Conditional aggregation-based Choquet integral as a Choquet integral on a hyperspace

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

Fuzzy Sets and Systems Pub Date : 2024-06-25 DOI:10.1016/j.fss.2024.109055

Jana Borzová , Lenka Halčinová, Jaroslav Šupina

引用次数: 0

Abstract

We aim at representing the recently introduced conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset. The representation is one of transformations considered by R.R. Yager and R. Mesiar in 2015. Thus we study the properties of the conditional aggregation-based Choquet integral using well-known facts about the standard Choquet integral. In particular, we obtain several formulas for its computation. We also provide the representation of the conditional aggregation-based Choquet integral in terms of the Möbius transform.

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基于条件聚合的乔奎特积分作为超空间上的乔奎特积分

我们旨在将最近引入的基于条件聚集的乔奎特积分表示为超集上的标准乔奎特积分。该表示是 R.R. Yager 和 R. Mesiar 在 2015 年考虑的变换之一。因此，我们利用关于标准 Choquet 积分的众所周知的事实来研究基于条件聚集的 Choquet 积分的性质。特别是，我们得到了几个计算公式。我们还提供了基于条件聚集的乔奎特积分在莫比乌斯变换方面的表示。

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.