1-Lipschitz aggregation operators and quasi-copulas. (English) Zbl 1249.60018

Kolesárová, Anna

Kybernetika 39, No. 5, 615-629 (2003).

Summary: 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.

MSC:

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

Keywords:

aggregation operator; 1-Lipschitz aggregation operator; copula; quasi-copula; kernel aggregation operator

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