Pub Date : 2025-01-27DOI: 10.1016/j.fss.2025.109296
Illych Alvarez , Antoni López-Martínez , Alfred Peris
We study for a dynamical system some of the principal topological recurrence-kind properties with respect to the induced maps , on the hyperspace of non-empty compact subsets of X, and , on the space of normal fuzzy sets consisting of the upper-semicontinuous functions with compact support and such that . In particular, we characterize the properties of topological and multiple recurrence for the extended systems and , which cover the cases of the so-called nonwandering and Van der Waerden systems. Special attention is given to the case where the underlying space is completely metrizable, for which we obtain some stronger point-recurrence equivalences.
{"title":"Recurrence in collective dynamics: From the hyperspace to fuzzy dynamical systems","authors":"Illych Alvarez , Antoni López-Martínez , Alfred Peris","doi":"10.1016/j.fss.2025.109296","DOIUrl":"10.1016/j.fss.2025.109296","url":null,"abstract":"<div><div>We study for a dynamical system <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>⟶</mo><mi>X</mi></math></span> some of the principal topological recurrence-kind properties with respect to the induced maps <span><math><mover><mrow><mi>f</mi></mrow><mo>‾</mo></mover><mo>:</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>⟶</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, on the hyperspace of non-empty compact subsets of <em>X</em>, and <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>:</mo><mi>F</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>⟶</mo><mi>F</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, on the space of normal fuzzy sets consisting of the upper-semicontinuous functions <span><math><mi>u</mi><mo>:</mo><mi>X</mi><mo>⟶</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with compact support and such that <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mo>{</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>≠</mo><mo>∅</mo></math></span>. In particular, we characterize the properties of topological and multiple recurrence for the extended systems <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>f</mi></mrow><mo>‾</mo></mover><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>F</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span>, which cover the cases of the so-called nonwandering and Van der Waerden systems. Special attention is given to the case where the underlying space is completely metrizable, for which we obtain some stronger point-recurrence equivalences.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109296"},"PeriodicalIF":3.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on the scaled consensus problem of interval type-2 Takagi-Sugeno (IT-2 T-S) fuzzy multi-agent systems with external disturbance under directed graphs on the basis of dynamic event-triggered mechanisms (DETMs). An extended dissipative performance (EDP) index is introduced in the paper to cope with system disturbances. The , , passivity and -dissipative performances of the system can also be satisfied by tuning the weighting matrices. In this paper, a novel sampling-based DETM with flexible parameters and dynamic internal variable is proposed for the first time. It effectively reduces unnecessary continuous monitoring and improves the utilization of network resources. Then, an output feedback-based fuzzy control protocol is designed for the situation where the state information is not completely known. Furthermore, a sufficient condition for MAS to achieve scale consensus while satisfying the EDP is obtained using Lyapunov stability theory and linear matrix inequality methods. Finally, the effectiveness and applicability of the proposed method are verified by an numerical simulation and a mass-spring-damper system.
{"title":"Dynamic event-triggered extended dissipative scaled consensus control for nonlinear multi-agent systems","authors":"Lihong Feng , Bonan Huang , Huaguang Zhang , Jiayue Sun","doi":"10.1016/j.fss.2025.109286","DOIUrl":"10.1016/j.fss.2025.109286","url":null,"abstract":"<div><div>This paper focuses on the scaled consensus problem of interval type-2 Takagi-Sugeno (IT-2 T-S) fuzzy multi-agent systems with external disturbance under directed graphs on the basis of dynamic event-triggered mechanisms (DETMs). An extended dissipative performance (EDP) index is introduced in the paper to cope with system disturbances. The <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, passivity and <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>R</mi><mo>)</mo><mo>−</mo><mi>α</mi></math></span>-dissipative performances of the system can also be satisfied by tuning the weighting matrices. In this paper, a novel sampling-based DETM with flexible parameters and dynamic internal variable is proposed for the first time. It effectively reduces unnecessary continuous monitoring and improves the utilization of network resources. Then, an output feedback-based fuzzy control protocol is designed for the situation where the state information is not completely known. Furthermore, a sufficient condition for MAS to achieve scale consensus while satisfying the EDP is obtained using Lyapunov stability theory and linear matrix inequality methods. Finally, the effectiveness and applicability of the proposed method are verified by an numerical simulation and a mass-spring-damper system.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109286"},"PeriodicalIF":3.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138621","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 : 2025-01-23DOI: 10.1016/j.fss.2025.109284
Feng-Liang Zhao , Zi-Peng Wang , Fangyu Li , Junfei Qiao , Huai-Ning Wu
Under spatially point measurements (SPMs), this paper addresses event-triggered sampled-data (ETSD) fuzzy secure control for nonlinear space-varying parabolic partial differential equation (PDE) systems with stochastic actuator failures and deception attacks. Initially, a T-S fuzzy PDE model is presented to exactly describe the nonlinear space-varying parabolic PDE systems subject to stochastic actuator failures and deception attacks. Secondly, in order to reduce the unnecessary sampled-data and adapt to the variation of system dynamics subject to stochastic actuator failures and deception attacks, an ETSD fuzzy secure control scheme is proposed under SPMs. Then, by constructing an appropriate Lyapunov functional, the mean square exponential stability conditions of closed-loop nonlinear space-varying parabolic PDE systems via spatial linear matrix inequalities (SLMIs) are presented. Furthermore, to solve SLMIs, the ETSD fuzzy secure control design problem for nonlinear space-varying parabolic PDE systems under SPMs with stochastic actuator failures and deception attacks is formulated as an linear matrix inequality feasibility problem. Finally, simulation results of two examples are presented to demonstrate the effectiveness of the proposed design approach.
{"title":"Event-triggered sampled–data fuzzy secure control for nonlinear parabolic PDE systems subject to stochastic actuator failures and deception attacks","authors":"Feng-Liang Zhao , Zi-Peng Wang , Fangyu Li , Junfei Qiao , Huai-Ning Wu","doi":"10.1016/j.fss.2025.109284","DOIUrl":"10.1016/j.fss.2025.109284","url":null,"abstract":"<div><div>Under spatially point measurements (SPMs), this paper addresses event-triggered sampled-data (ETSD) fuzzy secure control for nonlinear space-varying parabolic partial differential equation (PDE) systems with stochastic actuator failures and deception attacks. Initially, a T-S fuzzy PDE model is presented to exactly describe the nonlinear space-varying parabolic PDE systems subject to stochastic actuator failures and deception attacks. Secondly, in order to reduce the unnecessary sampled-data and adapt to the variation of system dynamics subject to stochastic actuator failures and deception attacks, an ETSD fuzzy secure control scheme is proposed under SPMs. Then, by constructing an appropriate Lyapunov functional, the mean square exponential stability conditions of closed-loop nonlinear space-varying parabolic PDE systems via spatial linear matrix inequalities (SLMIs) are presented. Furthermore, to solve SLMIs, the ETSD fuzzy secure control design problem for nonlinear space-varying parabolic PDE systems under SPMs with stochastic actuator failures and deception attacks is formulated as an linear matrix inequality feasibility problem. Finally, simulation results of two examples are presented to demonstrate the effectiveness of the proposed design approach.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109284"},"PeriodicalIF":3.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138619","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 : 2025-01-21DOI: 10.1016/j.fss.2025.109285
Cheng Zhang , Feng Qin , Michał Baczyński
The laws of contraposition, which are based on fuzzy implications and negations, play pivotal roles in fuzzy logic. This study introduces and exemplifies two novel types of fuzzy implications: -implications and -implications. These are derived from aggregation functions, disjunctors (conjunctors), and fuzzy negations. Prominent fuzzy implications like , , , , , and -implications can be subclassified under these newly introduced types. Then, we provide an axiomatic characterization of these two novel types of fuzzy implications based on the laws of contraposition. Furthermore, this research not only broadens our understanding of the axiomatic characterization of well-known fuzzy implications, such as -implications and -implications but also introduces a fresh perspective for interpreting relations between these implications.
{"title":"Characterizations of fuzzy implications by the laws of contraposition","authors":"Cheng Zhang , Feng Qin , Michał Baczyński","doi":"10.1016/j.fss.2025.109285","DOIUrl":"10.1016/j.fss.2025.109285","url":null,"abstract":"<div><div>The laws of contraposition, which are based on fuzzy implications and negations, play pivotal roles in fuzzy logic. This study introduces and exemplifies two novel types of fuzzy implications: <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications and <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications. These are derived from aggregation functions, disjunctors (conjunctors), and fuzzy negations. Prominent fuzzy implications like <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, <span><math><mo>(</mo><msup><mrow><mi>U</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, <span><math><mo>(</mo><msup><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, and <span><math><mo>(</mo><mi>T</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications can be subclassified under these newly introduced types. Then, we provide an axiomatic characterization of these two novel types of fuzzy implications based on the laws of contraposition. Furthermore, this research not only broadens our understanding of the axiomatic characterization of well-known fuzzy implications, such as <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications and <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications but also introduces a fresh perspective for interpreting relations between these implications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109285"},"PeriodicalIF":3.2,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181035","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 : 2025-01-20DOI: 10.1016/j.fss.2025.109283
Tingting Wang , Wenwen Zong , Yong Su , Radko Mesiar
The homogeneity and its extensions reflect the regularity of aggregation functions with respect to the inputs with the same ratio and play an essential role in decision making, economics and image processing. In this paper, the relationships among generalized homogeneities and characterizations of abstractly homogeneous aggregation functions with respect to a given continuous t-norm are presented.
同质性及其扩展反映了相对于相同比率输入的聚集函数的规律性，在决策、经济学和图像处理中发挥着重要作用。本文介绍了广义同质性之间的关系，以及相对于给定连续 t 准则的抽象同质性聚集函数的特征。
{"title":"Abstractly homogeneous aggregation functions with respect to a given continuous t-norm","authors":"Tingting Wang , Wenwen Zong , Yong Su , Radko Mesiar","doi":"10.1016/j.fss.2025.109283","DOIUrl":"10.1016/j.fss.2025.109283","url":null,"abstract":"<div><div>The homogeneity and its extensions reflect the regularity of aggregation functions with respect to the inputs with the same ratio and play an essential role in decision making, economics and image processing. In this paper, the relationships among generalized homogeneities and characterizations of abstractly homogeneous aggregation functions with respect to a given continuous t-norm are presented.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109283"},"PeriodicalIF":3.2,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181036","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 : 2025-01-16DOI: 10.1016/j.fss.2025.109278
Ping Li , Jufang Yang , Yongming Li , Chao Yang , Wenyu Xue
The paper introduces ε-bisimulation relation, surjective -functional ε-bisimulation relation, surjective functional ε-bisimulation relation, bijective functional ε-bisimulation relation and ε-isomorphism from fuzzy automata to by fuzzy matrices. Then it is proved that the behavior of a fuzzy automaton differs from the behavior of a fuzzy automaton by at most ε if there exists a ε-bisimulation relation between them. In particular, if there exists a surjective -functional ε-bisimulation relation between them, we give a more concise proof of above conclusion by fuzzy matrices. Moreover, the notion of ε-bisimulation equivalence relation on a fuzzy automaton is given by fuzzy matrices. Based on two different constructions of quotient fuzzy automata, the relationships between ε-bisimulation relations and ε-bisimulation equivalence relations and the ε-Isomorphism theorems of quotient fuzzy automata are given.
本文介绍了ε-二拟合关系、投射 L 函数ε-二拟合关系、投射函数ε-二拟合关系、双投射函数ε-二拟合关系以及模糊矩阵从模糊自动机 A 到 B 的ε-同构。然后证明，如果模糊自动机 A 与模糊自动机 B 之间存在ε-二拟合关系，则它们的行为最多相差 ε。特别是，如果它们之间存在一个投射 L 函数ε-双拟合关系，我们将通过模糊矩阵对上述结论给出更简洁的证明。此外，模糊矩阵给出了模糊自动机上的ε-双模拟等价关系概念。基于商模糊自动机的两种不同构造，给出了ε-双拟合关系和ε-双拟合等价关系之间的关系以及商模糊自动机的ε-同构定理。
{"title":"Algebraic properties of approximate bisimulation relations for fuzzy automata","authors":"Ping Li , Jufang Yang , Yongming Li , Chao Yang , Wenyu Xue","doi":"10.1016/j.fss.2025.109278","DOIUrl":"10.1016/j.fss.2025.109278","url":null,"abstract":"<div><div>The paper introduces <em>ε</em>-bisimulation relation, surjective <span><math><mi>L</mi></math></span>-functional <em>ε</em>-bisimulation relation, surjective functional <em>ε</em>-bisimulation relation, bijective functional <em>ε</em>-bisimulation relation and <em>ε</em>-isomorphism from fuzzy automata <span><math><mi>A</mi></math></span> to <span><math><mi>B</mi></math></span> by fuzzy matrices. Then it is proved that the behavior of a fuzzy automaton <span><math><mi>A</mi></math></span> differs from the behavior of a fuzzy automaton <span><math><mi>B</mi></math></span> by at most <em>ε</em> if there exists a <em>ε</em>-bisimulation relation between them. In particular, if there exists a surjective <span><math><mi>L</mi></math></span>-functional <em>ε</em>-bisimulation relation between them, we give a more concise proof of above conclusion by fuzzy matrices. Moreover, the notion of <em>ε</em>-bisimulation equivalence relation on a fuzzy automaton is given by fuzzy matrices. Based on two different constructions of quotient fuzzy automata, the relationships between <em>ε</em>-bisimulation relations and <em>ε</em>-bisimulation equivalence relations and the <em>ε</em>-Isomorphism theorems of quotient fuzzy automata are given.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109278"},"PeriodicalIF":3.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181059","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 : 2025-01-16DOI: 10.1016/j.fss.2025.109279
Yuhua Gao , Cheng Hu , Juan Yu
Considering the function diversity of individuals in the actual system, the uncertainty and fuzziness in modeling network dynamics, a class of T-S fuzzy multilayered networks is concerned in this article, and the fixed/preassigned-time output synchronization is explored to overcome the immeasurability of node states. Firstly, to remove the connectivity restriction of network topology, the synchronous state, which can be any specified smooth orbit, is added to the original network as a virtual individual. Subsequently, a type of continuous fuzzy control law is developed to realize fixed/preassigned-time output synchronization for multilayered networks, and several synchronization criteria are gained based on fixed-time stability theory and inequality technique. Notice that the link between the estimate of settling-time and the number of network layers is revealed, and the restriction on the output matrix is largely weakened compared to some previous researches. Lastly, the proposed fuzzy control schemes and output synchronization criteria are verified by numerical simulations and are applied to signal security communication, in which the robustness and sensitivity of the developed control method are analyzed.
{"title":"Output synchronization in fixed/preassigned-time of T-S fuzzy multilayered networks","authors":"Yuhua Gao , Cheng Hu , Juan Yu","doi":"10.1016/j.fss.2025.109279","DOIUrl":"10.1016/j.fss.2025.109279","url":null,"abstract":"<div><div>Considering the function diversity of individuals in the actual system, the uncertainty and fuzziness in modeling network dynamics, a class of T-S fuzzy multilayered networks is concerned in this article, and the fixed/preassigned-time output synchronization is explored to overcome the immeasurability of node states. Firstly, to remove the connectivity restriction of network topology, the synchronous state, which can be any specified smooth orbit, is added to the original network as a virtual individual. Subsequently, a type of continuous fuzzy control law is developed to realize fixed/preassigned-time output synchronization for multilayered networks, and several synchronization criteria are gained based on fixed-time stability theory and inequality technique. Notice that the link between the estimate of settling-time and the number of network layers is revealed, and the restriction on the output matrix is largely weakened compared to some previous researches. Lastly, the proposed fuzzy control schemes and output synchronization criteria are verified by numerical simulations and are applied to signal security communication, in which the robustness and sensitivity of the developed control method are analyzed.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109279"},"PeriodicalIF":3.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181645","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 : 2025-01-16DOI: 10.1016/j.fss.2025.109282
Xiyan Cao , Fucai Lin , Wen Sun , Jinjin Li , Peijin Lin
Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. A discriminative knowledge structure is reducing redundant items to vary the test with the aim of lightening the workload for students, and the bi-discriminative knowledge structure is useful for evaluating ‘relative independence’ items or knowledge points. Moreover, it is highly significant to determine the type of fuzzy skill multimap that delineates a discriminative or bi-discriminative knowledge structure. Additionally, we provide a characterization of fuzzy skill multimaps in order to delineate knowledge spaces, learning spaces and simple closure spaces respectively. Furthermore, there are some interesting applications in the meshing of the delineated knowledge structures and the distributed fuzzy skill multimaps. We also give a more precise analysis regarding the separability (resp. bi-separability) on which condition the information collected within a local assessment can reflect an assessment at the global level, and which condition any of the local domains can localize from given global assessment.
{"title":"A note on knowledge structures delineated by fuzzy skill multimaps","authors":"Xiyan Cao , Fucai Lin , Wen Sun , Jinjin Li , Peijin Lin","doi":"10.1016/j.fss.2025.109282","DOIUrl":"10.1016/j.fss.2025.109282","url":null,"abstract":"<div><div>Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. A discriminative knowledge structure is reducing redundant items to vary the test with the aim of lightening the workload for students, and the bi-discriminative knowledge structure is useful for evaluating ‘relative independence’ items or knowledge points. Moreover, it is highly significant to determine the type of fuzzy skill multimap that delineates a discriminative or bi-discriminative knowledge structure. Additionally, we provide a characterization of fuzzy skill multimaps in order to delineate knowledge spaces, learning spaces and simple closure spaces respectively. Furthermore, there are some interesting applications in the meshing of the delineated knowledge structures and the distributed fuzzy skill multimaps. We also give a more precise analysis regarding the separability (resp. bi-separability) on which condition the information collected within a local assessment can reflect an assessment at the global level, and which condition any of the local domains can localize from given global assessment.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109282"},"PeriodicalIF":3.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181644","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 : 2025-01-16DOI: 10.1016/j.fss.2025.109280
Guojun Wu , Wei Yao , Qingguo Li
With a commutative unital quantale as the truth value table, this study focuses on representations of -domains by means of generalized -closure spaces. First, the notions of interpolative generalized -closure spaces and directed closed sets are introduced. It is proved that for an interpolative generalized -closure space (resp., a -closure space), the collection of directed closed sets with respect to the inclusion -order forms a continuous -dcpo (resp., an algebraic -dcpo). Conversely, it is shown that every continuous -dcpo (resp., algebraic -dcpo) can be reconstructed from an interpolative generalized -closure space (resp., a -closure space). Second, the notion of dense subspaces of generalized -closure spaces is provided. By means of dense subspaces, an alternative representation for algebraic -dcpos is given. Furthermore, the notion of approximable -relations between interpolative generalized -closure spaces is introduced. Consequently, a categorical equivalence is established between the category of interpolative generalized -closure spaces (resp., -closure spaces) with approximable -relations and that of continuous -dcpos (resp., algebraic -dcpos) with Scott continuous mappings.
{"title":"A categorical equivalence between Q-domains and interpolative generalized Q-closure spaces","authors":"Guojun Wu , Wei Yao , Qingguo Li","doi":"10.1016/j.fss.2025.109280","DOIUrl":"10.1016/j.fss.2025.109280","url":null,"abstract":"<div><div>With a commutative unital quantale <span><math><mi>Q</mi></math></span> as the truth value table, this study focuses on representations of <span><math><mi>Q</mi></math></span>-domains by means of generalized <span><math><mi>Q</mi></math></span>-closure spaces. First, the notions of interpolative generalized <span><math><mi>Q</mi></math></span>-closure spaces and directed closed sets are introduced. It is proved that for an interpolative generalized <span><math><mi>Q</mi></math></span>-closure space (resp., a <span><math><mi>Q</mi></math></span>-closure space), the collection of directed closed sets with respect to the inclusion <span><math><mi>Q</mi></math></span>-order forms a continuous <span><math><mi>Q</mi></math></span>-dcpo (resp., an algebraic <span><math><mi>Q</mi></math></span>-dcpo). Conversely, it is shown that every continuous <span><math><mi>Q</mi></math></span>-dcpo (resp., algebraic <span><math><mi>Q</mi></math></span>-dcpo) can be reconstructed from an interpolative generalized <span><math><mi>Q</mi></math></span>-closure space (resp., a <span><math><mi>Q</mi></math></span>-closure space). Second, the notion of dense subspaces of generalized <span><math><mi>Q</mi></math></span>-closure spaces is provided. By means of dense subspaces, an alternative representation for algebraic <span><math><mi>Q</mi></math></span>-dcpos is given. Furthermore, the notion of approximable <span><math><mi>Q</mi></math></span>-relations between interpolative generalized <span><math><mi>Q</mi></math></span>-closure spaces is introduced. Consequently, a categorical equivalence is established between the category of interpolative generalized <span><math><mi>Q</mi></math></span>-closure spaces (resp., <span><math><mi>Q</mi></math></span>-closure spaces) with approximable <span><math><mi>Q</mi></math></span>-relations and that of continuous <span><math><mi>Q</mi></math></span>-dcpos (resp., algebraic <span><math><mi>Q</mi></math></span>-dcpos) with Scott continuous mappings.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109280"},"PeriodicalIF":3.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181056","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 : 2025-01-15DOI: 10.1016/j.fss.2025.109277
A.F. Roldán López de Hierro , A. Cruz , R.H.N. Santiago , C. Roldán , D. García-Zamora , F. Neres , H. Bustince
Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the α-order on the family of all triangular fuzzy numbers with support on .
{"title":"Fuzzy dissimilarities and the fuzzy Choquet integral of triangular fuzzy numbers on [0,1]","authors":"A.F. Roldán López de Hierro , A. Cruz , R.H.N. Santiago , C. Roldán , D. García-Zamora , F. Neres , H. Bustince","doi":"10.1016/j.fss.2025.109277","DOIUrl":"10.1016/j.fss.2025.109277","url":null,"abstract":"<div><div>Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the <em>α</em>-order on the family of all triangular fuzzy numbers with support on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109277"},"PeriodicalIF":3.2,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181058","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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