{"title":"Fuzzifications of matroids relying on overlap functions","authors":"Shao-Yu Zhang , Bin Pang","doi":"10.1016/j.fss.2025.109297","DOIUrl":null,"url":null,"abstract":"<div><div>Matroid theory provides a broad theoretical framework with a wide range of applications. On this basis, fuzzy matroids have also undergone significant development based on lattice theory, fuzzy topology, fuzzy convexity, etc. In this paper, we select an overlap function to model conjunction to provide two fuzzification approaches to matroids. Taking an arbitrary overlap function ⊗, we introduce ⊗-fuzzifying matroids and ⊗-fuzzy matroids and study their relations with classical matroids, respectively. Then we explore the relations between ⊗-fuzzifying matroids and (closed, perfect) ⊗-fuzzy matroids. These findings not only provide a theoretical application of overlap functions but also elucidate the connections between different fuzzifications of matroids.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"506 ","pages":"Article 109297"},"PeriodicalIF":2.7000,"publicationDate":"2025-04-15","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/S0165011425000363","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/28 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Matroid theory provides a broad theoretical framework with a wide range of applications. On this basis, fuzzy matroids have also undergone significant development based on lattice theory, fuzzy topology, fuzzy convexity, etc. In this paper, we select an overlap function to model conjunction to provide two fuzzification approaches to matroids. Taking an arbitrary overlap function ⊗, we introduce ⊗-fuzzifying matroids and ⊗-fuzzy matroids and study their relations with classical matroids, respectively. Then we explore the relations between ⊗-fuzzifying matroids and (closed, perfect) ⊗-fuzzy matroids. These findings not only provide a theoretical application of overlap functions but also elucidate the connections between different fuzzifications of matroids.
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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