# 1-Lipschitz aggregation operators and quasi-copulas

Kybernetika (2003)

- Volume: 39, Issue: 5, page [615]-629
- ISSN: 0023-5954

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topKolesárová, Anna. "1-Lipschitz aggregation operators and quasi-copulas." Kybernetika 39.5 (2003): [615]-629. <http://eudml.org/doc/33669>.

@article{Kolesárová2003,

abstract = {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.},

author = {Kolesárová, Anna},

journal = {Kybernetika},

keywords = {aggregation operator; 1-Lipschitz aggregation operator; copula; quasi-copula; kernel aggregation operator; aggregation operator; 1-Lipschitz aggregation operator; copula; quasi-copula; kernel aggregation operator},

language = {eng},

number = {5},

pages = {[615]-629},

publisher = {Institute of Information Theory and Automation AS CR},

title = {1-Lipschitz aggregation operators and quasi-copulas},

url = {http://eudml.org/doc/33669},

volume = {39},

year = {2003},

}

TY - JOUR

AU - Kolesárová, Anna

TI - 1-Lipschitz aggregation operators and quasi-copulas

JO - Kybernetika

PY - 2003

PB - Institute of Information Theory and Automation AS CR

VL - 39

IS - 5

SP - [615]

EP - 629

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/33669

ER -

## References

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## Citations in EuDML Documents

top- Manuel Úbeda-Flores, A new family of trivariate proper quasi-copulas
- Erich Peter Klement, Anna Kolesárová, Extension to copulas and quasi-copulas as special $1$-Lipschitz aggregation operators
- Fabrizio Durante, Carlo Sempi, Semicopulæ
- José Antonio Rodríguez–Lallena, Manuel Úbeda-Flores, Quasi-copulas with quadratic sections in one variable

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