Pub Date : 2026-04-01Epub Date: 2025-11-29DOI: 10.1016/j.fss.2025.109699
L.C. Barros , M. Shahidi , E. Esmi , T. Allahviranloo
In this paper, we extend the concepts of differentiability and integrability to some classes of multivariable fuzzy functions, called A-linearly correlated bivariate fuzzy processes. We introduce key concepts such as the A-total and A-directional derivatives for A-linearly correlated bivariate fuzzy processes, along with a tangent plane interpretation and the A-Jacobian matrix. Their properties and relationships are also examined. Moreover, we present the second order Fréchet differentiability for A-linearly correlated bivariate fuzzy processes and define the A-Hessian matrix. Furthermore, we introduce the concept of the A-double integral and apply Fubini’s Theorem to A-linearly correlated bivariate fuzzy processes. We provide several examples demonstrating its practical applications.
{"title":"Interactive calculus: Theory and applications of A-linearly correlated bivariate fuzzy processes","authors":"L.C. Barros , M. Shahidi , E. Esmi , T. Allahviranloo","doi":"10.1016/j.fss.2025.109699","DOIUrl":"10.1016/j.fss.2025.109699","url":null,"abstract":"<div><div>In this paper, we extend the concepts of differentiability and integrability to some classes of multivariable fuzzy functions, called <em>A</em>-linearly correlated bivariate fuzzy processes. We introduce key concepts such as the <em>A</em>-total and <em>A</em>-directional derivatives for <em>A</em>-linearly correlated bivariate fuzzy processes, along with a tangent plane interpretation and the <em>A</em>-Jacobian matrix. Their properties and relationships are also examined. Moreover, we present the second order Fréchet differentiability for <em>A</em>-linearly correlated bivariate fuzzy processes and define the <em>A</em>-Hessian matrix. Furthermore, we introduce the concept of the <em>A</em>-double integral and apply Fubini’s Theorem to <em>A</em>-linearly correlated bivariate fuzzy processes. We provide several examples demonstrating its practical applications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109699"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685552","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: 2025-12-03DOI: 10.1016/j.fss.2025.109717
Firas Kaabi
We introduce the Fuzzy Life-Cycle Gender Equality Index (FLGEI). It treats gender (in)equality as graded membership in a normative set of equal-opportunity life-cycle states. Indicators are aggregated with a non-additive Choquet integral to capture complementarities and limited substitutability across domains. FLGEI separates de jure rights (Women, Business and the Law) from de facto outcomes (household surveys, ILOSTAT, time-use) and defines their difference as an implementation gap. A delay-aversion axiom penalizes persistent late-stage shortfalls. Shapley values and interaction indices provide transparent domain-level attribution. We also describe how the index is identified and estimated, how uncertainty is quantified, and how it can be used in simple counterfactual simulations. A Tunisia-MENA pilot (2000-2024) shows that childcare access and safety constraints jointly limit labor equality even under strong legal frameworks. Relative to additive and crisp alternatives, FLGEI is more stable to small perturbations and improves budget-targeting performance.
{"title":"Beyond parity: A fuzzy life-cycle index of gender equality with legal–Practical implementation gaps","authors":"Firas Kaabi","doi":"10.1016/j.fss.2025.109717","DOIUrl":"10.1016/j.fss.2025.109717","url":null,"abstract":"<div><div>We introduce the <em>Fuzzy Life-Cycle Gender Equality Index</em> (<span>FLGEI</span>). It treats gender (in)equality as graded membership in a normative set of equal-opportunity life-cycle states. Indicators are aggregated with a non-additive Choquet integral to capture complementarities and limited substitutability across domains. <span>FLGEI</span> separates <em>de jure</em> rights (Women, Business and the Law) from <em>de facto</em> outcomes (household surveys, ILOSTAT, time-use) and defines their difference as an implementation gap. A delay-aversion axiom penalizes persistent late-stage shortfalls. Shapley values and interaction indices provide transparent domain-level attribution. We also describe how the index is identified and estimated, how uncertainty is quantified, and how it can be used in simple counterfactual simulations. A Tunisia-MENA pilot (2000-2024) shows that childcare access and safety constraints jointly limit labor equality even under strong legal frameworks. Relative to additive and crisp alternatives, <span>FLGEI</span> is more stable to small perturbations and improves budget-targeting performance.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109717"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737900","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: 2025-12-12DOI: 10.1016/j.fss.2025.109728
Tong Kang , Jun Li , Leifan Yan , Ran Wang
In this note, we present a necessary and sufficient condition of the coincidence for the concave integral and the pan-integral. The previous results on this topic are improved.
本文给出了凹积分与泛积分重合的一个充分必要条件。之前关于这个主题的结果得到了改进。
{"title":"A sufficient and necessary condition of coincidence of the concave integral and the pan-integral","authors":"Tong Kang , Jun Li , Leifan Yan , Ran Wang","doi":"10.1016/j.fss.2025.109728","DOIUrl":"10.1016/j.fss.2025.109728","url":null,"abstract":"<div><div>In this note, we present a necessary and sufficient condition of the coincidence for the concave integral and the pan-integral. The previous results on this topic are improved.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109728"},"PeriodicalIF":2.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790851","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 : 2026-03-15Epub Date: 2025-11-16DOI: 10.1016/j.fss.2025.109677
José R. González de Mendívil , Zorana Jančić , Aitor González de Mendívil Grau , Ivana Micić , Stefan Stanimirović
Minimization of fuzzy deterministic finite automata (FDfAs) is a challenging problem due to two main reasons. First, the graded nature of transitions and state memberships makes traditional minimization techniques difficult to apply. Second, a minimal FDfA is not necessarily unique, as multiple equivalent FDfAs of the same size may exist. In this paper, we focus on finding a polynomial-time minimization method that constructs a minimal FDfA for a given FDfA. Our approach is based on establishing isomorphisms between well-known polynomial-time constructions, providing a mathematical foundation for the proposed method. Specifically, we introduce the notion of quasi-deterministic fuzzy finite automata (QDFfAs) and explore their isomorphism properties with the Myhill-Nerode automaton of a fuzzy language. We show that the determinization via factorization of a QDFfA preserves strong isomorphism with the generalized Myhill-Nerode automaton of the recognized fuzzy language. This insight enables the development of an efficient minimization method by leveraging the interpretable backward replica of an FDfA.
{"title":"Quasi-deterministic fuzzy automata: Isomorphisms and fuzzy deterministic automata minimization","authors":"José R. González de Mendívil , Zorana Jančić , Aitor González de Mendívil Grau , Ivana Micić , Stefan Stanimirović","doi":"10.1016/j.fss.2025.109677","DOIUrl":"10.1016/j.fss.2025.109677","url":null,"abstract":"<div><div>Minimization of fuzzy deterministic finite automata (FDfAs) is a challenging problem due to two main reasons. First, the graded nature of transitions and state memberships makes traditional minimization techniques difficult to apply. Second, a minimal FDfA is not necessarily unique, as multiple equivalent FDfAs of the same size may exist. In this paper, we focus on finding a polynomial-time minimization method that constructs a minimal FDfA for a given FDfA. Our approach is based on establishing isomorphisms between well-known polynomial-time constructions, providing a mathematical foundation for the proposed method. Specifically, we introduce the notion of quasi-deterministic fuzzy finite automata (QDFfAs) and explore their isomorphism properties with the Myhill-Nerode automaton of a fuzzy language. We show that the determinization via factorization of a QDFfA preserves strong isomorphism with the generalized Myhill-Nerode automaton of the recognized fuzzy language. This insight enables the development of an efficient minimization method by leveraging the interpretable backward replica of an FDfA.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109677"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584368","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 : 2026-03-15Epub Date: 2025-11-22DOI: 10.1016/j.fss.2025.109698
Matjaž Omladič , Martin Vuk , Aljaž Zalar
The recent survey [3] nicknamed “Hitchhiker’s Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work we addressed the question of extreme values of the mass distribution associated with a mutidimensional quasi–copulas. Using linear programming approach we were able to settle [3, Open Problem 5] up to and disprove a recent conjecture from [14] on solution to that problem. In this note we use an analytical approach to provide a complete answer to the original question.
{"title":"Extreme mass distributions for quasi-copulas","authors":"Matjaž Omladič , Martin Vuk , Aljaž Zalar","doi":"10.1016/j.fss.2025.109698","DOIUrl":"10.1016/j.fss.2025.109698","url":null,"abstract":"<div><div>The recent survey [3] nicknamed “Hitchhiker’s Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work we addressed the question of extreme values of the mass distribution associated with a mutidimensional quasi–copulas. Using linear programming approach we were able to settle <span><span>[3, Open Problem 5]</span></span> up to <span><math><mrow><mi>d</mi><mo>=</mo><mn>17</mn></mrow></math></span> and disprove a recent conjecture from [14] on solution to that problem. In this note we use an analytical approach to provide a complete answer to the original question.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109698"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625041","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 : 2026-03-15Epub Date: 2025-11-19DOI: 10.1016/j.fss.2025.109664
Serafina Lapenta , Sebastiano Napolitano
We investigate the computational complexity of various satisfiability problems in Łukasiewicz logic, restricting attention to valuations in the standard MV-algebra [0,1]. Specifically, we focus on maximal r-satisfiability – the task of maximizing the number of formulas whose valuation is at least a given rational r ∈ (0, 1]. We also consider the decisional and weighted versions of this problem, as well as the partial (weighted) r-satisfiability problem.
{"title":"Computational complexity of some MaxSAT problems in Łukasiewicz logic","authors":"Serafina Lapenta , Sebastiano Napolitano","doi":"10.1016/j.fss.2025.109664","DOIUrl":"10.1016/j.fss.2025.109664","url":null,"abstract":"<div><div>We investigate the computational complexity of various satisfiability problems in Łukasiewicz logic, restricting attention to valuations in the standard MV-algebra [0,1]. Specifically, we focus on maximal <em>r</em>-satisfiability – the task of maximizing the number of formulas whose valuation is at least a given rational <em>r</em> ∈ (0, 1]. We also consider the decisional and weighted versions of this problem, as well as the partial (weighted) <em>r</em>-satisfiability problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109664"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625042","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 : 2026-03-15Epub Date: 2025-11-20DOI: 10.1016/j.fss.2025.109695
Ta Zhou , Yuanqing Yang , Wei Yan , Weiqin Liu , Xibei Yang , Weiping Ding , Jing Cai , Shitong Wang
Distant metastasis (DM) as a major cause of treatment failure of nasopharyngeal cancer (NPC) actually occurs with a considerably gradual development in the early stage. Therefore, an ideal DM prediction model should be an efficient and interpretable model and simultaneously reflect/simulate this characteristic during its training. Towards such a goal, this study proposes a hierarchical Takagi-Sugeno-Kang (TSK) fuzzy classifier (H-TSKFC) to assure both enhanced classification performance and diversified generation of interpretable fuzzy rules therein through full-partial-rule-transmission fusion for simulating gradual development of DM. Profiting from full-partial-rule-transmission fusion between sub-classifiers, H-TSKFC was endowed with the following benefits. Firstly, a novel stacking mechanism without any use of residuals between sub-classifiers enhances its generalization capability. Secondly, the generation of interpretable fuzzy rules from the second TSK fuzzy sub-classifier provides a diversified way. That is, its useful rules fusion transmitted fully or partially from previous sub-classifier guarantees considerable consistency between sub-classifiers, while its remaining rules reflect gradual difference between them. In this way, the H-TSKFC’s structure naturally mimics the gradual development of DM. Finally, each sub-classifier therein can be trained sequentially and quickly with an analytical solution to accomplish an individual prediction on the original inputs and outputs. Experimental results indeed demonstrate that H-TSKFC possesses linguistic interpretability, along with considerable classification and generalization performance.
{"title":"Fully & partially-transmitted-rule fusion: A novel hierarchical fuzzy classification with application to nasopharyngeal cancer’s metastasis prediction","authors":"Ta Zhou , Yuanqing Yang , Wei Yan , Weiqin Liu , Xibei Yang , Weiping Ding , Jing Cai , Shitong Wang","doi":"10.1016/j.fss.2025.109695","DOIUrl":"10.1016/j.fss.2025.109695","url":null,"abstract":"<div><div>Distant metastasis (DM) as a major cause of treatment failure of nasopharyngeal cancer (NPC) actually occurs with a considerably gradual development in the early stage. Therefore, an ideal DM prediction model should be an efficient and interpretable model and simultaneously reflect/simulate this characteristic during its training. Towards such a goal, this study proposes a hierarchical Takagi-Sugeno-Kang (TSK) fuzzy classifier (H-TSKFC) to assure both enhanced classification performance and diversified generation of interpretable fuzzy rules therein through full-partial-rule-transmission fusion for simulating gradual development of DM. Profiting from full-partial-rule-transmission fusion between sub-classifiers, H-TSKFC was endowed with the following benefits. Firstly, a novel stacking mechanism without any use of residuals between sub-classifiers enhances its generalization capability. Secondly, the generation of interpretable fuzzy rules from the second TSK fuzzy sub-classifier provides a diversified way. That is, its useful rules fusion transmitted fully or partially from previous sub-classifier guarantees considerable consistency between sub-classifiers, while its remaining rules reflect gradual difference between them. In this way, the H-TSKFC’s structure naturally mimics the gradual development of DM. Finally, each sub-classifier therein can be trained sequentially and quickly with an analytical solution to accomplish an individual prediction on the original inputs and outputs. Experimental results indeed demonstrate that H-TSKFC possesses linguistic interpretability, along with considerable classification and generalization performance.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109695"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625047","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 : 2026-03-15Epub Date: 2025-11-23DOI: 10.1016/j.fss.2025.109694
Xinyu Shi , Liwen Ma
In this paper, we introduce a novel neighborhood system in covering rough set theory, which is employed to define the upper and lower approximations of rough sets. This neighborhood system not only overcomes the limitations of directly applying the classical neighborhood definition to infinite universes but also coincides with the classical neighborhood in the finite case. We then investigate the fundamental relations between the upper and lower approximations, and in particular, extend the six-set approximation theorem from finite to infinite universes. Furthermore, we propose a new concept of convergent sequence to intuitively characterize rough set approximations and their interrelations. Finally, we analyze the transformations of neighborhood systems, sequences, and approximations under mappings between two infinite universes. To illustrate the applicability of our approach, examples inspired by simulated cell division are presented throughout the paper.
{"title":"A novel approach to rough set model via neighborhood systems","authors":"Xinyu Shi , Liwen Ma","doi":"10.1016/j.fss.2025.109694","DOIUrl":"10.1016/j.fss.2025.109694","url":null,"abstract":"<div><div>In this paper, we introduce a novel neighborhood system in covering rough set theory, which is employed to define the upper and lower approximations of rough sets. This neighborhood system not only overcomes the limitations of directly applying the classical neighborhood definition to infinite universes but also coincides with the classical neighborhood in the finite case. We then investigate the fundamental relations between the upper and lower approximations, and in particular, extend the six-set approximation theorem from finite to infinite universes. Furthermore, we propose a new concept of convergent sequence to intuitively characterize rough set approximations and their interrelations. Finally, we analyze the transformations of neighborhood systems, sequences, and approximations under mappings between two infinite universes. To illustrate the applicability of our approach, examples inspired by simulated cell division are presented throughout the paper.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109694"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625043","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 : 2026-03-15Epub Date: 2025-11-22DOI: 10.1016/j.fss.2025.109700
Yi Shi , Hui Yang
Dress in 1984 introduced the concept of tight span of a metric space, allowing the space to be isometrically embedded into a larger metric space. This paper aims to extend this theory to fuzzy metric setting. More concretely, we define tight spans of fuzzy metric spaces as a key tool in the study of the appropriate extension. It is shown that any fuzzy metric space can be isometrically embedded into its tight span, with the embedding being an isomorphism when the fuzzy metric space is hyperconvex (or, equivalently, injective). Additionally, we explore tight extensions and essential extensions of fuzzy metric spaces, providing a precise formulation of their hyperconvex hulls and injective hulls.
{"title":"Tight spans of fuzzy metric spaces","authors":"Yi Shi , Hui Yang","doi":"10.1016/j.fss.2025.109700","DOIUrl":"10.1016/j.fss.2025.109700","url":null,"abstract":"<div><div>Dress in 1984 introduced the concept of tight span of a metric space, allowing the space to be isometrically embedded into a larger metric space. This paper aims to extend this theory to fuzzy metric setting. More concretely, we define tight spans of fuzzy metric spaces as a key tool in the study of the appropriate extension. It is shown that any fuzzy metric space can be isometrically embedded into its tight span, with the embedding being an isomorphism when the fuzzy metric space is hyperconvex (or, equivalently, injective). Additionally, we explore tight extensions and essential extensions of fuzzy metric spaces, providing a precise formulation of their hyperconvex hulls and injective hulls.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109700"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694463","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 : 2026-03-15Epub Date: 2025-11-27DOI: 10.1016/j.fss.2025.109697
Aysegul Yabaci Tak , Nihat Tak
Type-1 Fuzzy Functions (T1FFs) have emerged as a rule-free alternative to classical fuzzy inference systems for tackling forecasting problems, especially in the presence of uncertainty and nonlinearity. This study provides a comprehensive literature review and a bibliometric analysis of T1FFs in the context of forecasting. A dataset of 25 articles indexed in the Web of Science Core Collection was examined to assess research trends, author collaboration networks, influential publications, source journals, and key thematic areas. Our review identifies four main components in the design of T1FF-based models: input structure, clustering methods, forecasting models, and objective function optimization. Through citation and co-authorship network analysis, we highlight prominent researchers and collaborations within the field. Source journal analysis reveals publication hotspots, while co-word analysis identifies dominant themes such as “forecasting,” “robust regression,” and “metaheuristic optimization.” The results suggest growing academic interest and methodological diversification in the use of T1FFs, with Turkey leading international contributions. This study serves as a roadmap for researchers aiming to build or extend T1FF-based forecasting systems.
1型模糊函数（t1ff）已成为经典模糊推理系统的无规则替代方案，用于解决预测问题，特别是在存在不确定性和非线性的情况下。本研究提供了全面的文献综述和文献计量学分析在预测背景下的T1FFs。研究人员研究了Web of Science核心合集收录的25篇文章的数据集，以评估研究趋势、作者合作网络、有影响力的出版物、来源期刊和关键主题领域。我们的综述确定了基于t1ff模型设计的四个主要组成部分：输入结构、聚类方法、预测模型和目标函数优化。通过引文和合著者网络分析，我们突出了该领域的杰出研究人员和合作。源期刊分析揭示了出版热点，而共词分析确定了主导主题，如“预测”、“稳健回归”和“元启发式优化”。研究结果表明，在T1FFs的使用方面，学术兴趣和方法多样化日益增加，土耳其在国际上的贡献领先。这项研究为旨在建立或扩展基于t1ff的预测系统的研究人员提供了路线图。
{"title":"Type-1 fuzzy functions for forecasting: A literature review and bibliometric analysis","authors":"Aysegul Yabaci Tak , Nihat Tak","doi":"10.1016/j.fss.2025.109697","DOIUrl":"10.1016/j.fss.2025.109697","url":null,"abstract":"<div><div>Type-1 Fuzzy Functions (T1FFs) have emerged as a rule-free alternative to classical fuzzy inference systems for tackling forecasting problems, especially in the presence of uncertainty and nonlinearity. This study provides a comprehensive literature review and a bibliometric analysis of T1FFs in the context of forecasting. A dataset of 25 articles indexed in the Web of Science Core Collection was examined to assess research trends, author collaboration networks, influential publications, source journals, and key thematic areas. Our review identifies four main components in the design of T1FF-based models: input structure, clustering methods, forecasting models, and objective function optimization. Through citation and co-authorship network analysis, we highlight prominent researchers and collaborations within the field. Source journal analysis reveals publication hotspots, while co-word analysis identifies dominant themes such as “forecasting,” “robust regression,” and “metaheuristic optimization.” The results suggest growing academic interest and methodological diversification in the use of T1FFs, with Turkey leading international contributions. This study serves as a roadmap for researchers aiming to build or extend T1FF-based forecasting systems.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109697"},"PeriodicalIF":2.7,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625046","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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