分解积分的一些新性质及模糊熵的推广

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

Fuzzy Sets and Systems Pub Date : 2025-09-09 DOI:10.1016/j.fss.2025.109577

Rui Lv , Jun Li , Yuhuan Wang , Zhanxin Yang

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引用次数: 0

摘要

本文进一步研究了分解积分的一些重要特征，给出了几个具有普遍性的基本性质。主要讨论了四种常用的重要分解积分——Choquet积分、泛积分、凹积分和Shilkret积分。分别证明了这些积分的一些有趣的性质。利用这些性质，将连续域上模糊集的熵从勒贝格测度空间推广到模糊测度空间，并建立了基于分解积分的各种形式的模糊熵。我们分别给出了四种广义Knopfmacher熵和广义Yager熵。以前Knopfmacher和Yager得到的模糊熵的结果成为我们结果的特例。

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Some new properties of decomposition integrals and the extensions of fuzzy entropies

In this paper, we further investigate some important characteristics of decomposition integrals and present several fundamental properties with universality. We mainly focus on the Choquet integral, the pan-integral, the concave integral and the Shilkret integral, which are four commonly used and important decomposition integrals. Some interesting properties of these integrals are demonstrated, respectively. By utilizing these properties, we generalize the entropy of fuzzy sets on continuous domain from Lebesgue measure spaces to fuzzy measure spaces, and establish various forms of fuzzy entropies based on decomposition integrals. We show four kinds of the generalized Knopfmacher entropies and the generalized Yager entropies, respectively. The previous results of fuzzy entropies obtained by Knopfmacher and Yager become special cases of our results.

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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.