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.
引用
收藏
页数：15
相关论文
共 50 条
  • [41] Bivariate measure-inducing quasi-copulas
    Stopar, Nik
    FUZZY SETS AND SYSTEMS, 2024, 492
  • [42] On a new construction of 1-Lipschitz aggregation functions, quasi-copulas and copulas
    Kolesarova, Anna
    Mesiar, Radko
    Kalicka, Jana
    FUZZY SETS AND SYSTEMS, 2013, 226 : 19 - 31
  • [43] Characterization of bivariate quadratic transformations of quasi-copulas
    Tongjundee, P.
    Boonyasri, V.
    Tasena, S.
    IRANIAN JOURNAL OF FUZZY SYSTEMS, 2023, 20 (04): : 165 - 178
  • [44] 1-Lipschitz aggregation operators, quasi-copulas and copulas with given diagonals
    Klement, EP
    Kolesárová, A
    SOFT METHODOLOGY AND RANDOM INFORMATION SYSTEMS, 2004, : 205 - 211
  • [45] The unwalked path between quasi-copulas and copulas: Stepping stones in higher dimensions
    Arias-García, J.J.
    Mesiar, R.
    De Baets, B.
    International Journal of Approximate Reasoning, 2017, 80 : 89 - 99
  • [46] Bell-type inequalities for quasi-copulas
    Janssens, S
    De Baets, B
    De Meyer, H
    FUZZY SETS AND SYSTEMS, 2004, 148 (02) : 263 - 278
  • [47] Some new characterizations and properties of quasi-copulas
    Rodriguez-Lallena, Jose Antonio
    Ubeda-Flores, Manuel
    FUZZY SETS AND SYSTEMS, 2009, 160 (06) : 717 - 725
  • [48] A new family of trivariate proper quasi-copulas
    Ubeda-Flores, Manuel
    KYBERNETIKA, 2007, 43 (01) : 75 - 85
  • [49] QUASI-COPULAS WITH QUADRATIC SECTIONS IN ONE VARIABLE
    Rodriguez-Lallena, Jose Antonio
    Ubeda-Flores, Manuel
    KYBERNETIKA, 2008, 44 (06) : 879 - 890
  • [50] On the lattice structure of the set of supermodular quasi-copulas
    Arias-Garcia, J. J.
    De Baets, B.
    FUZZY SETS AND SYSTEMS, 2019, 354 : 74 - 83
12345