Quasi-copulas as linear combinations of copulas

被引：3
|
作者：
Dolinar, Gregor [1 ,2 ]
Kuzma, Bojan [2 ,3 ]
Stopar, Nik [2 ,4 ]
机构：
[1] Univ Ljubljana, Fac Elect Engn, Ljubljana, Slovenia
[2] Inst Math Phys & Mech, Ljubljana, Slovenia
[3] Univ Primorska, Fac Math, Nat Sci & Informat Technol, Koper, Slovenia
[4] Univ Ljubljana, Fac Civil & Geodet Engn, Ljubljana, Slovenia
来源：
FUZZY SETS AND SYSTEMS | 2024年 / 477卷
关键词：
Quasi-copula; Copula; Linear combination; Affine combination; Minkowski norm; BOUNDS;
D O I：
10.1016/j.fss.2023.108821
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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 Fernandez-Sanchez, Quesada-Molina, and ubeda-Flores who considered linear combinations of discrete copulas.
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页数：15
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