Extreme values of the mass distribution associated with d-quasi-copulas via linear programming

Belšak, Matej (author), Omladič, Matjaž (author), Vuk, Martin (author), Zalar, Aljaž (author)

The recent survey (J.J. Arias-García, R. Mesiar, B. De Baets, A hitchhiker’s guide to quasi-copulas, Fuzzy Sets Syst. 393 (2020) 1–28.) nicknamed “Hitchhiker's Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. This paper concentrates on Open Problem 5 of this list concerning bounds on the volume of a d-variate quasi-copula. We disprove a recent conjecture (M. Úbeda-Flores, Extreme values of the mass distribution associated with a tetravariate quasi-copula, Fuzzy Sets Syst. 473 (2023).) on the lower bound of this volume. We also give evidence that the problem is much more difficult than suspected, and give some hints towards its final solution.

• Language: English
• Keywords: mass distribution, d-quasi-copula, volume, Lipschitz condition, bounds
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science ; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 17 str.
• Numbering: Vol. 517, art. 109457
• PID: 20.500.12556/RUL-169445
• UDC: 519.2
• ISSN on article: 0165-0114
• DOI: 10.1016/j.fss.2025.109457
• COBISS.SI-ID: 237374979
• Publication date in RUL: 28.05.2025

Record is a part of a journal

• Title: Fuzzy sets and systems : international journal of soft computing and intelligence
• Shortened title: Fuzzy sets syst.
• Publisher: Elsevier
• ISSN: 0165-0114
• COBISS.SI-ID: 25498624

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• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
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