Fuzzy Sets and Systems最新文献

{"title":"Fuzzy iterative learning control for nonlinear parabolic distributed parameter systems","authors":"Xisheng Dai ,&nbsp;Yanxue Wang ,&nbsp;Senping Tian ,&nbsp;Yangquan Chen ,&nbsp;Zhijia Zhao","doi":"10.1016/j.fss.2025.109603","DOIUrl":"10.1016/j.fss.2025.109603","url":null,"abstract":"<div><div>This study investigates fuzzy iterative learning control (ILC) for a class of nonlinear parabolic distributed parameter system (DPS). A Takagi-Sugeno (T-S) fuzzy DPS model with parameter uncertainty is proposed to approximate the nonlinear DPS. Based on this model, a fuzzy p-type ILC algorithm related to membership function is designed, which can adjust learning gain according to the system output error. Moreover, the fuzzy learning gain of this algorithm can be obtained by solving linear matrix inequality (LMI). By constructing a Lyapunov function, the system's tracking error in terms of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm is proven to converge to zero, while input error is proved monotonically convergent as well. Finally, the effectiveness of the algorithm is verified by two numerical simulations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109603"},"PeriodicalIF":2.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159428","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}

{"title":"Rational linear kernelized weighted fuzzy rough attribute selection with class separability","authors":"Yue Yang ,&nbsp;Jihong Wan ,&nbsp;Xiaoping Li ,&nbsp;Xiaoling Yang ,&nbsp;Hongmei Chen ,&nbsp;Kay Chen Tan ,&nbsp;Chris Cornelis","doi":"10.1016/j.fss.2025.109600","DOIUrl":"10.1016/j.fss.2025.109600","url":null,"abstract":"<div><div>Attribute selection is widely used in data mining to reduce dimensionality and computational overhead, which improves the generalization and efficiency of machine learning models. However, it is a challenging task to select the most representative subset of attributes from data characterized by uncertainty, sparsity, and heterogeneity. Most existing fuzzy rough set-based attribute selection methods focus on improving specific characteristics without a comprehensive consideration, limiting their effectiveness. Moreover, these methods overlook the class distribution information in data, which leads to poor representation of the selected attribute subset. Motivated by these issues, a Rational Linear kernelized weighted fuzzy rough attribute selection method with class separability (RLWAS-CS) is proposed in this paper. A Rational Linear (RL) kernelized fuzzy similarity relation, derived from the Rational Quadratic kernel and mixed attribute distance measure, is first defined to accurately capture sample similarities in sparse and heterogeneous space. On this basis, an RL kernelized weighted fuzzy rough set model (RLWFRS) is proposed. In this model, the weight comprehensively reflects the membership between the sample and each class in the complete attribute space, which improves the discriminability of fuzzy approximation membership and enhances its ability to handle uncertainty. Additionally, an attribute evaluation function is designed based on the RLWFRS model. It integrates class separability and captures both the class distribution characteristics and the dynamic relation between attribute separability and redundancy. Finally, the RLWAS-CS algorithm is presented for the attribute selection. Experimental results show that RLWAS-CS outperforms baseline methods in effectiveness.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109600"},"PeriodicalIF":2.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159429","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}

{"title":"Quotient approximation spaces under fuzzy β−coverings","authors":"Liwen Ma ,&nbsp;Shizhe Zhang","doi":"10.1016/j.fss.2025.109601","DOIUrl":"10.1016/j.fss.2025.109601","url":null,"abstract":"<div><div>The quotient space is the main research object in the process of transforming a fine-grained space into a coarse-grained space. However, in order to achieve better application results, we are relatively lacking in effective rough operator models to realize the regular approximation transformations between the original space and its quotient space. In response to this situation, we will attempt to adopt a completely new approach to define novel and effective fuzzy <em>β</em>-covering rough set operator models on the original space and its quotient space, thereby establishing a better transformation relationships and related applications. Firstly, we define an induced fuzzy quotient mapping by the natural quotient mapping. This allowed the series of concepts and related conclusions of crisp subsets under the natural mapping to be extended to the fuzzy subsets under the induced fuzzy quotient mapping. Then the quotient fuzzy <em>β</em>-covering approximation space is defined, and novel fuzzy <em>β</em>-covering rough set operator models are built. We not only study their interesting transformation properties, but also compare the new models with the existing ones. Furthermore, a wealth of examples are provided to explain each new concept and demonstrate the simple applications of the main results. More importantly, the profound topological essence and significance revealed lies in that, under the induced fuzzy quotient mapping, the transformations of the lower approximation and the upper approximation exhibit exactly the same behavior as the transformations of the interior and closure under a topological continuous mapping. Finally, the shortcomings of this paper are summarized and the prospects for future research are presented.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"522 ","pages":"Article 109601"},"PeriodicalIF":2.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160334","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}

{"title":"Nullnorms on bounded trellises","authors":"Zhenyu Xiu ,&nbsp;Xu Zheng","doi":"10.1016/j.fss.2025.109599","DOIUrl":"10.1016/j.fss.2025.109599","url":null,"abstract":"<div><div>In this paper, we first introduce the notion of nullnorms on bounded trellises and investigate their fundamental properties. Then, based on the existence of t-norms, t-conorms, two order-preserving functions, and a conditionally associative, commutative and increasing function, we propose a method for constructing nullnorms on bounded trellises. Finally, we prove that the class of nullnorms on bounded trellises, denoted by <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span>, can be completely characterized by these four components. Meanwhile, our results on nullnorms extend and unify several well-known results in the literature.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109599"},"PeriodicalIF":2.7,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121141","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}

{"title":"Optimal H∞ adaptive fuzzy observer-based reference tracking control of nonlinear stochastic systems under uncertain measurement function and noise","authors":"Bor-Sen Chen,&nbsp;Chung-Hsun Hsueh,&nbsp;Ruei-Syuan Wu","doi":"10.1016/j.fss.2025.109597","DOIUrl":"10.1016/j.fss.2025.109597","url":null,"abstract":"<div><div>The optimal <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> adaptive fuzzy observer-based indirect reference tracking control designs are proposed in this study for both uncertain SISO and MIMO nonlinear stochastic systems with nonlinear uncertain measurement functions and measurement noise. In contrast to conventional observer-based adaptive control designs that assume exact linear output measurement functions and ignore measurement noise, the proposed method utilizes adaptive fuzzy logic system (FLS) embedded in indirect adaptive controller and observer to effectively cancel the nonlinear uncertain system function and measurement function, respectively. Then, the optimal <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> adaptive observer-based reference tracking control design strategy is proposed to efficiently minimize the worst-case effect of the adaptive FLS approximation errors, environmental disturbance and output measurement noise on both the reference tracking error and state estimation error of uncertain nonlinear stochastic systems. The study demonstrates that achieving the optimal <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> adaptive observer-based reference tracking control design strategy requires solving a linear matrix inequalities (LMIs)-constrained optimization problem for the adaptive laws and the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> adaptive observer-based reference tracking control law. Finally, we provide two simulation examples to validate the proposed optimal <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> adaptive observer-based reference tracking control design in SISO and MIMO nonlinear stochastic systems with nonlinear uncertain system functions, measurement functions, environmental disturbance and measurement noise.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109597"},"PeriodicalIF":2.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121142","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}

{"title":"Directly compatible copulas","authors":"Roberto Ghiselli Ricci","doi":"10.1016/j.fss.2025.109594","DOIUrl":"10.1016/j.fss.2025.109594","url":null,"abstract":"<div><div>In this paper, we deal with the problem of preserving the copula property by means of a suitable composition of a multivariate copula with a bivariate one. A deep connection with a general method of construction of copulas, called distortion, is shown. The methodology is grounded in a general theorem connecting the <em>d</em>-increasingness property of a real function of <em>d</em>-variables to its partial derivatives. A characterization theorem is proved. Several examples are presented.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109594"},"PeriodicalIF":2.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099652","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}

{"title":"Mixed H∞/passive fuzzy control for singularly perturbed semi-Markov jump systems under weighted try-once-discard protocol","authors":"Hao Shen ,&nbsp;Chao Jiang ,&nbsp;Jing Wang ,&nbsp;Jinde Cao","doi":"10.1016/j.fss.2025.109593","DOIUrl":"10.1016/j.fss.2025.109593","url":null,"abstract":"<div><div>In this paper, the output feedback control problem is addressed for fuzzy singularly perturbed semi-Markov jump systems with a weighted try-once-discard protocol. To ensure effective information transmission, a weighted try-once-discard protocol is employed to conserve communication resources under limited bandwidth. Additionally, the Kronecker delta function is utilized to model the rate of information updates. By analyzing the expected value of the Lyapunov function at the virtual point, the mean square exponential stability criterion is derived. Next, the mixed performance of the discrete-time systems is systematically evaluated. Then, a static output feedback controller based on the weighted try-once-discard protocol is designed. Finally, two simulation examples are presented to demonstrate the effectiveness and practicality of the designed controller.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109593"},"PeriodicalIF":2.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099653","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}

{"title":"An OWA-based multi-granulation fuzzy rough set model using Choquet integrals and its applications","authors":"Jingqian Wang ,&nbsp;Xiaohong Zhang ,&nbsp;Lingling Mao","doi":"10.1016/j.fss.2025.109595","DOIUrl":"10.1016/j.fss.2025.109595","url":null,"abstract":"<div><div>Rough set theory has been widely utilized in the field of intelligent information processing for representing and managing uncertain knowledge. However, most existing fuzzy rough set models rely on simple logical operators (e.g., ⋁ and ⋀) to aggregate information from multiple granules, which limits their flexibility and adaptability in complex data environments. This paper proposes a new multi-granulation fuzzy rough set model based on ordered weighted averaging (OWA) approaches by using Choquet integrals. The model leverages the flexibility of OWA aggregation and the nonlinear integration capability of Choquet integrals to effectively fuse information from multiple fuzzy relations. First, a new multi-granulation fuzzy rough set model is established using Choquet integrals with fuzzy measures. When the fuzzy measure is symmetric, the model simplifies to an OWA-based aggregation of fuzzy rough approximations, providing a more flexible and powerful framework for multi-granulation fusion. Next, the relevant characteristics of the model are explored. The presented model satisfies almost all the properties of the classical rough set model. Several innovative concepts for data mining are introduced, including fuzzy rough integral positive region, fuzzy rough integral dependency, and integral dependency reduction. Finally, a quick feature selection algorithm under this new model is proposed. Additionally, the proposed approach is evaluated against existing methods in classification tasks, demonstrating its feasibility and effectiveness through several public datasets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109595"},"PeriodicalIF":2.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121144","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}

{"title":"Parameterized fuzzy β-covering relations-based fuzzy rough set models and their applications to three-way decision and attribute reduction","authors":"Yaoyao Fan ,&nbsp;Xiaohong Zhang ,&nbsp;Jun Liu ,&nbsp;Jingqian Wang","doi":"10.1016/j.fss.2025.109596","DOIUrl":"10.1016/j.fss.2025.109596","url":null,"abstract":"<div><div>In the existing research on fuzzy <em>β</em>-covering rough set (F<em>β</em>-CRS) models, it is often required that the parameter <em>β</em> of each covering be equal, which seriously restricts the flexibility and practical efficiency of the model in applications. Additionally, the existing fuzzy <em>β</em>-neighborhood operators (F<em>β</em>-NOs) have limited expressive power, as most of them fail to satisfy reflexivity or symmetry. Therefore, it is necessary to study a more flexible and general model. To address this issue, this paper constructs some novel F<em>β</em>-NOs and F<em>β</em>-CRS models within a new variable-scale fuzzy <em>β</em>-covering approximation space (VSF<em>β</em>-CAS), and explores their properties. First, based on overlap functions and grouping functions, four types of F<em>β</em>-NOs satisfying reflexivity and symmetry are proposed in VSF<em>β</em>-CAS, which include parameterized fuzzy <em>β</em>-neighborhoods and parameterized fuzzy complementary <em>β</em>-neighborhoods. Their properties are demonstrated and it is proven that all conform to the structural requirements of fuzzy <em>β</em>-covering relations. On this theoretical basis, four F<em>β</em>-CRS models with upper approximation-inclusion lower approximation relations are further constructed. The basic properties of the models and the interrelationships among different models are discussed. Finally, based on the four constructed models, we designed experiments for both samples and attributes, i.e., three-way decision and attribute reduction. First, we applied the four proposed models to three-way decision tasks: we defined both fuzzy and crisp three-way regions, and performed comparative experiments on public datasets using six measurements. Meanwhile, we introduced fuzzy dependency functions and fuzzy composite functions, and developed some variable-scale attribute reduction algorithms. We then conducted in-depth analyses on how different <em>β</em> values and function configurations affect experimental results, and carried out comparative experiments with existing models on public datasets. The experimental results indicate that our models not only demonstrate advantages and rationality in addressing both sample and attribute-related issues, but also exhibit higher flexibility—further validating the strong generalization ability of the proposed models.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109596"},"PeriodicalIF":2.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121143","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}

{"title":"Almost automorphic dynamics to stochastic octonion-valued fuzzy neural networks with delays","authors":"Bing Li ,&nbsp;Yongkun Li ,&nbsp;Huili Xu","doi":"10.1016/j.fss.2025.109592","DOIUrl":"10.1016/j.fss.2025.109592","url":null,"abstract":"<div><div>In this paper, we are concerned with the almost automorphic dynamics for a class of stochastic octonion-valued fuzzy neural networks (SOVFNNs) with delays. Using a non-decomposition approach and without assuming that the activation functions satisfy the global Lipschitz condition, we investigate the existence and uniqueness of almost automorphic solutions in finite-dimensional distributions to this class of SOVFNNs and the global exponential stability of the unique almost automorphic solution in mean square sense, respectively. Firstly, we use the Banach contraction principle to establish the existence of a unique <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-bounded and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-uniformly continuous solution of SOVFNNs in a suitable complete space. Then, we employ some inequality tricks to demonstrate that this unique solution is also an almost automorphic one in finite-dimensional distributions. In addition, we establish the global exponential stability of this almost automorphic solution by contradiction method. Finally, we present an example to validate the obtained results. The results gained in this paper are completely new even when the SOVFNNs degenerate into real-valued neural networks (RVNNs).</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109592"},"PeriodicalIF":2.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061398","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}