j.fss.2025.109716
G. Caterina
We develop a moment-preserving defuzzifier based on the Cafagna-Caterina characterization theorem. Given the first n Fourier moments of a membership function f ∈ [0, 1] on S1, it returns a crisp function χn which is a union of n arcs and whose first n moments match those of f exactly. For , corresponding to mass and centroid, we give a closed-form solution for the arc endpoints, whereas for n > 2 we present two numerical methods to compute those arcs. As an application, we apply the method to California Independent System Operator (CAISO) net demand data, and show that the four-arc solution automatically produces a midday gap that captures the solar valley, with arc locations emerging from moment-matching constraints rather than threshold selection or manual specification.
{"title":"A moment-preserving spectral defuzzification on the circle: From theory to practice","authors":"G. Caterina","doi":"10.1016/j.fss.2025.109716","DOIUrl":"10.1016/j.fss.2025.109716","url":null,"abstract":"<div><div>We develop a moment-preserving defuzzifier based on the Cafagna-Caterina characterization theorem. Given the first <em>n</em> Fourier moments of a membership function <em>f</em> ∈ [0, 1] on <em>S</em><sup>1</sup>, it returns a crisp function <em>χ<sub>n</sub></em> which is a union of <em>n</em> arcs and whose first <em>n</em> moments match those of <em>f</em> exactly. For <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span>, corresponding to mass and centroid, we give a closed-form solution for the arc endpoints, whereas for <em>n</em> > 2 we present two numerical methods to compute those arcs. As an application, we apply the method to California Independent System Operator (CAISO) net demand data, and show that the four-arc solution automatically produces a midday gap that captures the solar valley, with arc locations emerging from moment-matching constraints rather than threshold selection or manual specification.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109716"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737889","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}
The present study explores the issue of fixed-time control for nonlinear systems that are affected by stochastic perturbations. The issue of infinite gain is effectively addressed by employing a function defined by variable gain over time, and two novel theorems are established. In the first theorem, the scenario is analysed in which both the drift and diffusion terms in stochastic nonlinear systems are known, and this demonstrates that the system achieves fixed-time stability in probability. However, given the potential imperfections inherent in real-world systems, such as model uncertainties and external disturbances, the concept of practical mean-square fixed-time stability is further introduced in Theorem 2. Traditional approaches typically rely on parameter-dependent upper-bound functions to estimate the settling time, which lack flexibility and adaptability to varying system requirements. In contrast, the proposed fixed-time control strategy, which includes a prescribed upper-bound on the dwell time, provides greater flexibility. It enables users to specify the upper limit of the dwell time in accordance with practical requirements. Furthermore, the design of the state-feedback controller employs fuzzy logic systems to approximate the unknown drift and diffusion terms in stochastic nonlinear systems, and by integrating a time-varying gain function, it enables the arbitrary specification of the upper bound on the dwell time. To verify the validity of the prescribed control scheme, this paper presents two simulation case analyses. A comparison and analysis of the results with those obtained by alternative methods demonstrates the rationality and quality of the prescribed control mechanism.
{"title":"Fixed-time stability of unknown stochastic nonlinear systems: A new approach with prescribed upper bound","authors":"Yixuan Yuan , Liping Xie , Junsheng Zhao , Kanjian Zhang","doi":"10.1016/j.fss.2025.109707","DOIUrl":"10.1016/j.fss.2025.109707","url":null,"abstract":"<div><div>The present study explores the issue of fixed-time control for nonlinear systems that are affected by stochastic perturbations. The issue of infinite gain is effectively addressed by employing a function defined by variable gain over time, and two novel theorems are established. In the first theorem, the scenario is analysed in which both the drift and diffusion terms in stochastic nonlinear systems are known, and this demonstrates that the system achieves fixed-time stability in probability. However, given the potential imperfections inherent in real-world systems, such as model uncertainties and external disturbances, the concept of practical mean-square fixed-time stability is further introduced in Theorem 2. Traditional approaches typically rely on parameter-dependent upper-bound functions to estimate the settling time, which lack flexibility and adaptability to varying system requirements. In contrast, the proposed fixed-time control strategy, which includes a prescribed upper-bound on the dwell time, provides greater flexibility. It enables users to specify the upper limit of the dwell time in accordance with practical requirements. Furthermore, the design of the state-feedback controller employs fuzzy logic systems to approximate the unknown drift and diffusion terms in stochastic nonlinear systems, and by integrating a time-varying gain function, it enables the arbitrary specification of the upper bound on the dwell time. To verify the validity of the prescribed control scheme, this paper presents two simulation case analyses. A comparison and analysis of the results with those obtained by alternative methods demonstrates the rationality and quality of the prescribed control mechanism.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109707"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685550","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}
Pub Date : 2026-04-01Epub Date: 2025-11-19DOI: 10.1016/j.fss.2025.109676
Gleb Beliakov , Peiqi Sun , Jian-Zhang Wu
Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization that involve fuzzy integrals as a model to aggregate dependent inputs. We address the problem of random generation of fuzzy measures with specific additional constraints on their values and their combinations that reflect decision maker preferences. We present a range of approaches to handle sparse linear equality constraints and analyse their computational complexity. Some approaches involve random walks in the affine subspaces while others are based on projecting random points in an order polytope onto those affine spaces. We also examine special cases of linear constraints that arise in generation of k-additive fuzzy measures, and provide recommendations on the applicability of the approaches that we examined.
{"title":"Random projections of constrained fuzzy measures","authors":"Gleb Beliakov , Peiqi Sun , Jian-Zhang Wu","doi":"10.1016/j.fss.2025.109676","DOIUrl":"10.1016/j.fss.2025.109676","url":null,"abstract":"<div><div>Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization that involve fuzzy integrals as a model to aggregate dependent inputs. We address the problem of random generation of fuzzy measures with specific additional constraints on their values and their combinations that reflect decision maker preferences. We present a range of approaches to handle sparse linear equality constraints and analyse their computational complexity. Some approaches involve random walks in the affine subspaces while others are based on projecting random points in an order polytope onto those affine spaces. We also examine special cases of linear constraints that arise in generation of k-additive fuzzy measures, and provide recommendations on the applicability of the approaches that we examined.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109676"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790848","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}
Pub Date : 2026-04-01Epub Date: 2025-12-11DOI: 10.1016/j.fss.2025.109729
Keyi Xiao , Yong Su , Wenwen Zong
The modularity holds a significant position in fuzzy set theory, which is closely related to the distributivity and can be viewed as a restricted general associativity equation. In this paper, we study the modularity between semi-t-operators and bi-uninorms, and completely describe the structure of such a pair of functions without any additional assumptions. Several examples are also provided to illustrate the theoretical results.
{"title":"The modularity condition for semi-t-operators and Bi-uninorms","authors":"Keyi Xiao , Yong Su , Wenwen Zong","doi":"10.1016/j.fss.2025.109729","DOIUrl":"10.1016/j.fss.2025.109729","url":null,"abstract":"<div><div>The modularity holds a significant position in fuzzy set theory, which is closely related to the distributivity and can be viewed as a restricted general associativity equation. In this paper, we study the modularity between semi-t-operators and bi-uninorms, and completely describe the structure of such a pair of functions without any additional assumptions. Several examples are also provided to illustrate the theoretical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109729"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790849","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}
Pub Date : 2026-04-01Epub Date: 2025-11-30DOI: 10.1016/j.fss.2025.109706
Roberto G. Aragón , Pascual Jara , Jesús Medina
Lattice-based sum provides a procedure to obtain posets and lattices from families of posets and lattices, respectively. Establishing sufficient conditions to ensure the lattice structure was the most significant challenge achieved in previous works. Next steps are to consider structures with general operators defined on the lattices of the family, introduce a sum of these operators on the obtained lattice-based sum and study the properties preserved by this new definition. We will prove that the natural definition preserve, in general, the monotonicity, associativity, commutativity, etc. This paper also introduces a new mechanism focused on preserving the left-continuity property of the operators defined on the lattices. This new approach also preserves the associativity and the infimum of non-empty subsets, and takes into account (infinite) complete lattices, unlike the previous works.
{"title":"General and left-continuous operators on lattice-based sums","authors":"Roberto G. Aragón , Pascual Jara , Jesús Medina","doi":"10.1016/j.fss.2025.109706","DOIUrl":"10.1016/j.fss.2025.109706","url":null,"abstract":"<div><div>Lattice-based sum provides a procedure to obtain posets and lattices from families of posets and lattices, respectively. Establishing sufficient conditions to ensure the lattice structure was the most significant challenge achieved in previous works. Next steps are to consider structures with general operators defined on the lattices of the family, introduce a sum of these operators on the obtained lattice-based sum and study the properties preserved by this new definition. We will prove that the natural definition preserve, in general, the monotonicity, associativity, commutativity, etc. This paper also introduces a new mechanism focused on preserving the left-continuity property of the operators defined on the lattices. This new approach also preserves the associativity and the infimum of non-empty subsets, and takes into account (infinite) complete lattices, unlike the previous works.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109706"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685549","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}
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