{"title":"On granular-ball fuzzy rough sets and applications in attribute evaluations","authors":"Anhui Tan , Danlu Feng , Jinjin Li , Wei-Zhi Wu","doi":"10.1016/j.fss.2025.109520","DOIUrl":null,"url":null,"abstract":"<div><div>Granular-ball computing has emerged as a powerful framework for managing uncertainty, offering a more adaptive and interpretable approach to data analysis. In contrast, traditional fuzzy rough sets, which rely on fuzzy relations between individual data points, often suffer from limited granularity control, sensitivity to noise, and difficulties in handling large-scale or complex datasets. Moreover, the point-wise nature of fuzzy relations restricts the ability to capture group-based structural information inherent in real-world data. To address these limitations, we propose the granular-ball fuzzy rough set model, which integrates fuzzy rough set theory with the granular-ball computing paradigm. This novel model represents data in the form of fuzzy granular-balls, each encompassing a group of similar instances, thereby enhancing granularity management and improving robustness against noise and data sparsity. The lower and upper approximations in this model are redefined using these fuzzy granular-balls rather than individual objects, with the purity of each granular-ball directly influencing the certainty and precision of classification boundaries. This approach facilitates smoother and more stable delineations of positive, negative, and boundary regions in uncertain classification tasks. Additionally, the model introduces monotonous fuzzy granular-ball partitions that evolve with expanding attribute sets, providing a practical mechanism for evaluating attribute significance in feature selection. Overall, the proposed model retains the mathematical rigor of traditional fuzzy rough set theory while offering enhanced flexibility, interpretability, and effectiveness in handling real-world uncertain data.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109520"},"PeriodicalIF":3.2000,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011425002593","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Granular-ball computing has emerged as a powerful framework for managing uncertainty, offering a more adaptive and interpretable approach to data analysis. In contrast, traditional fuzzy rough sets, which rely on fuzzy relations between individual data points, often suffer from limited granularity control, sensitivity to noise, and difficulties in handling large-scale or complex datasets. Moreover, the point-wise nature of fuzzy relations restricts the ability to capture group-based structural information inherent in real-world data. To address these limitations, we propose the granular-ball fuzzy rough set model, which integrates fuzzy rough set theory with the granular-ball computing paradigm. This novel model represents data in the form of fuzzy granular-balls, each encompassing a group of similar instances, thereby enhancing granularity management and improving robustness against noise and data sparsity. The lower and upper approximations in this model are redefined using these fuzzy granular-balls rather than individual objects, with the purity of each granular-ball directly influencing the certainty and precision of classification boundaries. This approach facilitates smoother and more stable delineations of positive, negative, and boundary regions in uncertain classification tasks. Additionally, the model introduces monotonous fuzzy granular-ball partitions that evolve with expanding attribute sets, providing a practical mechanism for evaluating attribute significance in feature selection. Overall, the proposed model retains the mathematical rigor of traditional fuzzy rough set theory while offering enhanced flexibility, interpretability, and effectiveness in handling real-world uncertain data.
期刊介绍:
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.