Fuzzy Sets and Systems最新文献

{"title":"Aristotle's square for mining fuzzy concepts","authors":"Stefania Boffa ,&nbsp;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}

{"title":"Study of MV-algebras in view of R-ideals and 2R-ideals","authors":"Asiyeh Hassani Movahed ,&nbsp;Mahta Bedrood ,&nbsp;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}

{"title":"The necessary and sufficient conditions for bimigrativity of uninorms over overlap functions","authors":"Wanting Wang,&nbsp;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}

{"title":"Stability analysis of T-S fuzzy partially coupled complex networks with pinning impulsive controllers by step function method","authors":"Shiju Yang ,&nbsp;Tingting Huang ,&nbsp;Dongmei Ruan ,&nbsp;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}

{"title":"Combined disturbance observer-based fuzzy finite-time preassigned performance control for state-constrained nonlinear systems","authors":"Wei Liu ,&nbsp;Wei Tang ,&nbsp;Huanyu Zhao ,&nbsp;Shengyuan Xu ,&nbsp;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}

{"title":"Fuzzy rough label modification learning for unlabeled and mislabeled data","authors":"Changzhong Wang ,&nbsp;Changyue Wang ,&nbsp;Shuang An ,&nbsp;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}

{"title":"On four novel kinds of fuzzy β-covering-based rough sets and their applications to three-way approximations","authors":"Haibo Jiang ,&nbsp;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}

{"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}

{"title":"The 2-additive decomposition integrals and their applications","authors":"Radko Mesiar ,&nbsp;Jabbar Abbas ,&nbsp;Jun Li","doi":"10.1016/j.fss.2025.109316","DOIUrl":"10.1016/j.fss.2025.109316","url":null,"abstract":"<div><div>Decomposition integral with respect to a capacity (monotone measure) is a common framework for unifying some nonlinear integrals, such as the Choquet, the Shilkret, the PAN, the PC, and the concave integrals. The formula of decomposition integral concerning capacities depends on the distinguished decomposition system under some constraints on the sets being considered for each related integral. The Möbius representation of a monotone set function is a fundamental concept permitting the derivation of simple expressions of nonlinear integrals. In this paper, we propose Möbius representation of some decomposition integrals based on Lovász idea of an extension of pseudo-boolean functions for the decomposition systems to get different types of decomposition integrals. Then, we introduce a new type of integral to unify the Choquet, Shilkret, PAN, and PC integrals in terms of the Möbius transform. Consequently, we then propose the expressions of computing decomposition integrals concerning a 2-additive capacity. Finally, an illustrative example is used to demonstrate the applicability of the proposed results and simplicity of computing the 2-additive decomposition integrals.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"507 ","pages":"Article 109316"},"PeriodicalIF":3.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420278","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}

{"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}