{"title":"Chaos game algorithm for fuzzy iterated function systems","authors":"Marcin Kolenda , Filip Strobin , Kamil Wiśniewski","doi":"10.1016/j.fss.2024.109173","DOIUrl":null,"url":null,"abstract":"<div><div>We consider versions of the chaos game algorithm for generating attractors of fuzzy iterated function systems (FIFSs for short). We show that a naive approach fails in a general setting of contractive FIFSs and we present its natural modifications that work in all cases. Our approach bases on certain modifications of orbits and shadings of a given FIFS, generated by disjunctive drivers. To complete the picture, we present also a version of the deterministic algorithm.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109173"},"PeriodicalIF":3.2000,"publicationDate":"2024-11-13","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/S0165011424003191","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
We consider versions of the chaos game algorithm for generating attractors of fuzzy iterated function systems (FIFSs for short). We show that a naive approach fails in a general setting of contractive FIFSs and we present its natural modifications that work in all cases. Our approach bases on certain modifications of orbits and shadings of a given FIFS, generated by disjunctive drivers. To complete the picture, we present also a version of the deterministic algorithm.
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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