A complete characterization of maximal copulas with given track section

Omladič, Matjaž (author), Škulj, Damjan (author)

Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set substantially. We propose to study maximality of these families in the order theoretic sense. A copula $C$ with given diagonal section $\delta$ is called undominated if there is no copula $C' \ne C$ with the same diagonal section $\delta$ such that $C \le C'$. The main contribution of this paper is a new method that provides undominated copulas. They form a much wider class that contains the known upper bounds as a very small subclass. There was a recent call for the study of asymmetry which is addressed by our class better than by the known ones. Corresponding quasi-copulas can be obtained from our copulas via splicing techniques. Most results are given on the level of tracks.

• Language: English
• Keywords: bivariate copulas, quasi-copulas, diagonal section, track section, undominated copulas
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FDV - Faculty of Social Sciences; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 15 str.
• Numbering: Vol. 541, art. 109949
• PID: 20.500.12556/RUL-182583
• UDC: 519.2
• ISSN on article: 0165-0114
• DOI: 10.1016/j.fss.2026.109949
• COBISS.SI-ID: 278471427
• Publication date in RUL: 18.05.2026

Record is a part of a journal

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

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

• Language: Slovenian
• Keywords: matematika, verjetnosti

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0448
• Name: Stohastične metode in njihova uporaba

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P5-0168
• Name: Družboslovna metodologija, statistika in informatika