Coherence and avoidance of sure loss for standardized functions and semicopulas

Klement, Erich Peter (author), Kokol-Bukovšek, Damjana (author), Mojškerc, Blaž (author), Omladič, Matjaž (author), Saminger, Susanne (author), Stopar, Nik (author)

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, ▫$1$▫-increasing functions with value ▫$1$▫ at ▫$(1, 1, \ldots , 1)$▫. We characterize the existence of a ▫$k$▫-increasing ▫$n$▫-variate function ▫$C$▫ fulfilling ▫$A \le C \le B$▫ for standardized ▫$n$▫-variate functions ▫$A$▫, ▫$B$▫ and discuss methods for constructing such functions. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when ▫$A$▫ respectively ▫$B$▫ coincides with the pointwise infimum respectively supremum of the set of all ▫$k$▫-increasing ▫$n$▫-variate functions ▫$C$▫ fulfilling ▫$A \le C \le B$▫.

• Language: English
• Keywords: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: EF - School of Economics and Business; FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 20 str.
• Numbering: Vol. 165, article no. ǂ109089
• PID: 20.500.12556/RUL-159806
• UDC: 519.2
• ISSN on article: 0888-613X
• DOI: 10.1016/j.ijar.2023.109089
• COBISS.SI-ID: 174544131
• Publication date in RUL: 25.07.2024

Record is a part of a journal

• Title: International journal of approximate reasoning
• Shortened title: Int. j. approx. reason.
• Publisher: Elsevier
• ISSN: 0888-613X
• COBISS.SI-ID: 14231301

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.