On monotone measures that provide the coincidence of the Choquet integral and the pan-integral

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

Fuzzy Sets and Systems Pub Date : 2025-06-06 DOI:10.1016/j.fss.2025.109501

M. Svistula

引用次数: 0

Abstract

It is known that the (M)-property and the weak (M)-property of monotone measures were introduced in the studying the coincidence of the Choquet integral and the pan-integral. We proved that for a finite monotone measure, which is continuous from above, these two properties are equivalent. Besides that, some new properties and a criterion for additivity of monotone measures with the (M)-property and the weak (M)-property were presented. We also introduce the notion of the middle (M)-property and rise an open problem with the relationship between this property and the weak (M)-property.

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提供Choquet积分与泛积分重合的单调测度

在研究Choquet积分与泛积分的重合时，引入单调测度的(M)-性质和弱(M)-性质。我们证明了对于连续的有限单调测度，这两个性质是等价的。此外，给出了单调测度具有(M)-性质和弱(M)-性质的一些新性质和一个可加性判据。我们还引入了中(M)-性质的概念，并提出了一个关于中(M)-性质与弱(M)-性质之间关系的开放问题。

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.