Pub Date : 2026-01-08DOI: 10.1016/j.fss.2026.109766
Zhenyu Xiu , Xu Zheng
In this paper, we primarily investigate methods for generating uninorms on complete lattices using monotone functions and their pseudo-inverses. First, we present a construction of a uninorm on a complete lattice based on a t-norm, a complete inf-homomorphism, and its pseudo-inverse. Next, we introduce a new method for generating a uninorm via a given uninorm, a complete inf-homomorphism, and its pseudo-inverse. Finally, we explore methods for constructing a uninorm on a complete lattice using a given uninorm together with an injective complete inf-homomorphism and its pseudo-inverse.
{"title":"Construction of uninorms on complete lattices by a monotone function and its pseudo-inverse","authors":"Zhenyu Xiu , Xu Zheng","doi":"10.1016/j.fss.2026.109766","DOIUrl":"10.1016/j.fss.2026.109766","url":null,"abstract":"<div><div>In this paper, we primarily investigate methods for generating uninorms on complete lattices using monotone functions and their pseudo-inverses. First, we present a construction of a uninorm on a complete lattice based on a t-norm, a complete inf-homomorphism, and its pseudo-inverse. Next, we introduce a new method for generating a uninorm via a given uninorm, a complete inf-homomorphism, and its pseudo-inverse. Finally, we explore methods for constructing a uninorm on a complete lattice using a given uninorm together with an injective complete inf-homomorphism and its pseudo-inverse.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"531 ","pages":"Article 109766"},"PeriodicalIF":2.7,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981151","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 : 2026-01-08DOI: 10.1016/j.fss.2026.109762
Qian Wang , Lian Duan , Lihong Huang , Xianwen Fang
It is known that finite-time synchronization is crucial in engineering applications, such as blockchain consensus protocols. Additionally, fields such as smart grids, UAV swarms, and autonomous driving rely on finite-time synchronization to enhance the robustness and real-time performance of cooperative control, preventing performance degradation or safety risks caused by communication delays. This paper is concerned with the finite-time synchronization problem of fuzzy delayed Cohen-Grossberg neural networks (CGNNs) in which the activation functions are discontinuous. By designing delay-independent feedback controllers combined with new analytical techniques, some novel finite-time synchronization criteria are established without using the widely employed finite-time stability theory, which greatly enriches the theory of complex neurodynamics. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
{"title":"New results on finite-time synchronization of fuzzy delayed Cohen-Grossberg neural networks with discontinuous activations","authors":"Qian Wang , Lian Duan , Lihong Huang , Xianwen Fang","doi":"10.1016/j.fss.2026.109762","DOIUrl":"10.1016/j.fss.2026.109762","url":null,"abstract":"<div><div>It is known that finite-time synchronization is crucial in engineering applications, such as blockchain consensus protocols. Additionally, fields such as smart grids, UAV swarms, and autonomous driving rely on finite-time synchronization to enhance the robustness and real-time performance of cooperative control, preventing performance degradation or safety risks caused by communication delays. This paper is concerned with the finite-time synchronization problem of fuzzy delayed Cohen-Grossberg neural networks (CGNNs) in which the activation functions are discontinuous. By designing delay-independent feedback controllers combined with new analytical techniques, some novel finite-time synchronization criteria are established without using the widely employed finite-time stability theory, which greatly enriches the theory of complex neurodynamics. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109762"},"PeriodicalIF":2.7,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978957","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 : 2026-01-07DOI: 10.1016/j.fss.2026.109761
Pavel Martinek
The paper provides a survey of several ways how to describe fuzzy multiset regular languages, i.e., languages generated by fuzzy multiset regular grammars. These languages can also be characterized by means of fuzzy multiset finite automata (both in general and in reduced forms), fuzzy multiset regular expressions, and as fuzzy multiset languages which can be expressed in a semilinear form. Moreover, it is pointed out that a prevailing number of already published papers concerning fuzzy multiset finite automata is based on a wrong definition. It is also shown that the name ‘deterministic fuzzy multiset finite automaton’ is often used incorrectly for automata deserving adjective pseudodeterministic.
{"title":"Fuzzy multiset regular languages and their basic characterizations","authors":"Pavel Martinek","doi":"10.1016/j.fss.2026.109761","DOIUrl":"10.1016/j.fss.2026.109761","url":null,"abstract":"<div><div>The paper provides a survey of several ways how to describe fuzzy multiset regular languages, i.e., languages generated by fuzzy multiset regular grammars. These languages can also be characterized by means of fuzzy multiset finite automata (both in general and in reduced forms), fuzzy multiset regular expressions, and as fuzzy multiset languages which can be expressed in a semilinear form. Moreover, it is pointed out that a prevailing number of already published papers concerning fuzzy multiset finite automata is based on a wrong definition. It is also shown that the name ‘deterministic fuzzy multiset finite automaton’ is often used incorrectly for automata deserving adjective pseudodeterministic.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"531 ","pages":"Article 109761"},"PeriodicalIF":2.7,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981150","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}
Long-term time series forecasting constitutes a significant area of research within data mining, pattern analysis, and recognition. Although the Gaussian linear fuzzy information granule (GLFIG) has garnered increasing attention as an efficient approach for long-term time series forecasting, it continues to face substantial challenges, including the quantification of trend extraction objectives, the non-metric nature of granular distance formulations, and the effective mining of granular structural information. To address these challenges, this study designs a long-term forecasting model based on GLFIGs, incorporating optimized trend information and enhanced periodic patterns. First, the model improves the extraction of trend information through an l1-trend filter, which provides a principled basis for parameter selection. Second, periodic structures within the granular time series are refined to mitigate structural distortions caused by real-world data complexity, and a metric-compliant distance formula for GLFIGs of unequal length is introduced for the first time. Finally, a CNN-LSTM architecture augmented with periodic information is employed for long-term forecasting, leveraging long short-term memory (LSTM) to complement the limited temporal sensitivity of convolutional neural networks (CNNs). Experiments conducted on ten publicly available time series datasets demonstrate that the proposed model achieves satisfactory predictive accuracy in long-term univariate time series forecasting.
{"title":"A long-term prediction model with Gaussian linear fuzzy granules based on convolutional neural networks and long short-term memory","authors":"Xueling Ma , Chenglong Zhu , Weiping Ding , Pierpaolo D’ Urso , Jianming Zhan","doi":"10.1016/j.fss.2026.109765","DOIUrl":"10.1016/j.fss.2026.109765","url":null,"abstract":"<div><div>Long-term time series forecasting constitutes a significant area of research within data mining, pattern analysis, and recognition. Although the Gaussian linear fuzzy information granule (GLFIG) has garnered increasing attention as an efficient approach for long-term time series forecasting, it continues to face substantial challenges, including the quantification of trend extraction objectives, the non-metric nature of granular distance formulations, and the effective mining of granular structural information. To address these challenges, this study designs a long-term forecasting model based on GLFIGs, incorporating optimized trend information and enhanced periodic patterns. First, the model improves the extraction of trend information through an <em>l</em><sub>1</sub>-trend filter, which provides a principled basis for parameter selection. Second, periodic structures within the granular time series are refined to mitigate structural distortions caused by real-world data complexity, and a metric-compliant distance formula for GLFIGs of unequal length is introduced for the first time. Finally, a CNN-LSTM architecture augmented with periodic information is employed for long-term forecasting, leveraging long short-term memory (LSTM) to complement the limited temporal sensitivity of convolutional neural networks (CNNs). Experiments conducted on ten publicly available time series datasets demonstrate that the proposed model achieves satisfactory predictive accuracy in long-term univariate time series forecasting.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109765"},"PeriodicalIF":2.7,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940523","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 : 2026-01-06DOI: 10.1016/j.fss.2026.109764
Yao Ouyang , Qiuyu Cao , Hua-Peng Zhang
Given a curvilinear section, there are three known copulas. We prove that two of them are always singular and the third one is also singular under some mild condition. With the aid of the two always singular copulas and by employing the rectangular patchwork of copulas, we explore when there exists an absolutely continuous copula with a given curvilinear section. Several sufficient conditions and one necessary condition are discovered for the existence problem. The Durante-Jaworski theorem is retrieved when the curvilinear section reduces to a diagonal section.
{"title":"Absolutely continuous copulas with a given curvilinear section","authors":"Yao Ouyang , Qiuyu Cao , Hua-Peng Zhang","doi":"10.1016/j.fss.2026.109764","DOIUrl":"10.1016/j.fss.2026.109764","url":null,"abstract":"<div><div>Given a curvilinear section, there are three known copulas. We prove that two of them are always singular and the third one is also singular under some mild condition. With the aid of the two always singular copulas and by employing the rectangular patchwork of copulas, we explore when there exists an absolutely continuous copula with a given curvilinear section. Several sufficient conditions and one necessary condition are discovered for the existence problem. The Durante-Jaworski theorem is retrieved when the curvilinear section reduces to a diagonal section.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109764"},"PeriodicalIF":2.7,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940521","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 : 2026-01-05DOI: 10.1016/j.fss.2025.109751
Luís Miguel Magalhães Torres , Ginalber Luiz de Oliveira Serra
This paper presents an evolving state-space interval type-2 Takagi-Sugeno identification algorithm. The methodology integrates an online particle swarm optimization scheme, which tunes the footprint of uncertainty by minimizing a coverage-width objective, with a filtering-based recursive estimation of fuzzy Markov parameters that provides unbiased consequent parameters under non-white noise. The antecedent structure is updated online through density-based rule creation, adaptation, and pruning. The approach is validated on a nonlinear benchmark with abrupt and gradual parameter changes and on a two-degrees-of-freedom helicopter. Compared to state-of-the-art methods, the proposed algorithm achieves lower error and higher-quality prediction intervals.
{"title":"Evolving interval type-2 fuzzy state-space identification using PSO-tuned footprint of uncertainty and filtered markov parameters","authors":"Luís Miguel Magalhães Torres , Ginalber Luiz de Oliveira Serra","doi":"10.1016/j.fss.2025.109751","DOIUrl":"10.1016/j.fss.2025.109751","url":null,"abstract":"<div><div>This paper presents an evolving state-space interval type-2 Takagi-Sugeno identification algorithm. The methodology integrates an online particle swarm optimization scheme, which tunes the footprint of uncertainty by minimizing a coverage-width objective, with a filtering-based recursive estimation of fuzzy Markov parameters that provides unbiased consequent parameters under non-white noise. The antecedent structure is updated online through density-based rule creation, adaptation, and pruning. The approach is validated on a nonlinear benchmark with abrupt and gradual parameter changes and on a two-degrees-of-freedom helicopter. Compared to state-of-the-art methods, the proposed algorithm achieves lower error and higher-quality prediction intervals.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109751"},"PeriodicalIF":2.7,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940522","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 : 2026-01-04DOI: 10.1016/j.fss.2026.109763
Jianzhang Wu
This comment concerns the paper “Another view on the non-additivity index of capacity” (Fuzzy Sets and Systems, Vol. 520, 2025, 109569). The classical non-additivity index (NI), defined through proper bipartitions, quantifies deviations from additivity. The generalized NI (GNI) proposed in the target paper extends this definition by including both the empty set and the coalition itself. We clarify that singleton cases are to be interpreted as importance rather than interaction, and show that the generalized extension adds little useful information and meanwhile misrepresents strict non-additivity. We further demonstrate that Properties 6, 7, and 8, together with the induced monotonicity constraints presented in the target paper as major contributions, are invalid and unreliable. Finally, we compare the properties of NI and GNI and emphasize that the classical NI uniquely satisfies key structural properties such as uniform range, maximality, and minimality.
{"title":"On “another view on the non-additivity index of capacity”","authors":"Jianzhang Wu","doi":"10.1016/j.fss.2026.109763","DOIUrl":"10.1016/j.fss.2026.109763","url":null,"abstract":"<div><div>This comment concerns the paper “Another view on the non-additivity index of capacity” (Fuzzy Sets and Systems, Vol. 520, 2025, 109569). The classical non-additivity index (NI), defined through proper bipartitions, quantifies deviations from additivity. The generalized NI (GNI) proposed in the target paper extends this definition by including both the empty set and the coalition itself. We clarify that singleton cases are to be interpreted as importance rather than interaction, and show that the generalized extension adds little useful information and meanwhile misrepresents strict non-additivity. We further demonstrate that Properties 6, 7, and 8, together with the induced monotonicity constraints presented in the target paper as major contributions, are invalid and unreliable. Finally, we compare the properties of NI and GNI and emphasize that the classical NI uniquely satisfies key structural properties such as uniform range, maximality, and minimality.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109763"},"PeriodicalIF":2.7,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940518","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 : 2026-01-01DOI: 10.1016/j.fss.2025.109747
Francisco David Camacho-Gonzalez , Jesús Ariel Carrasco-Ochoa , José Francisco Martínez-Trinidad
Goldman’s fuzzy reducts are subsets of attributes that allows for preserving the discernibility capacity of the whole set of attributes, in these subsets each attribute has an associated discernibility value, which can be interpreted as the capacity the correspeponing attribute has to discern objects of different class. Computing all Goldman’s fuzzy reducts is time-consuming, and few algorithms have been proposed in the literature. For these reasons, this paper introduces a new algorithm for computing all Goldman’s fuzzy reducts. The proposed algorithm traverses the search space following a new ordering and applies pruning properties, introduced in this paper, that help avoid exhaustively evaluating the reduct definition and discarding subsets. Additionally, we introduced a concept of density for simplified non-Boolean discernibility matrices that allows a density-based characterization of the algorithms’ performance. The proposed algorithm is evaluated and compared against state-of-the-art algorithms on synthetic and real decision systems. From our experiments, we determine the matrix type regarding density, where our algorithm performs the best.
{"title":"Algorithm for computing all Goldman’s fuzzy reducts","authors":"Francisco David Camacho-Gonzalez , Jesús Ariel Carrasco-Ochoa , José Francisco Martínez-Trinidad","doi":"10.1016/j.fss.2025.109747","DOIUrl":"10.1016/j.fss.2025.109747","url":null,"abstract":"<div><div>Goldman’s fuzzy reducts are subsets of attributes that allows for preserving the discernibility capacity of the whole set of attributes, in these subsets each attribute has an associated discernibility value, which can be interpreted as the capacity the correspeponing attribute has to discern objects of different class. Computing all Goldman’s fuzzy reducts is time-consuming, and few algorithms have been proposed in the literature. For these reasons, this paper introduces a new algorithm for computing all Goldman’s fuzzy reducts. The proposed algorithm traverses the search space following a new ordering and applies pruning properties, introduced in this paper, that help avoid exhaustively evaluating the reduct definition and discarding subsets. Additionally, we introduced a concept of density for simplified non-Boolean discernibility matrices that allows a density-based characterization of the algorithms’ performance. The proposed algorithm is evaluated and compared against state-of-the-art algorithms on synthetic and real decision systems. From our experiments, we determine the matrix type regarding density, where our algorithm performs the best.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109747"},"PeriodicalIF":2.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978883","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 : 2025-12-31DOI: 10.1016/j.fss.2025.109750
Zhilong He , Chuandong Li , Cheng Hu , Zhiyong Yu , Haijun Jiang , Shiping Wen
This paper investigates the stability and stabilization of nonlinear time-delay systems via a novel Takagi-Sugeno (T-S) fuzzy hybrid impulsive controller that explicitly accounts for both input delay and saturation, enhancing its practical applicability. The main contributions are threefold. First, a new impulse-time-related Lyapunov function (ITRLF) is constructed, which synergistically integrates the impulsive Razumikhin technique with an improved convex hull representation to handle saturation nonlinearities effectively. Second, sufficient conditions in the form of linear matrix inequalities (LMIs) are established to ensure local exponential stability. A key advantage of these conditions is that they depend only on the bounds of impulse delays and intervals, eliminating the restrictive requirement of a specific relationship between them, thus reducing conservatism. Third, novel LMI-based optimization algorithms are proposed to maximize the estimation of the region of attraction (ROA), effectively trading off computational complexity for significantly reduced conservatism compared to conventional methods. The effectiveness and advantages of the proposed approach are validated through numerical simulations using the MATLAB LMI toolbox.
{"title":"Stability analysis of T-S fuzzy delayed impulsive systems with input saturation via an impulse-time-related function method","authors":"Zhilong He , Chuandong Li , Cheng Hu , Zhiyong Yu , Haijun Jiang , Shiping Wen","doi":"10.1016/j.fss.2025.109750","DOIUrl":"10.1016/j.fss.2025.109750","url":null,"abstract":"<div><div>This paper investigates the stability and stabilization of nonlinear time-delay systems via a novel Takagi-Sugeno (T-S) fuzzy hybrid impulsive controller that explicitly accounts for both input delay and saturation, enhancing its practical applicability. The main contributions are threefold. First, a new impulse-time-related Lyapunov function (ITRLF) is constructed, which synergistically integrates the impulsive Razumikhin technique with an improved convex hull representation to handle saturation nonlinearities effectively. Second, sufficient conditions in the form of linear matrix inequalities (LMIs) are established to ensure local exponential stability. A key advantage of these conditions is that they depend only on the bounds of impulse delays and intervals, eliminating the restrictive requirement of a specific relationship between them, thus reducing conservatism. Third, novel LMI-based optimization algorithms are proposed to maximize the estimation of the region of attraction (ROA), effectively trading off computational complexity for significantly reduced conservatism compared to conventional methods. The effectiveness and advantages of the proposed approach are validated through numerical simulations using the MATLAB LMI toolbox.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109750"},"PeriodicalIF":2.7,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940524","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 : 2025-12-29DOI: 10.1016/j.fss.2025.109748
Ángel López Oriona, Ying Sun
The global approach has recently been shown to often outperform the local approach in time series forecasting. While the former fits a single model to all time series in a dataset, the latter fits a separate model to each series and therefore does not leverage potential similarities in the underlying structures across the time series collection. Empirical analyses have demonstrated that, in heterogeneous datasets, fitting per-cluster global models can further improve forecasting accuracy compared to the standard global approach. These methods obtain forecasts for a given time series using the global model associated with its corresponding cluster. In this paper, we show that combining the per-cluster approach with the fuzzy clustering paradigm can lead to even better predictive performance. Specifically, we propose a fuzzy clustering algorithm based on prediction accuracy of global models. The fuzzy partition is constructed by evaluating the prediction error of each series with respect to each global model. Forecasts for a given series are then obtained as a weighted average of the forecasts from all models, with weights determined by the corresponding membership degrees. The potential of the proposed approach is demonstrated using well-known time series datasets from several contexts. Improvements of up to 30% in forecasting error are achieved compared to the best of three strong benchmark methods.
{"title":"Forecasting time series collections via fuzzy clustering","authors":"Ángel López Oriona, Ying Sun","doi":"10.1016/j.fss.2025.109748","DOIUrl":"10.1016/j.fss.2025.109748","url":null,"abstract":"<div><div>The global approach has recently been shown to often outperform the local approach in time series forecasting. While the former fits a single model to all time series in a dataset, the latter fits a separate model to each series and therefore does not leverage potential similarities in the underlying structures across the time series collection. Empirical analyses have demonstrated that, in heterogeneous datasets, fitting per-cluster global models can further improve forecasting accuracy compared to the standard global approach. These methods obtain forecasts for a given time series using the global model associated with its corresponding cluster. In this paper, we show that combining the per-cluster approach with the fuzzy clustering paradigm can lead to even better predictive performance. Specifically, we propose a fuzzy clustering algorithm based on prediction accuracy of global models. The fuzzy partition is constructed by evaluating the prediction error of each series with respect to each global model. Forecasts for a given series are then obtained as a weighted average of the forecasts from all models, with weights determined by the corresponding membership degrees. The potential of the proposed approach is demonstrated using well-known time series datasets from several contexts. Improvements of up to 30% in forecasting error are achieved compared to the best of three strong benchmark methods.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"530 ","pages":"Article 109748"},"PeriodicalIF":2.7,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145877099","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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