{"title":"Lattice-valued coarse structures","authors":"Yongchao Wang , Bin Pang , Fu-Gui Shi","doi":"10.1016/j.fss.2024.109175","DOIUrl":null,"url":null,"abstract":"<div><div>Based on a complete residuated lattice <em>L</em>, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of <em>L</em>-entourages and <em>L</em>-(quasi, semi)-coarse structures and study the maps between <em>L</em>-coarse spaces. Secondly, we provide some examples of <em>L</em>-coarse structures from the aspects of <em>L</em>-metrics, <em>L</em>-relations and <em>L</em>-hyperstructures. Thirdly, we introduce the notion of <em>L</em>-ball structures to characterize <em>L</em>-coarse structures. Finally, we establish the relationship among <em>L</em>-entourage spaces, <em>L</em>-quasi-coarse spaces, <em>L</em>-semi-coarse spaces and <em>L</em>-coarse spaces in a categorical viewpoint.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-11-04","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/S016501142400321X","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
Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.
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.
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