Bivariate measure-inducing quasi-copulas

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

Fuzzy Sets and Systems Pub Date : 2024-07-02 DOI:10.1016/j.fss.2024.109068

Nik Stopar

引用次数: 0

Abstract

It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on ${[0, 1]}^{2}$ , but there exist bivariate quasi-copulas that do not induce a signed measure on the same σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.

查看原文本刊更多论文

二元计量诱导准公式

众所周知，每个双变量共线在[0,1]2 上的 Borel σ-代数上都会诱导出一个正量度，但存在着不在同一 σ-代数上诱导出有符号量度的双变量准共线。在本文中，我们证明了由双变量准可普拉斯诱导的有符号度量总是可以表示为由可普拉斯诱导的度量的无限组合。由此，我们首次给出了双变量环境下的计量诱导准共布尔的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.