{"title":"Average general fractal dimensions of typical compact metric spaces","authors":"Bilel Selmi","doi":"10.1016/j.fss.2024.109192","DOIUrl":null,"url":null,"abstract":"<div><div>The main objective of this paper is to investigate the average general fractal dimensions of typical compact metric spaces within the Gromov-Hausdorff space, using the Gromov-Hausdorff metric. As an application of the main results, we demonstrate that a typical compact metric space Σ exhibits such irregularity that the lower and upper average general Hewitt-Stromberg dimensions, as well as the general box dimensions corresponding to all higher-order Hölder and Cesàro averages, diverge significantly.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109192"},"PeriodicalIF":3.2000,"publicationDate":"2024-11-16","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/S0165011424003385","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
The main objective of this paper is to investigate the average general fractal dimensions of typical compact metric spaces within the Gromov-Hausdorff space, using the Gromov-Hausdorff metric. As an application of the main results, we demonstrate that a typical compact metric space Σ exhibits such irregularity that the lower and upper average general Hewitt-Stromberg dimensions, as well as the general box dimensions corresponding to all higher-order Hölder and Cesàro averages, diverge significantly.
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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