普遍化共同性：新的见解和双重观点

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

Fuzzy Sets and Systems Pub Date : 2025-03-10 DOI:10.1016/j.fss.2025.109364

M. Boczek, A. Hovana, O. Hutník

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引用次数: 0

摘要

我们回顾、举例说明并比较了最近引入的函数类，这些函数从两个角度概括了共单调函数：代数上通过- -相关函数和测量-理论上通过- -正相关函数，以及它们的对偶版本- - -相关函数和- -次可加函数。虽然m-次加性函数的概念在文献中有很好的记载，但“-美女超关联”的概念似乎是新颖的。此外，我们给出了这些函数类的几个应用，特别是关于广义Sugeno积分的积分不等式。此外，我们还提到了其他关于共单调性的扩展，包括弱共单调性和多元共单调性。

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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Generalizing comonotonicity: New insights and dual perspectives

We review, exemplify, and compare recently introduced classes of functions that generalize comonotone functions from two perspectives: algebraically through

⋆_{\inf}

-associated functions and measure-theoretically via m-positively dependent functions, along with their dual versions –

⋆_{\sup}

-associated functions and m-subadditive functions, respectively. While the concept of m-subadditive functions is well-documented in the literature, the concept of

⋆_{\sup}

-associatedness appears to be novel. Furthermore, we present several applications of these function classes, particularly concerning integral inequalities for the generalized Sugeno integral. Additionally, we mention other extensions of comonotonicity, including weak comonotonicity and multivariate comonotonicity.

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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.