Fuzzy Sets and Systems最新文献

{"title":"Filter-induced entailment relations in paraconsistent Gödel logics","authors":"Sabine Frittella ,&nbsp;Daniil Kozhemiachenko","doi":"10.1016/j.fss.2025.109563","DOIUrl":"10.1016/j.fss.2025.109563","url":null,"abstract":"<div><div>We consider two expansions of Gödel logic <span><math><mi>G</mi></math></span> with two versions of paraconsistent negation. The first one is <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>inv</mi></mrow></msub></math></span> — the expansion of <span><math><mi>G</mi></math></span> with an <em>involuitive</em> negation <span><math><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub></math></span> defined via <span><math><mi>v</mi><mo>(</mo><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub><mi>ϕ</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>v</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math></span>. The second one is <figure><img></figure> — an expansion with a so-called ‘strong negation’ ¬. This logic utilises <em>two independent</em> valuations on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> — <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> (support of truth or positive support) and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> (support of falsity or negative support) that are connected with ¬. Two valuations in <figure><img></figure> can be combined into one valuation <em>v</em> on <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span> — the twisted product of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with itself — with two components <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. The two logics are closely connected as <span><math><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub></math></span> and ¬ allow for similar definitions of <em>co-implication</em> — <figure><img></figure> and <figure><img></figure> — but do not coincide since the set of values of <figure><img></figure> is not ordered linearly.</div><div>Our main goal is to study different entailment relations in <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>inv</mi></mrow></msub></math></span> and <figure><img></figure> that are induced by filters on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span>, respectively. In particular, we determine the exact number of such relations in both cases, establish whether any of them coincide with the entailment defined via the order on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span>, and obtain their hierarchy. We also construct reductions of filter-induced entailment relations to the ones defined via the order.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109563"},"PeriodicalIF":2.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810243","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 fuzzy fractions formation","authors":"Naser Zamani ,&nbsp;Zeinab Rezaei","doi":"10.1016/j.fss.2025.109562","DOIUrl":"10.1016/j.fss.2025.109562","url":null,"abstract":"<div><div>Let <em>R</em> be a commutative ring, <em>S</em> a multiplicatively closed subset of <em>R</em> and let <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi></math></span> be the ring of fractions over <em>S</em>. For a typical fuzzy submodule <em>η</em> of the <em>R</em>-module <em>M</em>, the fuzzy fractions <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>η</mi></math></span> of <em>μ</em> is a fuzzy submodule of the <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi></math></span>-module (of fractions) <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>M</mi></math></span>. In this note, it is shown that if <span><math><mi>μ</mi><mo>⊆</mo><mi>λ</mi></math></span> are two fuzzy submodules of <em>M</em>, both having sup property, then there exist a (fuzzy sense) isomorphism between <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>λ</mi><mo>/</mo><mi>μ</mi><mo>)</mo></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>λ</mi><mo>/</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>μ</mi></math></span>. Then, it is seen that local global principle holds true for fuzzy submodules. Furthermore, after providing some auxiliary results, it is proved that under some mild conditions, fuzzy fractions formation commutes with fuzzy residual quotient.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109562"},"PeriodicalIF":2.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861064","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":"Efficiency of decision rule sets in fuzzy rough set theory","authors":"Fernando Chacón-Gómez,&nbsp;M. Eugenia Cornejo,&nbsp;Jesús Medina","doi":"10.1016/j.fss.2025.109548","DOIUrl":"10.1016/j.fss.2025.109548","url":null,"abstract":"<div><div>Datasets have been interpreted in (fuzzy) rough set theory as decision tables to obtain useful information to be used, for example, in decision making. These tables have been modeled through a collection of decision rules, which was called decision algorithm by Pawlak. These algorithms are analyzed by the notion of efficiency, which evaluates their quality of classification. This paper presents two different approaches for defining the notion of efficiency in the fuzzy framework. The first approach is a direct generalization to the classical case, while the second one is focused on obtaining a bounded efficiency preserving the philosophy of the classical framework. Both approaches are illustrated by means of different properties and examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109548"},"PeriodicalIF":2.7,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826621","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":"Temporally adaptive hierarchical Choquet integrals: A measure-theoretic framework for dynamic non-additive integration in approximate reasoning","authors":"Jih-Jeng Huang ,&nbsp;Chin-Yi Chen","doi":"10.1016/j.fss.2025.109550","DOIUrl":"10.1016/j.fss.2025.109550","url":null,"abstract":"<div><div>This paper introduces the Temporally Adaptive Hierarchical Choquet Integral (TAHCI), a novel theoretical framework that extends classical Choquet integration to address temporal dynamics and high-dimensional data through hierarchical structures and time-evolving fuzzy measures. We develop a rigorous measure-theoretic foundation for this framework, including a complete axiomatic characterization, uniqueness results, and preservation properties. The proposed formulation overcomes theoretical limitations of traditional models by offering tractable parameterization (reducing complexity from <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> to <span><math><mi>O</mi><mo>(</mo><mi>R</mi><mi>n</mi><mi>d</mi><mo>)</mo></math></span>, where <em>R</em> is the tensor rank, <em>n</em> is the feature dimensionality, and <em>d</em> is the hierarchy depth) while preserving key measure-theoretic properties. We establish fundamental mathematical results including convergence rates, expressivity bounds, and stability under perturbations. Our theoretical analysis reveals several novel classes of non-additive measures with unique properties that emerge from the temporal adaptation process. We characterize TAHCI's well-defined fixed points and convergence behavior under various conditions. This work advances non-additive measure theory by providing a mathematically principled approach to integrating temporal dynamics with hierarchical measure structures, with direct implications for reasoning under uncertainty and imprecision.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109550"},"PeriodicalIF":2.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780243","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":"θg - fuzzy graphs and transitivity: Optimizing data transmission in interconnection networks","authors":"Aswathi Prabhath ,&nbsp;Sunil Mathew ,&nbsp;J.N. Mordeson","doi":"10.1016/j.fss.2025.109549","DOIUrl":"10.1016/j.fss.2025.109549","url":null,"abstract":"<div><div>An optimal flow of data is essential for interconnection networks in order to ensure effective communication within the network. Hence, it is important to consider fuzzy graph structures representing networks which minimizes disruption of the flow and consequent failure of the network. This article discusses <span><math><msup><mrow><mi>θ</mi></mrow><mrow><mi>g</mi></mrow></msup></math></span> - fuzzy graphs, a special category of fuzzy graphs having the properties mentioned above. Apart from a characterization for <span><math><msup><mrow><mi>θ</mi></mrow><mrow><mi>g</mi></mrow></msup></math></span> - fuzzy graphs, this paper discusses a new kind of transitivity, called <span><math><msup><mrow><mi>θ</mi></mrow><mrow><mi>g</mi></mrow></msup></math></span> - transitivity, using the generalized cycle connectivity between a pair of vertices within the structure. Generalized cycle connectivity of certain fuzzy graph structures like fuzzy blocks and line graphs is also obtained. An application of <span><math><msup><mrow><mi>θ</mi></mrow><mrow><mi>g</mi></mrow></msup></math></span> - fuzzy graphs in network theory is also proposed in the paper.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109549"},"PeriodicalIF":2.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780244","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 the convergence of measurable functions: Solutions to two open problems","authors":"Do Huy Hoang ,&nbsp;Tran Nhat Luan","doi":"10.1016/j.fss.2025.109552","DOIUrl":"10.1016/j.fss.2025.109552","url":null,"abstract":"<div><div>In this paper, we provide solutions of open problems 2.18 and 2.19 in the paper “The smallest semicopula-based universal integrals II: Convergence theorems” (Fuzzy Sets and Systems 271(2015), 18-30) which were posed by Hutník. It is shown that strict convergence in measure is equivalent to convergence in measure and convergence in mean if and only if the underlying monotone measure is the zero measure.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109552"},"PeriodicalIF":2.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770888","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 feature selection via stripped decision β-neighborhood set and misclassification ratio","authors":"Xiongtao Zou ,&nbsp;Jianhua Dai","doi":"10.1016/j.fss.2025.109544","DOIUrl":"10.1016/j.fss.2025.109544","url":null,"abstract":"<div><div>Fuzzy <em>β</em>-covering is a type of granular structure for knowledge representation that has been widely used for machine learning and data mining in recent years. In evaluations of the reduction and redundancy of fuzzy <em>β</em>-coverings, most of the existing methods generate a new fuzzy <em>β</em>-covering for describing the similarity between objects to select important fuzzy <em>β</em>-coverings. However, not all fuzzy <em>β</em>-neighborhoods in the generated fuzzy <em>β</em>-covering are necessary for further determining important fuzzy <em>β</em>-coverings. Therefore, in this study, we propose the concept of a stripped decision <em>β</em>-neighborhood set, and present a fuzzy <em>β</em>-covering reduction approach based on the misclassification ratio for feature subset selection. Inspired by the lower approximation operator of rough sets, the concept of a stripped decision <em>β</em>-neighborhood set is first proposed to remove some unnecessary <em>β</em>-neighborhoods for further determining important fuzzy <em>β</em>-coverings. Moreover, the connection between the stripped decision <em>β</em>-neighborhood set and positive region is discussed in a fuzzy <em>β</em>-covering group decision system. The misclassification ratio for fuzzy <em>β</em>-coverings is then defined on this basis. An accurate feature selection method is presented based on the knowledge represented by fuzzy <em>β</em>-coverings and fuzzy <em>β</em>-covering reduction by using the misclassification ratio. Finally, the experimental results demonstrated the effectiveness of our method compared with several other excellent feature selection methods under four classical classifiers.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109544"},"PeriodicalIF":2.7,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770817","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 class of associative aggregation functions","authors":"Lingli Wang ,&nbsp;Wenwen Zong ,&nbsp;Yong Su ,&nbsp;Radko Mesiar","doi":"10.1016/j.fss.2025.109545","DOIUrl":"10.1016/j.fss.2025.109545","url":null,"abstract":"<div><div>In this paper, we characterize all associative aggregation functions <em>A</em> such that the semigroup <span><math><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>,</mo><mi>A</mi><mo>,</mo><mo>≤</mo><mo>)</mo></math></span> can be order-embedded into the additive semigroup of the extended reals.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109545"},"PeriodicalIF":2.7,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748874","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":"Terms that define nuclei on residuated lattices: A case study of BL-algebras","authors":"Sebastián Buss ,&nbsp;Diego Castaño ,&nbsp;José Patricio Díaz Varela","doi":"10.1016/j.fss.2025.109542","DOIUrl":"10.1016/j.fss.2025.109542","url":null,"abstract":"<div><div>A nucleus <em>γ</em> on a (bounded commutative integral) residuated lattice <strong>A</strong> is a closure operator that satisfies the inequality <span><math><mi>γ</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>⋅</mo><mi>γ</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>≤</mo><mi>γ</mi><mo>(</mo><mi>a</mi><mo>⋅</mo><mi>b</mi><mo>)</mo></math></span> for all <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mi>A</mi></math></span>. In this article, among several results, a description of an arbitrary nucleus on a residuated lattice is given. Special attention is given to terms that define a nucleus on every structure of a variety, as a means of generalizing the double negation operation. Some general results about these terms are presented, together with examples. The main result of this article consists of the description of all terms of this kind for every given subvariety of BL-algebras. We exhibit interesting nontrivial examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109542"},"PeriodicalIF":2.7,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721255","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":"Logical distance-based fuzzy rough set model and its application in feature selection","authors":"Wenchang Yu ,&nbsp;Wei Yao","doi":"10.1016/j.fss.2025.109543","DOIUrl":"10.1016/j.fss.2025.109543","url":null,"abstract":"<div><div>Fuzzy rough set models based on binary similarity relations and their applications in feature selection have been explored extensively. However, distance-based relations, a natural type of binary relations, are seldom directly applied in fuzzy rough set models, and let alone in feature selection algorithms. Additionally, the existing feature selection algorithms based on fuzzy rough set theory frequently encounter challenges such as the inflexibility of selection rate adjustment, the associated high computational costs, etc. To counter these issues, we introduce a concept of logical distance functions and use it to establish a kind of fuzzy rough set models. We analyze the uncertainty of decision tables using related fuzzy rough approximation operators. Then we propose a novel uncertainty index based on the difference between the distance of decision attributes and that of condition attributes. Building upon this foundation, we design a forward greedy feature selection algorithm based on this uncertainty index. Compared to existing state-of-the-art feature selection algorithms, experimental results validate the effectiveness and efficiency of our approach, particularly demonstrating superior efficiency.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109543"},"PeriodicalIF":2.7,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721253","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}