模糊集的熵与非线性积分

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-06-25 DOI:10.1016/j.fss.2025.109513

Rui Lv , Jun Li , Yuhuan Wang , Zhanxin Yang

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引用次数: 0

摘要

本文综述了模糊集和模糊测度的模糊熵，包括近年来在这一主题上的最新成果。给出了一些具有代表性的模糊熵及其构造方法。重点讨论了用非线性积分来定义连续域上模糊集和模糊测度的熵。给出了基于Sugeno积分和Choquet积分的模糊熵的一些新性质，简要介绍了三种重要的非线性积分——凹积分、凸积分和泛积分，并介绍了近年来关于这些积分的最新研究成果。我们还证明了凸积分的一些新的基本性质，并利用这些性质引入了模糊集的两类模糊熵：类knopfmacher模糊熵和类yager模糊熵。此外，我们还提到了用非线性积分定义模糊测度熵及其构造方法的阶段性研究成果。

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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On entropies of fuzzy sets and nonlinear integrals

This paper provides a summary of fuzzy entropies of fuzzy sets and of fuzzy measures, including the latest results in recent years on this topic. Some representative fuzzy entropies and their construction methods are shown. We focus on the discussion of using nonlinear integrals to define entropies of fuzzy sets and of fuzzy measures in continuous domain. Some new properties of the fuzzy entropies based on the Sugeno integrals and the Choquet integrals are obtained, and we briefly review three important nonlinear integrals — the concave, convex and pan-integrals, and present the latest achievements we have obtained for these integrals in recent years. We also demonstrate some new fundamental properties of convex integrals, and by means of these properties, we introduce two types of fuzzy entropies of fuzzy sets, the Knopfmacher-like and the Yager-like fuzzy entropies. In addition, we also mention our staged research results on defining the entropy of fuzzy measures via nonlinear integrals and their construction methods.

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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.