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Generalized F-spaces through the lens of fuzzy measures
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-14 DOI: 10.1016/j.fss.2025.109317
Mariam Taha, Vicenç Torra
{"title":"Generalized F-spaces through the lens of fuzzy measures","authors":"Mariam Taha,&nbsp;Vicenç Torra","doi":"10.1016/j.fss.2025.109317","DOIUrl":"10.1016/j.fss.2025.109317","url":null,"abstract":"<div><div>Probabilistic metric spaces are natural extensions of metric spaces, where the function that computes the distance outputs a distribution on the real numbers rather than a single value. Such a function is called a distribution function. F-spaces are constructions for probabilistic metric spaces, where the distribution functions are built for functions that map from a measurable space to a metric space.</div><div>In this paper, we propose an extension of F-spaces, called Generalized F-space. This construction replaces the metric space with a probabilistic metric space and uses fuzzy measures to evaluate sets of elements whose distances are probability distributions. We present several results that establish connections between the properties of the constructed space and specific fuzzy measures under particular triangular norms. Furthermore, we demonstrate how the space can be applied in machine learning to compute distances between different classifier models. Experimental results based on Sugeno <em>λ</em>-measures are consistent with our theoretical findings.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109317"},"PeriodicalIF":3.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429976","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}
引用次数: 0
A fuzzy β-covering rough set model for attribute reduction by composite measure
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-14 DOI: 10.1016/j.fss.2025.109314
Xiongtao Zou , Jianhua Dai
{"title":"A fuzzy β-covering rough set model for attribute reduction by composite measure","authors":"Xiongtao Zou ,&nbsp;Jianhua Dai","doi":"10.1016/j.fss.2025.109314","DOIUrl":"10.1016/j.fss.2025.109314","url":null,"abstract":"<div><div>Fuzzy <em>β</em>-covering rough sets, the state-of-the-art theory of covering-based rough sets, have received much attention. The key step in establishing a fuzzy rough set model is to construct the fuzzy binary relation between objects. However, under the environment of multiple fuzzy <em>β</em>-coverings, the existing fuzzy <em>β</em>-neighborhoods either do not satisfy the reflexivity of relation or rely on R-implication operators. For this reason, these fuzzy <em>β</em>-neighborhoods are not very suitable for characterizing the similarity between objects. In order to characterize the similarity between objects under the environment of multiple fuzzy <em>β</em>-coverings more reasonably, this paper constructs a <em>β</em>-neighborhood that satisfies the reflexivity and does not depend on any fuzzy operators. On this basis, a novel fuzzy <em>β</em>-covering rough set model is established. Based on the proposed model, several monotonic uncertainty measures of fuzzy <em>β</em>-coverings are defined. Finally, an attribute reduction method is presented, and the experimental analysis demonstrates the effectiveness of our proposed method compared with the other five excellent attribute reduction methods.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109314"},"PeriodicalIF":3.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428139","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}
引用次数: 0
Calculus and study of fuzzy dynamic equations for fuzzy vector functions on time scales
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-12 DOI: 10.1016/j.fss.2025.109307
M. Shahidi , T. Allahviranloo , M. Arana-Jiménez
{"title":"Calculus and study of fuzzy dynamic equations for fuzzy vector functions on time scales","authors":"M. Shahidi ,&nbsp;T. Allahviranloo ,&nbsp;M. Arana-Jiménez","doi":"10.1016/j.fss.2025.109307","DOIUrl":"10.1016/j.fss.2025.109307","url":null,"abstract":"<div><div>In this paper, we introduce the <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi><mi>H</mi></mrow></msub></math></span>-derivative as a novel concept for characterizing the differentiability of fuzzy vector functions on time scales. Building on this, we define two distinct types of <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi><mi>H</mi></mrow></msub></math></span>-differentiability: (<em>i</em>)-<span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi><mi>H</mi></mrow></msub></math></span>-differentiability and <span><math><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></math></span>-<span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi><mi>H</mi></mrow></msub></math></span>-differentiability, and study some of their properties. Within this framework, we investigate fuzzy dynamic equations for fuzzy vector functions on time scales and establish an existence theorem for these equations. Moreover, we examine first-order linear fuzzy dynamic equations and provide general expressions for their solutions. In the end, we present several examples to demonstrate our results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109307"},"PeriodicalIF":3.2,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396207","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}
引用次数: 0
Event-triggered computation-reducing fuzzy intelligence control incorporating fixed-time predefined behaviors in discrete-time
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-12 DOI: 10.1016/j.fss.2025.109311
Xiangwei Bu, Ruining Luo, Yupeng Gao
{"title":"Event-triggered computation-reducing fuzzy intelligence control incorporating fixed-time predefined behaviors in discrete-time","authors":"Xiangwei Bu,&nbsp;Ruining Luo,&nbsp;Yupeng Gao","doi":"10.1016/j.fss.2025.109311","DOIUrl":"10.1016/j.fss.2025.109311","url":null,"abstract":"<div><div>The focus of this article lies in the computation-reducing fuzzy intelligence control of discrete-time systems with unknown nonlinearities through the event-triggered mechanism, aiming to confine the system output within a prescribed envelope to satisfy a fixed convergence time and achieve a given steady-state value. Firstly, we introduce an innovative performance function that enforces fixed-time prescribed qualities on the discrete-time system output. Subsequently, we transform the boundary constraint into an error term which is further utilized to define an intermediate variable function. In contrast, instead of using the transformed error, we employ the intermediate variable function to design a discrete-time prescribed performance controller, presenting a new framework distinct from existing sliding-mode-control-based structures. Moreover, our approach requires only one fuzzy estimator for nonlinearity approximation while incorporating an event-triggered adaptive law for updating fuzzy weights, resulting in a low-complexity implementation with reduced computational cost. Finally, comparative simulation results validate its superiority.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109311"},"PeriodicalIF":3.2,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396206","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}
引用次数: 0
Non-commutative ordinal sum construction
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-07 DOI: 10.1016/j.fss.2025.109308
Andrea Mesiarová-Zemánková
{"title":"Non-commutative ordinal sum construction","authors":"Andrea Mesiarová-Zemánková","doi":"10.1016/j.fss.2025.109308","DOIUrl":"10.1016/j.fss.2025.109308","url":null,"abstract":"<div><div>The construction methods for associative functions are discussed. The focus is on summand-based construction methods as an extension of the ordinal sum and the <em>z</em>-ordinal sum. While the ordinal sum and the <em>z</em>-ordinal sum can be assumed to be commutative summand-based construction methods, since they construct commutative functions from commutative summands, the non-commutative ordinal sum, which constructs non-commutative functions from commutative summands is introduced. The decomposition of a semi-t-operator via a non-commutative ordinal sum is also shown.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109308"},"PeriodicalIF":3.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376531","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}
引用次数: 0
Approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-05 DOI: 10.1016/j.fss.2025.109299
Marko Stanković , Miroslav Ćirić , Stefan Stanimirović , Đorđe Stakić
{"title":"Approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras","authors":"Marko Stanković ,&nbsp;Miroslav Ćirić ,&nbsp;Stefan Stanimirović ,&nbsp;Đorđe Stakić","doi":"10.1016/j.fss.2025.109299","DOIUrl":"10.1016/j.fss.2025.109299","url":null,"abstract":"<div><div>In this paper, we study two types of <em>λ</em>-approximate simulations and five types of <em>λ</em>-approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras. The value <em>λ</em> is an element from a Heyting algebra, which serves to relax the conditions in the definitions of simulations and bisimulations. Additionally, <em>λ</em> represents the degree of modal equivalence between two worlds from distinct Kripke models, considering the given non-empty set of modal formulae. Further, we develop an efficient algorithm for computing the greatest <em>λ</em>-approximate simulation and bisimulation for every type. We also demonstrate the application of these algorithms in the state reduction of Kripke models in such a way that the reduced model preserves the same semantic properties to the extent determined by the scalar <em>λ</em>. We also present the algorithm that partitions the interval of the degrees of modal equivalence into subintervals with the same minimal corresponding factor fuzzy Kripke model.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109299"},"PeriodicalIF":3.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376530","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}
引用次数: 0
Non-fragile sampled and delayed fuzzy output feedback stabilization for uncertain nonlinear systems
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-04 DOI: 10.1016/j.fss.2025.109298
Zebin Wu , Meng Li , Chenguang Wu , Yanjun Shen
{"title":"Non-fragile sampled and delayed fuzzy output feedback stabilization for uncertain nonlinear systems","authors":"Zebin Wu ,&nbsp;Meng Li ,&nbsp;Chenguang Wu ,&nbsp;Yanjun Shen","doi":"10.1016/j.fss.2025.109298","DOIUrl":"10.1016/j.fss.2025.109298","url":null,"abstract":"<div><div>In this paper, the problem of fuzzy adaptive output feedback stabilization is investigated for a class of uncertain nonlinear systems with sampled and delayed outputs. There also exists unknown measurement noise. An extended fuzzy nonlinear system is obtained on the basis of an output filter and the fuzzy logical approximation theory. Subsequently, a non-fragile sampled output feedback controller is constructed in the light of a non-fragile fuzzy extended observer. By the time delay method, the closed-loop system is transformed into a continuous and delayed nonlinear system. Sufficient conditions are given to ensure the stability performance of the closed-loop system. Finally, the effectiveness of the proposed scheme is validated through a dynamic model of a single linkage robotic arm.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109298"},"PeriodicalIF":3.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138618","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}
引用次数: 0
Fuzzifications of matroids relying on overlap functions
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-28 DOI: 10.1016/j.fss.2025.109297
Shao-Yu Zhang , Bin Pang
{"title":"Fuzzifications of matroids relying on overlap functions","authors":"Shao-Yu Zhang ,&nbsp;Bin Pang","doi":"10.1016/j.fss.2025.109297","DOIUrl":"10.1016/j.fss.2025.109297","url":null,"abstract":"<div><div>Matroid theory provides a broad theoretical framework with a wide range of applications. On this basis, fuzzy matroids have also undergone significant development based on lattice theory, fuzzy topology, fuzzy convexity, etc. In this paper, we select an overlap function to model conjunction to provide two fuzzification approaches to matroids. Taking an arbitrary overlap function ⊗, we introduce ⊗-fuzzifying matroids and ⊗-fuzzy matroids and study their relations with classical matroids, respectively. Then we explore the relations between ⊗-fuzzifying matroids and (closed, perfect) ⊗-fuzzy matroids. These findings not only provide a theoretical application of overlap functions but also elucidate the connections between different fuzzifications of matroids.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109297"},"PeriodicalIF":3.2,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138620","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}
引用次数: 0
Distributed fuzzy adaptive fault-tolerant control with unknown time-varying power drift signals and asymmetric dead-zones
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-28 DOI: 10.1016/j.fss.2025.109295
Jiyu Zhu , Yadong Yang , Xuan Qiu , Tianping Zhang , Qikun Shen
{"title":"Distributed fuzzy adaptive fault-tolerant control with unknown time-varying power drift signals and asymmetric dead-zones","authors":"Jiyu Zhu ,&nbsp;Yadong Yang ,&nbsp;Xuan Qiu ,&nbsp;Tianping Zhang ,&nbsp;Qikun Shen","doi":"10.1016/j.fss.2025.109295","DOIUrl":"10.1016/j.fss.2025.109295","url":null,"abstract":"<div><div>In this study, we consider the distributed fuzzy fault-tolerant control (FTC) problem for a class of interconnected nonlinear systems with multiple unknown time-varying power drift signals, asymmetric actuator, and output dead-zones. Based on our proposed dead-zone models, an effective distributed finite-time adaptive FTC strategy is developed. In previous studies, the unknown system powers were assumed to be positive odd integers that are greater than or equal to one and their boundaries were also assumed to be positive odd integers, but we relax these assumptions, where the powers are assumed to be unknown time-varying bounded real functions and their boundaries are real constants, and not necessarily positive odd integers. In addition, the proposed output dead-zone approximation model can achieve full approximation within a limited adjustable range, rather than the asymptotic approximation found in previous studies. Theoretical analysis proves that the tracking error of each subsystem converges to a small neighborhood of the origin in finite time. Finally, a simulated coupled inverted pendulum example is presented to demonstrate the validity of the proposed FTC strategy.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109295"},"PeriodicalIF":3.2,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138622","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}
引用次数: 0
Recurrence in collective dynamics: From the hyperspace to fuzzy dynamical systems
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-27 DOI: 10.1016/j.fss.2025.109296
Illych Alvarez , Antoni López-Martínez , Alfred Peris
{"title":"Recurrence in collective dynamics: From the hyperspace to fuzzy dynamical systems","authors":"Illych Alvarez ,&nbsp;Antoni López-Martínez ,&nbsp;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}
引用次数: 0
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