Geodesic
Defects and transformations of quasi-copulas
Kybernetika, Tome 52 (2016) no. 6, pp. 848-865
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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 
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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

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