Geodesic
Defects and transformations of quasi-copulas
Kybernetika, Tome 52 (2016) no. 6, pp. 848-865 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being a fixed point of the transformation under consideration. Finally, an application to the construction of so-called imprecise copulas is given.
Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being a fixed point of the transformation under consideration. Finally, an application to the construction of so-called imprecise copulas is given.
DOI : 10.14736/kyb-2016-6-0848
Classification : 26B25, 26B35, 60E05, 62E10, 62H10
Keywords: copula; quasi-copula; transformation of quasi-copulas; imprecise copula 
@article{10_14736_kyb_2016_6_0848,
     author = {Dibala, Michal and Saminger-Platz, Susanne and Mesiar, Radko and Klement, Erich Peter},
     title = {Defects and transformations of quasi-copulas},
     journal = {Kybernetika},
     pages = {848--865},
     year = {2016},
     volume = {52},
     number = {6},
     doi = {10.14736/kyb-2016-6-0848},
     mrnumber = {3607851},
     zbl = {06707377},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-6-0848/}
}
TY  - JOUR
AU  - Dibala, Michal
AU  - Saminger-Platz, Susanne
AU  - Mesiar, Radko
AU  - Klement, Erich Peter
TI  - Defects and transformations of quasi-copulas
JO  - Kybernetika
PY  - 2016
SP  - 848
EP  - 865
VL  - 52
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-6-0848/
DO  - 10.14736/kyb-2016-6-0848
LA  - en
ID  - 10_14736_kyb_2016_6_0848
ER  - 
%0 Journal Article
%A Dibala, Michal
%A Saminger-Platz, Susanne
%A Mesiar, Radko
%A Klement, Erich Peter
%T Defects and transformations of quasi-copulas
%J Kybernetika
%D 2016
%P 848-865
%V 52
%N 6
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-6-0848/
%R 10.14736/kyb-2016-6-0848
%G en
%F 10_14736_kyb_2016_6_0848
Dibala, Michal; Saminger-Platz, Susanne; Mesiar, Radko; Klement, Erich Peter. Defects and transformations of quasi-copulas. Kybernetika, Tome 52 (2016) no. 6, pp. 848-865. doi: 10.14736/kyb-2016-6-0848

Cité par Sources :