模糊迭代函数系统的混沌博弈算法

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

Fuzzy Sets and Systems Pub Date : 2024-11-13 DOI:10.1016/j.fss.2024.109173

Marcin Kolenda , Filip Strobin , Kamil Wiśniewski

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引用次数: 0

摘要

我们考虑了生成模糊迭代函数系统（简称 FIFS）吸引子的各种版本的混沌博弈算法。我们证明了一种天真的方法在收缩 FIFS 的一般情况下是失败的，并提出了在所有情况下都有效的自然修正方法。我们的方法基于对给定 FIFS 的轨道和阴影的某些修改，这些轨道和阴影是由互斥驱动生成的。为了更全面地说明问题，我们还介绍了确定性算法的一个版本。

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Chaos game algorithm for fuzzy iterated function systems

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.

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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.