Kybernetika 41 no. 3, 329-348, 2005

Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators

Erich Peter Klement and Anna Kolesárová


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).