Fuzzy Sets and Systems最新文献

{"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}

{"title":"Ordinal sums of quasi-overlap functions on bounded lattices","authors":"Jun Geng ,&nbsp;Yutong Zhang ,&nbsp;Junsheng Qiao","doi":"10.1016/j.fss.2025.109581","DOIUrl":"10.1016/j.fss.2025.109581","url":null,"abstract":"<div><div>In this paper, we originally explore the ordinal sum equations of quasi-overlap functions on bounded lattices taking into account the potential incomparability of elements within the lattice structures. First, we give the ordinal sum of quasi-overlap functions on bounded lattices with more summands including finite and infinite cases, and establish the corresponding characterization theorems. Subsequently, we study another ordinal sum of quasi-overlap functions still being a quasi-overlap function on more general lattice structures. Finally, we investigate features of the underlying lattices to make the ordinal sum retains key properties of the given quasi-overlap functions. Additionally, some illustrative examples are provided for clarity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109581"},"PeriodicalIF":2.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049885","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 adaptive double-parameter softmin based Takagi-Sugeno-Kang fuzzy system for high-dimensional data","authors":"Ming Ma,&nbsp;Liyang Qian,&nbsp;Yi Zhang,&nbsp;Qi Fang,&nbsp;Guangdong Xue","doi":"10.1016/j.fss.2025.109582","DOIUrl":"10.1016/j.fss.2025.109582","url":null,"abstract":"<div><div>Fuzzy or neuro-fuzzy systems have been widely applied across numerous fields. However, they still face significant challenges when addressing high-dimensional problems. This is primarily due to the use of product T-norm, minimum T-norm and its softer variants. In this context, we construct an adaptive double-parameter softmin (ADP-softmin) based Takagi-Sugeno-Kang fuzzy model, called ADPTSK, where ADP-softmin is proposed to overcome the drawbacks of “numeric underflow” and “fake minimum” prevalent in existing fuzzy systems (FSs) when handling high-dimensional data. During the design process of ADP-softmin, we discover that the traditional Gaussian membership function (Gaussian TMF) may lead to ADPTSK FS crash due to its not having a positive infimum, prompting us to give a Gaussian membership function with a positive infimum (Gaussian PIMF). The effective combination of ADP-softmin and Gaussian PIMF enables ADPTSK to handle data with over one hundred thousand features. The ADPTSK is evaluated on 14 classification datasets with feature dimensions ranging from 1,024 to 120,432. The experimental results indicate that ADPTSK exhibits competitive performance in handling high-dimensional problems.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109582"},"PeriodicalIF":2.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049888","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":"Chain-based Sugeno-like operators: A new take on the Sugeno integral as a scientometric tool","authors":"Jana Borzová,&nbsp;Ondrej Hutník,&nbsp;Miriam Kleinová","doi":"10.1016/j.fss.2025.109578","DOIUrl":"10.1016/j.fss.2025.109578","url":null,"abstract":"<div><div>The Sugeno integral is a highly versatile aggregation tool with extensive applications across various mathematical disciplines. Traditionally, its formula operates on a rearranged nonnegative vector with respect to a monotone measure, whose values are subsequently aggregated through maximum and minimum operations. A key element behind this process is the maximal chain of sets generated by permuting the input vector. In this work, we extend the Sugeno integral by introducing a chain-based approach and generalizing the aggregation operators. This leads to a novel formulation of the chain-based Sugeno-like operator, providing a robust framework for analyzing and extending scientometric indices. After exemplifying its special cases from the literature and establishing its fundamental properties, we demonstrate how numerous scientometric indices emerge as special cases of the CSu-operator, presenting their integral representations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109578"},"PeriodicalIF":2.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049886","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":"Some new properties of decomposition integrals and the extensions of fuzzy entropies","authors":"Rui Lv ,&nbsp;Jun Li ,&nbsp;Yuhuan Wang ,&nbsp;Zhanxin Yang","doi":"10.1016/j.fss.2025.109577","DOIUrl":"10.1016/j.fss.2025.109577","url":null,"abstract":"<div><div>In this paper, we further investigate some important characteristics of decomposition integrals and present several fundamental properties with universality. We mainly focus on the Choquet integral, the pan-integral, the concave integral and the Shilkret integral, which are four commonly used and important decomposition integrals. Some interesting properties of these integrals are demonstrated, respectively. By utilizing these properties, we generalize the entropy of fuzzy sets on continuous domain from Lebesgue measure spaces to fuzzy measure spaces, and establish various forms of fuzzy entropies based on decomposition integrals. We show four kinds of the generalized Knopfmacher entropies and the generalized Yager entropies, respectively. The previous results of fuzzy entropies obtained by Knopfmacher and Yager become special cases of our results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"521 ","pages":"Article 109577"},"PeriodicalIF":2.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049884","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":"The ⁎-fuzzy Lebesgue-Radon-Nikodym theorem and differentiation in fuzzy measure theory","authors":"Abbas Ghaffari ,&nbsp;Reza Chaharpashlou","doi":"10.1016/j.fss.2025.109579","DOIUrl":"10.1016/j.fss.2025.109579","url":null,"abstract":"<div><div>Based on the foundational work by Ghaffari et al. (2022) <span><span>[2]</span></span>, which introduced a new framework for fuzzy measure theory and integration via triangular norm-based decomposable time-stamped fuzzy number-valued measures, this paper provides a comprehensive study of ⁎-fuzzy Lebesgue-Stieltjes measures and ⁎-fuzzy differentiation. We establish an analogue of the classical Lebesgue-Radon-Nikodym theorem in the fuzzy context, extending absolute continuity and measure decomposition concepts to fuzzy measure spaces where values are fuzzy numbers and operations are constructed through continuous triangular norms. Moreover, we present the Lebesgue differentiation theorem for ⁎-fuzzy Lebesgue measures on Euclidean spaces. Our results establish a robust analytical framework for fuzzy integration and differentiation, with potential applications in control theory, risk modeling, and the study of fuzzy differential equations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"523 ","pages":"Article 109579"},"PeriodicalIF":2.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145229862","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}