Pub Date : 2025-02-24DOI: 10.1016/j.fss.2025.109322
Sufang Han , Tianwei Zhang , Yanning Wang
This article considers global asymptotic and exponential stabilizations in the mean-square sense of space-time discrete Takagi-Sugeno (T-S) fuzzy genetic oscillator networks (GONs) with switching actuator failures and Dirichlet controlled boundaries. It presents some exciting results for the criteria of global asymptotic stabilization in the mean-square sense for the proposed discrete T-S fuzzy GONs via the approaches of the Lyapunov-Krasovskii function, the discrete Wirtinger inequality, and the discrete formula of integration by parts. Besides, our research delves into the exciting possibility of global exponential stabilization in the mean-square sense, which offers a more comprehensive view of stabilized T-S fuzzy GONs than asymptotic stabilization. More critically, this study shows that global mean-square stabilizations of space-time discrete T-S fuzzy GONs can be achieved better by taking the values with the smaller diffusion intensities, smaller coupling strengths and bigger connection weights. Compared to the previous literatures, this paper offers a framework to discuss the issues of global stabilizations for space-time discrete T-S fuzzy GONs with switching actuator failures through the boundary controls, and the results are applicable in a wide range of applications. And finally, an illustrative example is presented to prove the method's validity.
{"title":"Mean-squared exponential stabilization of Takagi-Sugeno fuzzy genetic oscillator networks involving switching control failures: A frame of spatio-temporal discretizations","authors":"Sufang Han , Tianwei Zhang , Yanning Wang","doi":"10.1016/j.fss.2025.109322","DOIUrl":"10.1016/j.fss.2025.109322","url":null,"abstract":"<div><div>This article considers global asymptotic and exponential stabilizations in the mean-square sense of space-time discrete Takagi-Sugeno (T-S) fuzzy genetic oscillator networks (GONs) with switching actuator failures and Dirichlet controlled boundaries. It presents some exciting results for the criteria of global asymptotic stabilization in the mean-square sense for the proposed discrete T-S fuzzy GONs via the approaches of the Lyapunov-Krasovskii function, the discrete Wirtinger inequality, and the discrete formula of integration by parts. Besides, our research delves into the exciting possibility of global exponential stabilization in the mean-square sense, which offers a more comprehensive view of stabilized T-S fuzzy GONs than asymptotic stabilization. More critically, this study shows that global mean-square stabilizations of space-time discrete T-S fuzzy GONs can be achieved better by taking the values with the smaller diffusion intensities, smaller coupling strengths and bigger connection weights. Compared to the previous literatures, this paper offers a framework to discuss the issues of global stabilizations for space-time discrete T-S fuzzy GONs with switching actuator failures through the boundary controls, and the results are applicable in a wide range of applications. And finally, an illustrative example is presented to prove the method's validity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109322"},"PeriodicalIF":3.2,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480422","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 : 2025-02-21DOI: 10.1016/j.fss.2025.109330
Wenjuan Liu , Zhongqiang Yang
For every non-degenerate convex subset Y of the n-dimensional Euclidean space , let denote the set of all fuzzy numbers, which are fuzzy sets that are upper semi-continuous, fuzzy convex and normal with compact supports contained in Y. Consider the sendograph metric defined on . Zhang has proven that is homeomorphic to the separable Hilbert space when Y is compact or . In this paper, we show that is homeomorphic to if and only if Y is topologically complete.
{"title":"The topological structures of the spaces of fuzzy numbers with the sendograph metric","authors":"Wenjuan Liu , Zhongqiang Yang","doi":"10.1016/j.fss.2025.109330","DOIUrl":"10.1016/j.fss.2025.109330","url":null,"abstract":"<div><div>For every non-degenerate convex subset <em>Y</em> of the <em>n</em>-dimensional Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, let <span><math><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> denote the set of all fuzzy numbers, which are fuzzy sets that are upper semi-continuous, fuzzy convex and normal with compact supports contained in <em>Y</em>. Consider the sendograph metric <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> defined on <span><math><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>. Zhang has proven that <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span> is homeomorphic to the separable Hilbert space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> when <em>Y</em> is compact or <span><math><mi>Y</mi><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In this paper, we show that <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span> is homeomorphic to <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> if and only if <em>Y</em> is topologically complete.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109330"},"PeriodicalIF":3.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474927","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 : 2025-02-21DOI: 10.1016/j.fss.2025.109331
Yin-Feng Zhou , Hai-Long Yang , Jin-Jin Li , Da-Li Wang
Skills represent potential cognitive abilities that need to be reflected by observing external performances. In competence-based knowledge space theory, whether individuals solve items in a knowledge domain correctly can reflect whether they have mastered the relevant skills. Currently, skill function that reflects the relationship between skills and items has been extended to fuzzy skill function on polytomous items. However, existing skill assessment techniques are not suitable to assess response data that are noisy under the fuzzy skill function. Based on the fact that individuals' learning process of skills is consistent with the cognitive learning process, this paper provides a skill assessment method from a concept-cognitive learning perspective. A special fuzzy skill function, conjunctive fuzzy skill function, is converted into a fuzzy formal context. For facilitating skill assessment, the definitions of well-formed item-skill context and subsequent state are given. Based on a well-formed item-skill context and the idea of upper and lower approximations in rough set theory, the approximate concepts are learned by using response patterns as cues to provide a skill assessment method. The empirical application shows that the skill assessment method proposed in this paper is feasible and has practical applications.
{"title":"Skill assessment method: A perspective from concept-cognitive learning","authors":"Yin-Feng Zhou , Hai-Long Yang , Jin-Jin Li , Da-Li Wang","doi":"10.1016/j.fss.2025.109331","DOIUrl":"10.1016/j.fss.2025.109331","url":null,"abstract":"<div><div>Skills represent potential cognitive abilities that need to be reflected by observing external performances. In competence-based knowledge space theory, whether individuals solve items in a knowledge domain correctly can reflect whether they have mastered the relevant skills. Currently, skill function that reflects the relationship between skills and items has been extended to fuzzy skill function on polytomous items. However, existing skill assessment techniques are not suitable to assess response data that are noisy under the fuzzy skill function. Based on the fact that individuals' learning process of skills is consistent with the cognitive learning process, this paper provides a skill assessment method from a concept-cognitive learning perspective. A special fuzzy skill function, conjunctive fuzzy skill function, is converted into a fuzzy formal context. For facilitating skill assessment, the definitions of well-formed item-skill context and subsequent state are given. Based on a well-formed item-skill context and the idea of upper and lower approximations in rough set theory, the approximate concepts are learned by using response patterns as cues to provide a skill assessment method. The empirical application shows that the skill assessment method proposed in this paper is feasible and has practical applications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109331"},"PeriodicalIF":3.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480423","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 : 2025-02-21DOI: 10.1016/j.fss.2025.109323
Stefania Boffa , Petra Murinová
Aristotle's Square also known as Square of Opposition, is a mathematical diagram dating back to Greek philosophy and exhibiting the connection between four logical propositions in a simple graphical form. Fuzzy Relational Concept Analysis (FRCA) is a technique for extracting special clusters called fuzzy concepts from a Fuzzy Relational Context Family (FRCF), which is a dataset organized as multiple fuzzy object-attribute and object-object relations. The primary FRCA tools to obtain information from data are special fuzzy quantifiers viewed as interpretations in a model of formulas of the formal theory of the intermediate generalized quantifiers. This work focuses on the issue of generating a collection of fuzzy concepts from a certain FRCF, by choosing one of four particular FRCA quantifiers: the positive universal quantifier , the negative universal quantifier , the positive existential quantifier , and the negative existential quantifier . Certainly, the selection of the quantifier is crucial in the FRCA procedure since it affects the final concept classification: diverse fuzzy concepts arise from varying quantifiers. As the initial objective, this article introduces the logical relations involving , , and , in order to arrange them in a graded version of the Aristotelian square. The second goal of this study is to examine the connections among fuzzy concepts produced by distinct quantifiers in . Therefore, our findings provide a twofold contribution to the advancement of Aristotle's square. Indeed, they reveal a novel interpretation of the square of opposition within the framework of Fuzzy Relational Concept Analysis, emphasizing its potential as a valuable tool for the analysis of data.
{"title":"Aristotle's square for mining fuzzy concepts","authors":"Stefania Boffa , Petra Murinová","doi":"10.1016/j.fss.2025.109323","DOIUrl":"10.1016/j.fss.2025.109323","url":null,"abstract":"<div><div><em>Aristotle's Square</em> also known as <em>Square of Opposition</em>, is a mathematical diagram dating back to Greek philosophy and exhibiting the connection between four logical propositions in a simple graphical form. <em>Fuzzy Relational Concept Analysis</em> (FRCA) is a technique for extracting special clusters called <em>fuzzy concepts</em> from a <em>Fuzzy Relational Context Family</em> (FRCF), which is a dataset organized as multiple fuzzy object-attribute and object-object relations. The primary FRCA tools to obtain information from data are special fuzzy quantifiers viewed as interpretations in a model of formulas of the <em>formal theory of the intermediate generalized quantifiers</em>. This work focuses on the issue of generating a collection of fuzzy concepts from a certain FRCF, by choosing one of four particular FRCA quantifiers: the <em>positive universal quantifier</em> <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, the <em>negative universal quantifier</em> <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, the <em>positive existential quantifier</em> <span><math><msub><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow></msub></math></span>, and the <em>negative existential quantifier</em> <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>. Certainly, the selection of the quantifier is crucial in the FRCA procedure since it affects the final concept classification: diverse fuzzy concepts arise from varying quantifiers. As the initial objective, this article introduces the logical relations involving <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow></msub></math></span>, and <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, in order to arrange them in a graded version of the Aristotelian square. The second goal of this study is to examine the connections among fuzzy concepts produced by distinct quantifiers in <span><math><mo>{</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><msub><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow></msub><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mo>∃</mo></mrow><mrow><mo>−</mo></mrow></msubsup><mo>}</mo></math></span>. Therefore, our findings provide a twofold contribution to the advancement of Aristotle's square. Indeed, they reveal a novel interpretation of the square of opposition within the framework of Fuzzy Relational Concept Analysis, emphasizing its potential as a valuable tool for the analysis of data.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109323"},"PeriodicalIF":3.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480421","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}
In this article, we introduce the concepts of R-ideal and 2R-ideal in MV-algebras. We explore various properties of these ideals and utilize them to characterize specific classes of MV-algebras, including MV-chains, (local, semisimple) MV-algebras. We clarify the relationships between R-ideals and 2R-ideals, and other types of ideals such as prime, primary, maximal and principal ideals. Finally, -multiplicatively closed system is defined and its relationship with R-ideals is examined.
{"title":"Study of MV-algebras in view of R-ideals and 2R-ideals","authors":"Asiyeh Hassani Movahed , Mahta Bedrood , Arsham Borumand Saeid","doi":"10.1016/j.fss.2025.109313","DOIUrl":"10.1016/j.fss.2025.109313","url":null,"abstract":"<div><div>In this article, we introduce the concepts of <em>R</em>-ideal and 2<em>R</em>-ideal in <em>MV</em>-algebras. We explore various properties of these ideals and utilize them to characterize specific classes of <em>MV</em>-algebras, including <em>MV</em>-chains, (local, semisimple) <em>MV</em>-algebras. We clarify the relationships between <em>R</em>-ideals and 2<em>R</em>-ideals, and other types of ideals such as prime, primary, maximal and principal ideals. Finally, <span><math><msub><mrow><mo>∧</mo></mrow><mrow><mi>R</mi></mrow></msub></math></span>-multiplicatively closed system is defined and its relationship with <em>R</em>-ideals is examined.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109313"},"PeriodicalIF":3.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474926","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 : 2025-02-19DOI: 10.1016/j.fss.2025.109319
Wanting Wang, Kuanyun Zhu
Building on the work of Lopez-Molina et al. [27], in this paper, we investigate the bimigrativity of uninorms over any fixed overlap function. First, we introduce the concept of -bimigrative uninorms with respect to a given overlap function O. Moreover, we provide detailed equivalent characterizations and related properties of the -bimigrativity equation for uninorms U that belong to different classes, including , , idempotent uninorms, representable uninorms, and continuous uninorms on .
{"title":"The necessary and sufficient conditions for bimigrativity of uninorms over overlap functions","authors":"Wanting Wang, Kuanyun Zhu","doi":"10.1016/j.fss.2025.109319","DOIUrl":"10.1016/j.fss.2025.109319","url":null,"abstract":"<div><div>Building on the work of Lopez-Molina et al. <span><span>[27]</span></span>, in this paper, we investigate the bimigrativity of uninorms over any fixed overlap function. First, we introduce the concept of <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span>-bimigrative uninorms with respect to a given overlap function <em>O</em>. Moreover, we provide detailed equivalent characterizations and related properties of the <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span>-bimigrativity equation for uninorms <em>U</em> that belong to different classes, including <span><math><mi>U</mi><mi>min</mi></math></span>, <span><math><mi>U</mi><mi>max</mi></math></span>, idempotent uninorms, representable uninorms, and continuous uninorms on <span><math><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109319"},"PeriodicalIF":3.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444952","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 : 2025-02-19DOI: 10.1016/j.fss.2025.109318
Shiju Yang , Tingting Huang , Dongmei Ruan , Hongsen He
This paper mainly discusses the stability of T-S fuzzy partially coupled complex networks (T-S FPCCNs) with pinning impulsive control. Different from the traditional impulsive control method, the analysis process of the stability can be divided into two parts by adopting the step-function method (the first part is one-span step-function and the second part is multi-span step-function). Then the stability of T-S fuzzy partially coupled complex networks with pinning impulsive control can be analyzed. In addition, the novel pinning impulsive controllers can be designed to ensure the network to achieve globally uniformly attractively stable (GUAS). Furthermore, a comparison system is constructed by using regrouping method and impulsive control theory, and several new sufficient criterions are given to ensure the stability of the T-S FPCCNs. Finally, the correctness of theoretical analysis is proved by experimental cases.
{"title":"Stability analysis of T-S fuzzy partially coupled complex networks with pinning impulsive controllers by step function method","authors":"Shiju Yang , Tingting Huang , Dongmei Ruan , Hongsen He","doi":"10.1016/j.fss.2025.109318","DOIUrl":"10.1016/j.fss.2025.109318","url":null,"abstract":"<div><div>This paper mainly discusses the stability of T-S fuzzy partially coupled complex networks (T-S FPCCNs) with pinning impulsive control. Different from the traditional impulsive control method, the analysis process of the stability can be divided into two parts by adopting the step-function method (the first part is one-span step-function and the second part is multi-span step-function). Then the stability of T-S fuzzy partially coupled complex networks with pinning impulsive control can be analyzed. In addition, the novel pinning impulsive controllers can be designed to ensure the network to achieve globally uniformly attractively stable (GUAS). Furthermore, a comparison system is constructed by using regrouping method and impulsive control theory, and several new sufficient criterions are given to ensure the stability of the T-S FPCCNs. Finally, the correctness of theoretical analysis is proved by experimental cases.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109318"},"PeriodicalIF":3.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444951","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 : 2025-02-18DOI: 10.1016/j.fss.2025.109321
Wei Liu , Wei Tang , Huanyu Zhao , Shengyuan Xu , Ju H. Park
This paper studies a fuzzy finite-time preassigned performance control challenge for state-constrained non-strict feedback nonlinear systems (NSFNSs) subject to input saturation and unmatched disturbances. By incorporating barrier Lyapunov function (BLF) with finite-time performance function, a new type of preassigned performance BLF is devised to address the issues of state constraints and achieve preassigned performance metrics (PPMs). Moreover, to address the design problem for NSFNSs and estimate unmatched disturbances, a combined nonlinear disturbances observer is developed. Additionally, a command-filter backstepping method is employed in the finite-time control scheme, thereby reducing the conservativeness of the assumptions on the desired signal. With stability analyses, all control aims can be completely acquired. The proposed approach is validated through two simulation examples.
{"title":"Combined disturbance observer-based fuzzy finite-time preassigned performance control for state-constrained nonlinear systems","authors":"Wei Liu , Wei Tang , Huanyu Zhao , Shengyuan Xu , Ju H. Park","doi":"10.1016/j.fss.2025.109321","DOIUrl":"10.1016/j.fss.2025.109321","url":null,"abstract":"<div><div>This paper studies a fuzzy finite-time preassigned performance control challenge for state-constrained non-strict feedback nonlinear systems (NSFNSs) subject to input saturation and unmatched disturbances. By incorporating barrier Lyapunov function (BLF) with finite-time performance function, a new type of preassigned performance BLF is devised to address the issues of state constraints and achieve preassigned performance metrics (PPMs). Moreover, to address the design problem for NSFNSs and estimate unmatched disturbances, a combined nonlinear disturbances observer is developed. Additionally, a command-filter backstepping method is employed in the finite-time control scheme, thereby reducing the conservativeness of the assumptions on the desired signal. With stability analyses, all control aims can be completely acquired. The proposed approach is validated through two simulation examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109321"},"PeriodicalIF":3.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464737","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 : 2025-02-15DOI: 10.1016/j.fss.2025.109315
Changzhong Wang , Changyue Wang , Shuang An , Jinhuan Zhao
Mislabeling is one of the major challenges in semi-supervised learning methods. Most existing approaches based on fuzzy rough sets typically assume that labeled data is accurate and free from errors. This assumption often overlooks the presence of incorrect labels, which can weaken the generalization ability and reduce the robustness of the learning algorithms. To address these shortcomings, we propose a new method for label modification based on fuzzy rough sets, called the Fuzzy Rough Set Label Modification Filter (RSLMF), which is designed to handle both unlabeled and mislabeled data. Specifically, the proposed RSLMF consists of two main steps: detection of mislabeled samples and their subsequent correction. The filter employs the theoretical framework of fuzzy rough sets to identify mislabeled samples in data and subsequently correct their labels. For unlabeled samples, their potential labels are inferred by analyzing their correlation with labeled data through fuzzy rough sets. Additionally, the topological structures of the corrected sample set and the boundary sample set are thoroughly explored during the label modification process. Experimental results demonstrate that the proposed method can accurately modify the labels of mislabeled samples and effectively suppress noise.
{"title":"Fuzzy rough label modification learning for unlabeled and mislabeled data","authors":"Changzhong Wang , Changyue Wang , Shuang An , Jinhuan Zhao","doi":"10.1016/j.fss.2025.109315","DOIUrl":"10.1016/j.fss.2025.109315","url":null,"abstract":"<div><div>Mislabeling is one of the major challenges in semi-supervised learning methods. Most existing approaches based on fuzzy rough sets typically assume that labeled data is accurate and free from errors. This assumption often overlooks the presence of incorrect labels, which can weaken the generalization ability and reduce the robustness of the learning algorithms. To address these shortcomings, we propose a new method for label modification based on fuzzy rough sets, called the Fuzzy Rough Set Label Modification Filter (RSLMF), which is designed to handle both unlabeled and mislabeled data. Specifically, the proposed RSLMF consists of two main steps: detection of mislabeled samples and their subsequent correction. The filter employs the theoretical framework of fuzzy rough sets to identify mislabeled samples in data and subsequently correct their labels. For unlabeled samples, their potential labels are inferred by analyzing their correlation with labeled data through fuzzy rough sets. Additionally, the topological structures of the corrected sample set and the boundary sample set are thoroughly explored during the label modification process. Experimental results demonstrate that the proposed method can accurately modify the labels of mislabeled samples and effectively suppress noise.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109315"},"PeriodicalIF":3.2,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428140","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 : 2025-02-14DOI: 10.1016/j.fss.2025.109312
Haibo Jiang , Bao Qing Hu
Fuzzy rough sets and three-way decisions, as effective approaches for uncertain knowledge representation, learning and transformation, are widely used in approximate learning of fuzzy concepts. As a new generalization of fuzzy rough sets, fuzzy β-covering-based rough sets can characterize uncertain information flexibly. However, there exist shortcomings of some concepts in fuzzy β-covering, which limits its popularization and application. On the one side, fuzzy β-neighborhood and fuzzy β-co-neighborhood can not guarantee that they have the reflexivity property, which is contrary to the crisp neighborhood operators with reflexivity and has semantic difficulties in understanding. On the other side, most fuzzy β-covering-based rough sets and their extended models cannot satisfy the property that upper approximations contain lower approximations when , which can not characterize a given objective concept accurately. To break through these defects, we first propose an indiscernible fuzzy β-neighborhood and an indiscernible fuzzy β-co-neighborhood in fuzzy β-covering, both of which fulfill reflexivity. Then, we define four novel kinds of fuzzy β-covering-based rough sets in fuzzy β-covering approximation space, which satisfy the inclusion relationship of the upper and lower approximations. At the same time, some essential properties and the interrelationships between different models are also discussed. Furthermore, we give the topological properties of four novel kinds of fuzzy β-covering-based rough sets. Finally, we present an application of fuzzy β-covering-based rough sets to three-way approximations of fuzzy concepts. The comparative experimental results between the existing fuzzy β-covering-based rough set models and four novel models demonstrate the effectiveness and superiority of the proposed models in approximation learning.
{"title":"On four novel kinds of fuzzy β-covering-based rough sets and their applications to three-way approximations","authors":"Haibo Jiang , Bao Qing Hu","doi":"10.1016/j.fss.2025.109312","DOIUrl":"10.1016/j.fss.2025.109312","url":null,"abstract":"<div><div>Fuzzy rough sets and three-way decisions, as effective approaches for uncertain knowledge representation, learning and transformation, are widely used in approximate learning of fuzzy concepts. As a new generalization of fuzzy rough sets, fuzzy <em>β</em>-covering-based rough sets can characterize uncertain information flexibly. However, there exist shortcomings of some concepts in fuzzy <em>β</em>-covering, which limits its popularization and application. On the one side, fuzzy <em>β</em>-neighborhood and fuzzy <em>β</em>-co-neighborhood can not guarantee that they have the reflexivity property, which is contrary to the crisp neighborhood operators with reflexivity and has semantic difficulties in understanding. On the other side, most fuzzy <em>β</em>-covering-based rough sets and their extended models cannot satisfy the property that upper approximations contain lower approximations when <span><math><mi>β</mi><mo>≠</mo><mn>1</mn></math></span>, which can not characterize a given objective concept accurately. To break through these defects, we first propose an indiscernible fuzzy <em>β</em>-neighborhood and an indiscernible fuzzy <em>β</em>-co-neighborhood in fuzzy <em>β</em>-covering, both of which fulfill reflexivity. Then, we define four novel kinds of fuzzy <em>β</em>-covering-based rough sets in fuzzy <em>β</em>-covering approximation space, which satisfy the inclusion relationship of the upper and lower approximations. At the same time, some essential properties and the interrelationships between different models are also discussed. Furthermore, we give the topological properties of four novel kinds of fuzzy <em>β</em>-covering-based rough sets. Finally, we present an application of fuzzy <em>β</em>-covering-based rough sets to three-way approximations of fuzzy concepts. The comparative experimental results between the existing fuzzy <em>β</em>-covering-based rough set models and four novel models demonstrate the effectiveness and superiority of the proposed models in approximation learning.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109312"},"PeriodicalIF":3.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420277","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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