Quasi-copulas as linear combinations of copulas

Dolinar, Gregor (author), Kuzma, Bojan (author), Stopar, Nik (author)

We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernández-Sánchez, Quesada-Molina, and Úbeda-Flores who considered linear combinations of discrete copulas.

• Language: English
• Keywords: quasi-copulas, copulas, linear combination, affine combination, Minkowski norm
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering; FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 15 str.
• Numbering: Vol. 477, art. 108821
• PID: 20.500.12556/RUL-153555
• UDC: 519.2
• ISSN on article: 0165-0114
• DOI: 10.1016/j.fss.2023.108821
• COBISS.SI-ID: 179977731
• Publication date in RUL: 15.01.2024

Record is a part of a journal

• Title: Fuzzy sets and systems
• Shortened title: Fuzzy sets syst.
• Publisher: Elsevier, International Fuzzy Systems Association
• ISSN: 0165-0114
• COBISS.SI-ID: 25498624

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.