Average general fractal dimensions of typical compact metric spaces

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-11-16 DOI:10.1016/j.fss.2024.109192

Bilel Selmi

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.

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典型紧凑公制空间的平均一般分形维数

本文的主要目的是利用格罗莫夫-豪斯多夫度量，研究格罗莫夫-豪斯多夫空间内典型紧凑度量空间的平均一般分形维数。作为主要结果的一个应用，我们证明了典型的紧凑度量空间Σ表现出这样的不规则性，以至于一般休伊特-斯特罗姆伯格维度的下限和上限平均值，以及对应于所有高阶霍尔德和塞萨罗平均值的一般盒维度，都显著发散。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

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.