Kybernetika 52 no. 6, 848-865, 2016

Defects and transformations of quasi-copulas

Michal Dibala, Susanne Saminger-Platz, Radko Mesiar and Erich Peter KlementDOI: 10.14736/kyb-2016-6-0848


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.


copula, quasi-copula, transformation of quasi-copulas, imprecise copula


26B25, 62E10, 26B35, 60E05, 62H10


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