1-Lipschitz aggregation operators and quasi-copulas

Kolesárová, Anna

Kybernetika, Tome 39 (2003) no. 5, pp. 615-629

Abstract (VO)

In the paper, binary 1-Lipschitz aggregation operators and specially quasi-copulas are studied. The characterization of 1-Lipschitz aggregation operators as solutions to a functional equation similar to the Frank functional equation is recalled, and moreover, the importance of quasi-copulas and dual quasi-copulas for describing the structure of 1-Lipschitz aggregation operators with neutral element or annihilator is shown. Also a characterization of quasi-copulas as solutions to a certain functional equation is proved. Finally, the composition of 1-Lipschitz aggregation operators, and specially quasi-copulas, is studied.

Détail

Classification : 26B35, 26B99, 60E05
Keywords: aggregation operator; 1-Lipschitz aggregation operator; copula; quasi-copula; kernel aggregation operator

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