Fuzzy Sets and Systems最新文献_第8页

The general algebraic solution of dual fuzzy linear systems and fuzzy Stein matrix equations 对偶模糊线性系统和模糊斯坦因矩阵方程的一般代数解法

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-05-06 DOI: 10.1016/j.fss.2024.108997

Đorđe Dragić, Biljana Mihailović, Ljubo Nedović

{"title":"The general algebraic solution of dual fuzzy linear systems and fuzzy Stein matrix equations","authors":"Đorđe Dragić, Biljana Mihailović, Ljubo Nedović","doi":"10.1016/j.fss.2024.108997","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108997","url":null,"abstract":"<div>In this paper, we present a new method for solving a dual fuzzy linear system (DFLS), <math><mi>A</mi><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>+</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>=</mo><mi>B</mi><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>+</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover></math>, where the coefficient matrices A and B are arbitrary real <math><mi>m</mi><mo>×</mo><mi>n</mi></math> matrices and <math><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> and <math><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> are given fuzzy number vectors. A necessary and sufficient condition for the <math><mi>R</mi></math>-consistency of the associated system of linear equations is obtained. The straightforward method for solving <math><mi>m</mi><mo>×</mo><mi>n</mi></math> DFLS based on an arbitrary {1}-inverse of <math><mi>A</mi><mo>−</mo><mi>B</mi></math> is introduced. Also, as an application, we present the first algorithm for solving the fuzzy Stein matrix equations, based on {1}-inverses. Finally, these results are illustrated by examples.</div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140905476","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 Radon-Nikodym theorem for monotone measures 单调度量的拉顿-尼科迪姆定理

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-05-03 DOI: 10.1016/j.fss.2024.108995

Yao Ouyang , Jun Li

引用次数: 0

Dissipative control for quaternion-valued fuzzy memristive neural networks: Nonlinear scalarization approach 四元值模糊记忆神经网络的耗散控制：非线性标量化方法

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-05-03 DOI: 10.1016/j.fss.2024.108996

Hongzhi Wei , Hongjun Zhou , Ruoxia Li , Ning Li

引用次数: 0

On the representation of internal uninorms on a bounded lattice 论有界晶格上内部非矩形的表示

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-30 DOI: 10.1016/j.fss.2024.108994

Yao Ouyang , Hua-Peng Zhang , Zhudeng Wang , Bernard De Baets

{"title":"On the representation of internal uninorms on a bounded lattice","authors":"Yao Ouyang , Hua-Peng Zhang , Zhudeng Wang , Bernard De Baets","doi":"10.1016/j.fss.2024.108994","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108994","url":null,"abstract":"<div>Internal uninorms on a bounded lattice always output one of the two input values and are nothing else but idempotent uninorms when the lattice is a chain. In this paper, we study the existence and representation of internal uninorms with a given neutral element e on a bounded lattice. We obtain a necessary condition for the existence of such an internal uninorm. In the case that those elements that are incomparable with the neutral element (collected in the set <math><msub><mrow><mi>I</mi></mrow><mrow><mi>e</mi></mrow></msub></math>) constitute a chain, we prove that this necessary condition also becomes a sufficient one and allows to represent any internal uninorm on a bounded lattice in terms of an internal uninorm on the bounded chain obtained by deleting <math><msub><mrow><mi>I</mi></mrow><mrow><mi>e</mi></mrow></msub></math> from the lattice and an internal quasi-uninorm on <math><msub><mrow><mi>I</mi></mrow><mrow><mi>e</mi></mrow></msub></math> connected via a family of lower sets and a family of upper sets indexed by <math><msub><mrow><mi>I</mi></mrow><mrow><mi>e</mi></mrow></msub></math>.</div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140822315","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

Fuzzy three-way rule learning and its classification methods 模糊三向规则学习及其分类方法

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-30 DOI: 10.1016/j.fss.2024.108993

Mingjie Cai , Mingzhe Yan , Zhenhua Jia

引用次数: 0

Finite determinization of fuzzy automata using a parametric product-based t-norm 使用基于参数乘积的 t 准则对模糊自动机进行有限确定

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-26 DOI: 10.1016/j.fss.2024.108990

Ivana Micić , Stefan Stanimirović , José Ramón González de Mendívil , Miroslav Ćirić , Zorana Jančić

{"title":"Finite determinization of fuzzy automata using a parametric product-based t-norm","authors":"Ivana Micić , Stefan Stanimirović , José Ramón González de Mendívil , Miroslav Ćirić , Zorana Jančić","doi":"10.1016/j.fss.2024.108990","DOIUrl":"10.1016/j.fss.2024.108990","url":null,"abstract":"<div>This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm differs from the behavior of the fuzzy automaton over the product t-norm only in words with a degree of acceptance below the given parameter. However, using the parametric t-norm, we obtain an algorithm that outputs a finite minimal deterministic fuzzy automaton whose behavior differs from the starting fuzzy automaton described above. By setting the parameter to a sufficiently small value, the proposed algorithm provides a deterministic fuzzy automaton with behavior that differs insignificantly from the starting fuzzy automaton, as the difference is achieved only for words accepted by the starting fuzzy automaton with an insignificant value. As a tradeoff, the proposed approach provides finite determinization, even when all other determinization methods would result in an infinite deterministic automaton. We support this fact with an illustrative example.</div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931042","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

Projection depth and Lr-type depths for fuzzy random variables 模糊随机变量的投影深度和 Lr 型深度

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-26 DOI: 10.1016/j.fss.2024.108991

Luis González-de la Fuente , Alicia Nieto-Reyes , Pedro Terán

{"title":"Projection depth and Lr-type depths for fuzzy random variables","authors":"Luis González-de la Fuente , Alicia Nieto-Reyes , Pedro Terán","doi":"10.1016/j.fss.2024.108991","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108991","url":null,"abstract":"<div>Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate case) and there is a lack of parametric models, a fuzzy extension of depth-based methods is very interesting. In this paper, we adapt the multivariate depths projection depth and <math><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup></math>-type depth functions to the fuzzy setting, proposing different generalizations for the <math><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup></math>-type depths. We prove that the proposed fuzzy depth functions have very good properties, obtaining that the fuzzy projection depth is the second example in the literature to satisfy simultaneously the notion of semilinear and of geometric depth. This implies that the fuzzy projection depth is extremely well behave, to order fuzzy sets with respect to fuzzy random variables. Furthermore, we illustrate the good empirical behavior of the proposed fuzzy depth functions with a real data example of trapezoidal fuzzy sets and the used of fuzzy depths in depth-based classification procedures. Finally, as trapezoidal fuzzy sets can be represented by elements of <math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math>, we justify our proposals by also showing empirically the superiority of the fuzzy depths over the multivariate projection depth applied to fuzzy sets.</div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001374/pdfft?md5=70025cc44ef4b8f167f43710d841cf19&pid=1-s2.0-S0165011424001374-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813498","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

On fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic 基于t-规范模糊运算的模糊集合中的模糊秩

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-26 DOI: 10.1016/j.fss.2024.108992

Michał K. Urbański , Dominika Krawczyk , Kinga M. Wójcicka , Paweł M. Wójcicki

{"title":"On fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic","authors":"Michał K. Urbański , Dominika Krawczyk , Kinga M. Wójcicka , Paweł M. Wójcicki","doi":"10.1016/j.fss.2024.108992","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108992","url":null,"abstract":"<div>In this paper we study some fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic. The definition of the order comes from the extension principle for interval order: <math><mi>a</mi><mo>></mo><mi>b</mi></math> iff <math><mi>a</mi><mo>−</mo><mi>b</mi><mo>></mo><mn>0</mn></math> and from measurement sciences. In measurement sciences the order is given by a comparator whose operation is based on empirical determination of the difference of two input signals. Fuzzy comparison based on fuzzy sets subtraction is considered as an extension of substraction operation, namely a fuzzy set B is greater than a fuzzy set A if <math><mi>B</mi><mo>−</mo><mi>A</mi></math> is greater than zero in fuzzy arithmetic. In the paper we show that this fuzzy order is irreflexive, transitive, asymmetric and compact, subhomothetic, Archimedean and semi-Ferrers. Our idea refers to the work of M. K. Urbański (Modeling the measurement in algebraic fuzzy structures, Warsaw 2003, in polish) and to the fundamental problems in the measurement theory.</div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813499","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

On Stonean triangle algebras 关于斯通安三角代数

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-25 DOI: 10.1016/j.fss.2024.108989

Saeide Zahiri , Arsham Borumand Saeid

引用次数: 0

A relation algebraic approach to universal integrals 普遍积分的关系代数方法

IF 3.9 1区数学

Fuzzy Sets and Systems Pub Date : 2024-04-23 DOI: 10.1016/j.fss.2024.108987

Michael Winter

引用次数: 0