Pub Date : 2025-12-20DOI: 10.1016/j.fss.2025.109730
Narayan Choudhary, Aastha Nirvana, S.P. Tiwari
This work focuses on the categorical study of L-fuzzy automata with a pair of L-fuzzy relations as morphisms, where L is a complete regular residuated and co-residuated lattice. Specifically, we introduce and study the categorical concepts such as product, monics, and their duals in this category, as well as further examine the monoidal structure. Moreover, we investigate the relationship between the category of L-fuzzy automata and the category of non-deterministic automata. We show the existence of isomorphisms between the category of L-fuzzy automata and the category of chains of non-deterministic automata.
{"title":"L-fuzzy automata based on complete regular residuated and co-residuated lattice: A categorical study","authors":"Narayan Choudhary, Aastha Nirvana, S.P. Tiwari","doi":"10.1016/j.fss.2025.109730","DOIUrl":"10.1016/j.fss.2025.109730","url":null,"abstract":"<div><div>This work focuses on the categorical study of <em>L</em>-fuzzy automata with a pair of <em>L</em>-fuzzy relations as morphisms, where <em>L</em> is a complete regular residuated and co-residuated lattice. Specifically, we introduce and study the categorical concepts such as product, monics, and their duals in this category, as well as further examine the monoidal structure. Moreover, we investigate the relationship between the category of <em>L</em>-fuzzy automata and the category of non-deterministic automata. We show the existence of isomorphisms between the category of <em>L</em>-fuzzy automata and the category of chains of non-deterministic automata.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109730"},"PeriodicalIF":2.7,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.fss.2025.109744
Nicolás Marín , Gustavo Rivas-Gervilla , Daniel Sánchez
Specificity is a measure that tells us to what extent a fuzzy set is a singleton. The variety of application domains of this measure requires different specific forms of calculating it. One way to control the semantic nuances in the way specificity is computed is to generate it from other well-known measures in the Fuzzy Set Theory that have a wide range of evaluation functions with different axiomatics. Following this strategy, in this work we study in depth the inequality measures based on their axiomatics, we establish a method to use them as generators of specificity measures, and we analyze the semantics and the desired properties of specificity measures obtained according to the axioms satisfied by the inequality measures used as generators. As we will see, relevant results have been obtained that relate different families of specificity and inequality measures.
{"title":"Specificity measures based on fuzzy set inequality","authors":"Nicolás Marín , Gustavo Rivas-Gervilla , Daniel Sánchez","doi":"10.1016/j.fss.2025.109744","DOIUrl":"10.1016/j.fss.2025.109744","url":null,"abstract":"<div><div>Specificity is a measure that tells us to what extent a fuzzy set is a singleton. The variety of application domains of this measure requires different specific forms of calculating it. One way to control the semantic nuances in the way specificity is computed is to generate it from other well-known measures in the Fuzzy Set Theory that have a wide range of evaluation functions with different axiomatics. Following this strategy, in this work we study in depth the inequality measures based on their axiomatics, we establish a method to use them as generators of specificity measures, and we analyze the semantics and the desired properties of specificity measures obtained according to the axioms satisfied by the inequality measures used as generators. As we will see, relevant results have been obtained that relate different families of specificity and inequality measures.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109744"},"PeriodicalIF":2.7,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841808","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 : 2025-12-18DOI: 10.1016/j.fss.2025.109732
Guanglei Zhao , Xianyu Liu
This work studies the fixed-time event-triggered fault-tolerant containment control problem for nonlinear multi-agent system (MAS) with actuator faults. First, by leveraging fuzzy logic system to approximate unknown nonlinear dynamics, a state observer is designed to estimate unmeasurable state variables. Second, to handle the actuator fault, a novel projection operator compensation mechanism is developed. Furthermore, a fixed-time nonlinear filter design is given to solve the explosion problem and dynamic event-triggering mechanism is proposed to save system resources. Then, combined with dynamic surface control and fuzzy control techniques, fixed-time adaptive fault-tolerant containment control strategy is proposed with rigorous stability analysis, and all followers are able to converge to the convex hull constructed by leaders. In contrast with existing approaches, the main superiority of the proposed containment control strategy is that the projection operator can handle actuator faults more efficiently, multiple parameters of nonlinear filter enhance system flexibility and dynamic threshold in triggering conditions helps to reduce triggering frequency. Finally, simulation results confirm that the proposed method ensures fixed-time convergence of the containment errors.
{"title":"Fixed-time adaptive fuzzy event-triggered fault-tolerant containment control for nonlinear multi-agent systems","authors":"Guanglei Zhao , Xianyu Liu","doi":"10.1016/j.fss.2025.109732","DOIUrl":"10.1016/j.fss.2025.109732","url":null,"abstract":"<div><div>This work studies the fixed-time event-triggered fault-tolerant containment control problem for nonlinear multi-agent system (MAS) with actuator faults. First, by leveraging fuzzy logic system to approximate unknown nonlinear dynamics, a state observer is designed to estimate unmeasurable state variables. Second, to handle the actuator fault, a novel projection operator compensation mechanism is developed. Furthermore, a fixed-time nonlinear filter design is given to solve the explosion problem and dynamic event-triggering mechanism is proposed to save system resources. Then, combined with dynamic surface control and fuzzy control techniques, fixed-time adaptive fault-tolerant containment control strategy is proposed with rigorous stability analysis, and all followers are able to converge to the convex hull constructed by leaders. In contrast with existing approaches, the main superiority of the proposed containment control strategy is that the projection operator can handle actuator faults more efficiently, multiple parameters of nonlinear filter enhance system flexibility and dynamic threshold in triggering conditions helps to reduce triggering frequency. Finally, simulation results confirm that the proposed method ensures fixed-time convergence of the containment errors.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109732"},"PeriodicalIF":2.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842544","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}
In the paper [E. Jiménez-Fernández, J. Rodríguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space However, while the function ϕ is only required to be increasing, some results of the paper implicitly assume that ϕ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires ϕ to be also left-continuous.
在论文中[d]。Jiménez-Fernández， J. Rodríguez-López， E. a . Sánchez-Pérez, Fuzzy Sets and Systems 406(2021),66-81]，给出了模糊度量空间间实值模糊Lipschitz映射的McShane-Whitney扩展定理。具体来说，上域空间被认为是一个所谓的欧几里得模糊度量空间（R, m φ,g,*）。然而，虽然函数φ只需要增加，但本文的一些结果隐含地假设φ是可逆的，即使这没有明确说明。我们在这里提出了另一种可能性，只要求φ也是左连续的。
{"title":"A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps","authors":"Eduardo Jiménez-Fernández , Jesús Rodríguez-López , Aurora Sánchez-Martín-Orozco , Enrique A. Sánchez-Pérez","doi":"10.1016/j.fss.2025.109731","DOIUrl":"10.1016/j.fss.2025.109731","url":null,"abstract":"<div><div>In the paper [E. Jiménez-Fernández, J. Rodríguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space <span><math><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi>M</mi><mrow><mi>ϕ</mi><mo>,</mo><mi>g</mi></mrow></msub><mo>,</mo><mo>*</mo><mo>)</mo><mo>.</mo></mrow></math></span> However, while the function <em>ϕ</em> is only required to be increasing, some results of the paper implicitly assume that <em>ϕ</em> is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires <em>ϕ</em> to be also left-continuous.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109731"},"PeriodicalIF":2.7,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771992","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 : 2025-12-16DOI: 10.1016/j.fss.2025.109743
Guijie Li , Yang Zhan , Huimin Xue
To effectively characterize the effects of fuzzy uncertainties on structural systems, this study introduces a novel importance measure termed Possibilistic Variance-based Importance Measure (PVB-IM). By leveraging the High Dimensional Model Representation (HDMR) of the function, we extend the decomposition equation for fuzzy structural systems to establish the PVB-IM. This approach enables the identification of effects of fuzzy variables on system response within fuzzy uncertainties, thereby facilitating the design and optimization for such structural systems. We present a fundamental computational algorithm for PVB-IM using Monte Carlo simulation and propose an efficient algorithm based on the State Dependent Parameter (SDP) method for addressing complex engineering challenges. Through numerical and engineering examples, we validate the applicability and rationale of the PVB-IM, and demonstrate the accuracy and efficiency of the SDP algorithm.
{"title":"The uncertainty importance measure analysis for fuzzy structural systems based on possibilistic variance","authors":"Guijie Li , Yang Zhan , Huimin Xue","doi":"10.1016/j.fss.2025.109743","DOIUrl":"10.1016/j.fss.2025.109743","url":null,"abstract":"<div><div>To effectively characterize the effects of fuzzy uncertainties on structural systems, this study introduces a novel importance measure termed Possibilistic Variance-based Importance Measure (PVB-IM). By leveraging the High Dimensional Model Representation (HDMR) of the function, we extend the decomposition equation for fuzzy structural systems to establish the PVB-IM. This approach enables the identification of effects of fuzzy variables on system response within fuzzy uncertainties, thereby facilitating the design and optimization for such structural systems. We present a fundamental computational algorithm for PVB-IM using Monte Carlo simulation and propose an efficient algorithm based on the State Dependent Parameter (SDP) method for addressing complex engineering challenges. Through numerical and engineering examples, we validate the applicability and rationale of the PVB-IM, and demonstrate the accuracy and efficiency of the SDP algorithm.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109743"},"PeriodicalIF":2.7,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842546","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 : 2025-12-15DOI: 10.1016/j.fss.2025.109724
Weihua Xu, Chongze Zhang
Weighted Fuzzy Concept Cognitive Learning (WFCCL) improves concept learning by assigning different weights to attributes. However, existing weighting methods mainly rely on fuzzy entropy and fail to effectively handle the noise, uncertainty, and complexity commonly present in real-world data. Moreover, the key threshold λ for generating Advanced Weighted Fuzzy Concepts (AWFC) has not been thoroughly investigated, which may limit the depth of knowledge discovery and the applicability of the model. To address these issues, this paper proposes a Random Forest-Driven Weighted Fuzzy Concept Cognitive Learning (RF-WFCCL) method. The proposed approach leverages random forests to compute attribute importance, thereby making weight allocation more reflective of data characteristics and reducing the influence of noise and uncertainty. In addition, an adaptive optimization algorithm is designed to automatically determine the approximately optimal threshold for generating AWFC, enhancing the accuracy and applicability of concept cognition. Unlike traditional methods, our model not only improves the adaptability of weight allocation but also introduces a data-driven threshold optimization strategy to facilitate knowledge discovery. Finally, extensive experiments on 12 datasets using 12 classification algorithms demonstrate the feasibility and superiority of the proposed method.
{"title":"RF-WFCCL: A random forest-driven weighted fuzzy concept cognitive learning","authors":"Weihua Xu, Chongze Zhang","doi":"10.1016/j.fss.2025.109724","DOIUrl":"10.1016/j.fss.2025.109724","url":null,"abstract":"<div><div>Weighted Fuzzy Concept Cognitive Learning (WFCCL) improves concept learning by assigning different weights to attributes. However, existing weighting methods mainly rely on fuzzy entropy and fail to effectively handle the noise, uncertainty, and complexity commonly present in real-world data. Moreover, the key threshold <em>λ</em> for generating Advanced Weighted Fuzzy Concepts (AWFC) has not been thoroughly investigated, which may limit the depth of knowledge discovery and the applicability of the model. To address these issues, this paper proposes a Random Forest-Driven Weighted Fuzzy Concept Cognitive Learning (RF-WFCCL) method. The proposed approach leverages random forests to compute attribute importance, thereby making weight allocation more reflective of data characteristics and reducing the influence of noise and uncertainty. In addition, an adaptive optimization algorithm is designed to automatically determine the approximately optimal threshold <span><math><mrow><mover><mi>λ</mi><mo>^</mo></mover><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow></math></span> for generating AWFC, enhancing the accuracy and applicability of concept cognition. Unlike traditional methods, our model not only improves the adaptability of weight allocation but also introduces a data-driven threshold optimization strategy to facilitate knowledge discovery. Finally, extensive experiments on 12 datasets using 12 classification algorithms demonstrate the feasibility and superiority of the proposed method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"529 ","pages":"Article 109724"},"PeriodicalIF":2.7,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842543","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 : 2025-12-12DOI: 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":"2025-12-12","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 : 2025-12-11DOI: 10.1016/j.fss.2025.109729
Keyi Xiao , Yong Su , Wenwen Zong
The modularity holds a significant position in fuzzy set theory, which is closely related to the distributivity and can be viewed as a restricted general associativity equation. In this paper, we study the modularity between semi-t-operators and bi-uninorms, and completely describe the structure of such a pair of functions without any additional assumptions. Several examples are also provided to illustrate the theoretical results.
{"title":"The modularity condition for semi-t-operators and Bi-uninorms","authors":"Keyi Xiao , Yong Su , Wenwen Zong","doi":"10.1016/j.fss.2025.109729","DOIUrl":"10.1016/j.fss.2025.109729","url":null,"abstract":"<div><div>The modularity holds a significant position in fuzzy set theory, which is closely related to the distributivity and can be viewed as a restricted general associativity equation. In this paper, we study the modularity between semi-t-operators and bi-uninorms, and completely describe the structure of such a pair of functions without any additional assumptions. Several examples are also provided to illustrate the theoretical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109729"},"PeriodicalIF":2.7,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-07DOI: 10.1016/j.fss.2025.109725
Yu Kong, Hua-Wen Liu
<div><div>In this paper, we mainly study the classes of uninorms whose neutral elements are middle-transitive and not in any non-trivial cycle, defined on bounded pseudo-ordered sets. Firstly, to generalize the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> of uninorms on bounded lattices, we introduce the definitions of the classes <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of uninorms on bounded pseudo-ordered sets. Secondly, we characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-subnorms and uninorms. We characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-superconorms and uninorms. In addition, we introduce the definitions of the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets, generalizing the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> on bounded lattices. We introduce the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets as the extensions of the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mi>r</mi></msubs
{"title":"Several classes of uninorms on bounded pseudo-ordered sets","authors":"Yu Kong, Hua-Wen Liu","doi":"10.1016/j.fss.2025.109725","DOIUrl":"10.1016/j.fss.2025.109725","url":null,"abstract":"<div><div>In this paper, we mainly study the classes of uninorms whose neutral elements are middle-transitive and not in any non-trivial cycle, defined on bounded pseudo-ordered sets. Firstly, to generalize the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> of uninorms on bounded lattices, we introduce the definitions of the classes <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of uninorms on bounded pseudo-ordered sets. Secondly, we characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-subnorms and uninorms. We characterize the members of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets using strong t-superconorms and uninorms. In addition, we introduce the definitions of the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and the subclass <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mo>*</mo></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets, generalizing the definitions of <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>U</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> on bounded lattices. We introduce the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mi>r</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msubsup></mrow></math></span> on bounded pseudo-ordered sets as the extensions of the definitions of <span><math><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mi>r</mi></msubs","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109725"},"PeriodicalIF":2.7,"publicationDate":"2025-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-07DOI: 10.1016/j.fss.2025.109716
G. Caterina
We develop a moment-preserving defuzzifier based on the Cafagna-Caterina characterization theorem. Given the first n Fourier moments of a membership function f ∈ [0, 1] on S1, it returns a crisp function χn which is a union of n arcs and whose first n moments match those of f exactly. For , corresponding to mass and centroid, we give a closed-form solution for the arc endpoints, whereas for n > 2 we present two numerical methods to compute those arcs. As an application, we apply the method to California Independent System Operator (CAISO) net demand data, and show that the four-arc solution automatically produces a midday gap that captures the solar valley, with arc locations emerging from moment-matching constraints rather than threshold selection or manual specification.
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