Extension to copulas and quasi-copulas as special \(1\)-Lipschitz aggregation operators. (English) Zbl 1249.60017

Klement, Erich Peter; Kolesárová, Anna

Kybernetika 41, No. 3, 329-348 (2005).

Summary: Smallest and greatest \(1\)-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).

MSC:

60E05	Probability distributions: general theory
26B99	Functions of several variables

Keywords:

copula; quasi-copula; \(1\)-Lipschitz aggregation operator; diagonal

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