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General multifractal dimensions of measures 测量的一般多分形维度
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-11-05 DOI: 10.1016/j.fss.2024.109177
Bilel Selmi
{"title":"General multifractal dimensions of measures","authors":"Bilel Selmi","doi":"10.1016/j.fss.2024.109177","DOIUrl":"10.1016/j.fss.2024.109177","url":null,"abstract":"<div><div>The main aim of this paper is to present a comprehensive exploration of general multifractal dimensions of Borel probability measures, with a specific emphasis on the diverse methodologies available for their estimation or computation. We prove that these general dimensions enable us to compare a probability measure <em>ϑ</em> with the general multifractal Hausdorff or packing measure. Also, we aim to measure the degree of regularity or singularity of <em>ϑ</em>, and we examine the correlations between various approaches to defining the general multifractal exact dimension of Borel probability measures, using fractal analysis of the essential supports of these measures as the foundation.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593729","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
Subsethood measures based on cardinality of type-2 fuzzy sets 基于第 2 类模糊集心率的次优度量
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-11-04 DOI: 10.1016/j.fss.2024.109174
Carmen Torres-Blanc , Jesus Martinez-Mateo , Susana Cubillo , Luis Magdalena , Francisco Javier Talavera , Jorge Elorza
{"title":"Subsethood measures based on cardinality of type-2 fuzzy sets","authors":"Carmen Torres-Blanc ,&nbsp;Jesus Martinez-Mateo ,&nbsp;Susana Cubillo ,&nbsp;Luis Magdalena ,&nbsp;Francisco Javier Talavera ,&nbsp;Jorge Elorza","doi":"10.1016/j.fss.2024.109174","DOIUrl":"10.1016/j.fss.2024.109174","url":null,"abstract":"<div><div>In this work we present a novel axiomatic framework for subsethood measures in type-2 fuzzy sets. It differs from previous approaches in two key ways. First, the degree of membership is not simply a fuzzy set as considered in other papers, but rather a label of the variable <em>Truth</em>, more in line with Zadeh's original idea. Secondly, the concept of subsethood is approached in terms of its relationship with cardinality. Additionally, illustrative examples of such measures are provided.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593727","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
Lattice-valued coarse structures 格值粗结构
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-11-04 DOI: 10.1016/j.fss.2024.109175
Yongchao Wang , Bin Pang , Fu-Gui Shi
{"title":"Lattice-valued coarse structures","authors":"Yongchao Wang ,&nbsp;Bin Pang ,&nbsp;Fu-Gui Shi","doi":"10.1016/j.fss.2024.109175","DOIUrl":"10.1016/j.fss.2024.109175","url":null,"abstract":"<div><div>Based on a complete residuated lattice <em>L</em>, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of <em>L</em>-entourages and <em>L</em>-(quasi, semi)-coarse structures and study the maps between <em>L</em>-coarse spaces. Secondly, we provide some examples of <em>L</em>-coarse structures from the aspects of <em>L</em>-metrics, <em>L</em>-relations and <em>L</em>-hyperstructures. Thirdly, we introduce the notion of <em>L</em>-ball structures to characterize <em>L</em>-coarse structures. Finally, we establish the relationship among <em>L</em>-entourage spaces, <em>L</em>-quasi-coarse spaces, <em>L</em>-semi-coarse spaces and <em>L</em>-coarse spaces in a categorical viewpoint.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593728","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
A note on t-norms having additive generators 关于具有相加生成器的 t 准则的说明
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-31 DOI: 10.1016/j.fss.2024.109172
Wenwen Zong , Yong Su , Radko Mesiar
{"title":"A note on t-norms having additive generators","authors":"Wenwen Zong ,&nbsp;Yong Su ,&nbsp;Radko Mesiar","doi":"10.1016/j.fss.2024.109172","DOIUrl":"10.1016/j.fss.2024.109172","url":null,"abstract":"<div><div>This paper focuses on t-norms which have some additive generators. We show that a t-norm <em>T</em> has some additive generators if and only if the fully ordered semigroup induced by <em>T</em> can be embedded into some fully ordered semigroup induced by either the product <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>P</mi></mrow></msub></math></span> or the Lukasiewicz t-norm <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>L</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578848","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
Subresiduated Nelson algebras 亚残差纳尔逊代数
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-29 DOI: 10.1016/j.fss.2024.109170
Noemí Lubomirsky , Paula Menchón , Hernán Javier San Martín
{"title":"Subresiduated Nelson algebras","authors":"Noemí Lubomirsky ,&nbsp;Paula Menchón ,&nbsp;Hernán Javier San Martín","doi":"10.1016/j.fss.2024.109170","DOIUrl":"10.1016/j.fss.2024.109170","url":null,"abstract":"<div><div>In this paper we generalize the well known relation between Heyting algebras and Nelson algebras in the framework of subresiduated lattices. In order to make it possible, we introduce the variety of subresiduated Nelson algebras. The main tool for its study is the construction provided by Vakarelov. Using it, we characterize the lattice of congruences of a subresiduated Nelson algebra through some of its implicative filters. We use this characterization to describe simple and subdirectly irreducible algebras, as well as principal congruences. Moreover, we prove that the variety of subresiduated Nelson algebras has equationally definable principal congruences and also the congruence extension property. Additionally, we present an equational base for the variety generated by the totally ordered subresiduated Nelson algebras. Finally, we show that there exists an equivalence between the algebraic category of subresiduated lattices and the algebraic category of centedred subresiduated Nelson algebras.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560573","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
Output-feedback control design for Takagi-Sugeno fuzzy systems through Lyapunov functions depending polynomially on the states 通过取决于多项式状态的 Lyapunov 函数设计高木-菅野模糊系统的输出反馈控制装置
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-29 DOI: 10.1016/j.fss.2024.109156
Yara Quilles-Marinho, Ricardo C.L.F. Oliveira, Pedro L.D. Peres
{"title":"Output-feedback control design for Takagi-Sugeno fuzzy systems through Lyapunov functions depending polynomially on the states","authors":"Yara Quilles-Marinho,&nbsp;Ricardo C.L.F. Oliveira,&nbsp;Pedro L.D. Peres","doi":"10.1016/j.fss.2024.109156","DOIUrl":"10.1016/j.fss.2024.109156","url":null,"abstract":"<div><div>This paper proposes a new strategy based on linear matrix inequalities (LMIs) for the synthesis of state- and output-feedback controllers through parallel distributed compensation for continuous-time Takagi-Sugeno fuzzy systems. The main novelty of the proposed design technique is the use of homogeneous polynomial Lyapunov functions of degree larger than two on the states, generalizing the results based on quadratic functions. Parametrized in terms of a constant matrix, those homogeneous polynomial Lyapunov functions provide less conservative results in terms of stability and decay rate of trajectories when dealing with membership functions whose time-derivatives have unknown bounds. The synthesis procedure is formulated in terms of a locally convergent iterative algorithm, where a set of LMIs defined in an augmented parameter space is solved at each iteration. Numerical examples are used to compare the proposed method with quadratic stabilizability techniques available in the literature, illustrating the advantages of higher degree Lyapunov functions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578750","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
A design of sliding mode control for uncertain T-S fuzzy systems with multiple input matrices 具有多输入矩阵的不确定 T-S 模糊系统的滑模控制设计
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-28 DOI: 10.1016/j.fss.2024.109154
Yingying Wang, Jianyu Zhang, Xin Li, Qing Luo
{"title":"A design of sliding mode control for uncertain T-S fuzzy systems with multiple input matrices","authors":"Yingying Wang,&nbsp;Jianyu Zhang,&nbsp;Xin Li,&nbsp;Qing Luo","doi":"10.1016/j.fss.2024.109154","DOIUrl":"10.1016/j.fss.2024.109154","url":null,"abstract":"<div><div>This paper investigates how to design a sliding mode surface and construct a sliding controller to stabilize a uncertain T-S fuzzy system with multiple input matrices and matched disturbances. The method proposed in this paper can expand the effective scope of sliding mode control into uncertain fuzzy systems even if there are not assumptions of input matrices. In order to expand the effective scope of controlled systems, firstly, transform the form of input matrices of system plants into a new input matrix <em>B</em>. Secondly, design a new sliding mode surface according to all the input matrices. It contains <em>q</em> sub-sliding surfaces. The number <em>q</em> is the column number of input matrix <em>B</em>. Thirdly, according to sliding mode theorem, the equivalent controller can be deduced. But, it may be nonexistence. A judgment criterion for the existence of the controller is given as a lemma. By use of the proposed sliding surface, a new sliding controller is constructed. It can settle the confliction difficult between sliding surface and input matrices. And it can make the system reach the sliding surface and keep on it thereafter. At last, two examples are given to illustrate the effectiveness of this paper.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552855","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
ECM+: An improved evidential c-means with adaptive distance ECM+：具有自适应距离的改进型证据 c-means
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-24 DOI: 10.1016/j.fss.2024.109168
Benoît Albert, Violaine Antoine, Jonas Koko
{"title":"ECM+: An improved evidential c-means with adaptive distance","authors":"Benoît Albert,&nbsp;Violaine Antoine,&nbsp;Jonas Koko","doi":"10.1016/j.fss.2024.109168","DOIUrl":"10.1016/j.fss.2024.109168","url":null,"abstract":"<div><div>Evidential c-means (ECM) is a prototype-based clustering algorithm that generates a credal partition. Such a partition encompasses the notions that can be encountered with a hard, fuzzy or possibilistic partition, allowing the representation of various situations concerning the class membership of an object. The ECM method provides a prototype for each subset of the possible classes, calculated by averaging the prototypes of the classes included in the subsets. Although this definition perfectly suits ECM when employing a Euclidean distance, it becomes inappropriate when using a Mahalanobis distance. In this context, a new definition of prototypes for the subsets is proposed. The ECM objective function is then optimized using the new definition of prototypes. The subsequent algorithm, named ECM+, is finally tested on various synthetic and real data sets to demonstrate its interest compared to ECM.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552857","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
Stability of high-order nonlinear Takagi–Sugeno fuzzy impulsive delayed coupled systems 高阶非线性高木-菅野模糊脉冲延迟耦合系统的稳定性
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-22 DOI: 10.1016/j.fss.2024.109164
Haoming Han , Shixu Zhao , Jing Zhang , Yan Liu
{"title":"Stability of high-order nonlinear Takagi–Sugeno fuzzy impulsive delayed coupled systems","authors":"Haoming Han ,&nbsp;Shixu Zhao ,&nbsp;Jing Zhang ,&nbsp;Yan Liu","doi":"10.1016/j.fss.2024.109164","DOIUrl":"10.1016/j.fss.2024.109164","url":null,"abstract":"<div><div>In this study, we consider the stability of high-order nonlinear Takagi–Sugeno fuzzy impulsive delayed coupled systems (TSFICSs). It should be noted that the linear growth condition is removed in the investigation of high-order nonlinear TSFICSs, which weakens the conditions compared with previous studies of impulsive systems. In addition, the existing research methods do not work for high-order nonlinear TSFICSs, so novel impulsive differential inequalities with high-order terms are established to investigate the stabilization of high-order nonlinear TSFICSs and develop the classic impulsive differential inequalities for high-order nonlinear situations. Next, sufficient conditions for the stability are obtained based on the new impulsive differential inequalities together with graph theory and the Lyapunov method. Finally, the theoretical results are applied to modified impulsive delayed coupled Fitzhugh–Nagumo models, and numerical simulations are provided to illustrate the practical value of the derived results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533114","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
Bhatia-Davis inequalities for lower and upper previsions and covariances Bhatia-Davis 下部和上部前值及协方差不等式
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-10-18 DOI: 10.1016/j.fss.2024.109145
Renato Pelessoni, Paolo Vicig
{"title":"Bhatia-Davis inequalities for lower and upper previsions and covariances","authors":"Renato Pelessoni,&nbsp;Paolo Vicig","doi":"10.1016/j.fss.2024.109145","DOIUrl":"10.1016/j.fss.2024.109145","url":null,"abstract":"<div><div>We explore how the classical Bhatia-Davis inequality bounding variances can be extended to uncertainty evaluations of gambles (bounded random numbers) by means of imprecise (lower or upper) previsions with different degrees of consistency. Firstly, a number of extensions are found with 2-coherent imprecise previsions. Subsequently, bounds with coherent lower and upper previsions are investigated, together with applications bounding lower and upper variances as well as p-boxes. Finally, bounds for covariances and for lower and upper covariances are obtained. Like the classical situation, imprecise Bhatia-Davis inequalities require a reduced amount of uncertainty information to be applied. When even less information is available, we show that various versions of Popoviciu's inequality obtain.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533113","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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