Distorted copulas

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

Fuzzy Sets and Systems Pub Date : 2024-03-21 DOI:10.1016/j.fss.2024.108947

Roberto Ghiselli Ricci

引用次数: 0

Abstract

In this paper, we deal with the problem of preserving the copula property by means of a transformation called distortion where automorphisms of the real unit interval are involved. A new methodological approach is followed by resorting to a special branch of group theory. The crucial role of absolute continuity of one-dimensional sections of a distorted copula is illustrated. Some necessary and sufficient conditions concerning the automorphisms which preserve the copula property for a large class of bivariate copulas are proved. Several examples are presented.

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扭曲的协方差

在本文中，我们讨论了通过一种称为变形的变换来保留共轭性质的问题，其中涉及实数单位区间的自动变形。本文采用了一种新的方法论，借助于群论的一个特殊分支。变形协整的一维截面的绝对连续性的关键作用得到了说明。证明了有关保持一大类二变量共线性的共线性的自动形态的一些必要条件和充分条件。并列举了几个实例。

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.