# 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

top- Alsina C., Nelsen R. B., Schweizer B., 10.1016/0167-7152(93)90001-Y, Statist. Probab. Lett. 17 (1993) 85–89 (1993) MR1223530DOI10.1016/0167-7152(93)90001-Y
- Calvo T., Kolesárová A., Komorníková, M., Mesiar R., Aggregation operators: properties, classes and construction methods, In: Aggregation Operators (T. Calvo, G. Mayor and R. Mesiar, eds.), Physica–Verlag, Heidelberg, 2002, pp. 3–104 Zbl1039.03015MR1936384
- Calvo T., Baets, B. De, Fodor J. C., The functional equations of Alsina and Frank for uninorms and nullnorms, Fuzzy Sets and Systems 120 (2001), 385–394 MR1829256
- Calvo T., Mesiar R., Stability of aggegation operators, In: Proc. 1st Internat. Conference in Fuzzy Logic and Technology (EUSFLAT’2001), Leicester, 2001, pp. 475–478
- Baets B. De, Fodor J., Generator triplets of additive fuzzy preference structures, In: Proc. Sixth Internat. Workshop on Relational Methods in Computer Science, Tilburg, The Netherlands 2001, pp. 306–315
- DeḂaets B., T-norms and copulas in fuzzy preference modeling, In: Proc. Linz Seminar’2003, Linz, 2003, p. 101
- Fodor J. C., Yager R. R., Rybalov, 10.1142/S0218488597000312, Internat. J. of Uncertainty, Fuzziness and Knowledge-based Systems 5 (1997), 411–427 (1997) Zbl1232.03015MR1471619DOI10.1142/S0218488597000312
- Frank M. J., 10.1007/BF02189866, Aequationes Math. 19 (1979), 194–226 (1979) Zbl0444.39003MR0556722DOI10.1007/BF02189866
- Genest C., Molina L., Lallena, L., Sempi C., 10.1006/jmva.1998.1809, J. Multivariate Anal. 69 (1999), 193–205 (1999) Zbl0935.62059MR1703371DOI10.1006/jmva.1998.1809
- Janssens S., Baets B. De, Meyer H. De, Bell-type inequalities for commutative quasi-copulas, Preprint, 2003
- Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer, Dordrecht 2000 Zbl1087.20041MR1790096
- Kolesárová A., Mordelová J., 1-Lipschitz and kernel aggregation operators, In: Proc. Summer School on Aggregation Operators (AGOP’2001), Oviedo, Spain 2001, pp. 71–76
- Kolesárová A., Mordelová, J., Muel E., Kernel aggregation operators and their marginals, Fuzzy Sets and Systems, accepted Zbl1043.03040MR2045341
- Kolesárová A., Mordelová, J., Muel E., 10.1142/S0218488502001818, Internat. J. of Uncertainty, Fuzziness and Knowledge-based Systems 10/s (2002), 37–50 MR1962667DOI10.1142/S0218488502001818
- Kolesárová A., Mordelová, J., Muel E., A review of of binary kernel aggregation operators, In: Proc. Summer School on Aggregation Operators (AGOP’2003), Alcalá de Henares, Spain 2003, pp. 97–102
- Mesiar R., Compensatory operators based on triangular norms, In: Proc. Third European Congress on Intelligent Techniques and Soft Computing (EUFIT’95), Aachen 1995, pp. 131–135 (1995)
- Nelsen R. B., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics 139.) Springer, New York 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
- Nelsen R. B., Copulas: an introduction to their properties and applications, Preprint, 2003 Zbl1079.60021

## Citations in EuDML Documents

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

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