Geodesic
1-Lipschitz aggregation operators and quasi-copulas
Kybernetika, Tome 39 (2003) no. 5, p. [615]

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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.
Classification : 26B35, 26B99, 60E05
Keywords: aggregation operator; 1-Lipschitz aggregation operator; copula; quasi-copula; kernel aggregation operator 
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     author = {Koles\'arov\'a, Anna},
     title = {1-Lipschitz aggregation operators and quasi-copulas},
     journal = {Kybernetika},
     pages = {[615]},
     publisher = {mathdoc},
     volume = {39},
     number = {5},
     year = {2003},
     mrnumber = {2042344},
     zbl = {1249.60018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003__39_5_a8/}
}
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Kolesárová, Anna. 1-Lipschitz aggregation operators and quasi-copulas. Kybernetika, Tome 39 (2003) no. 5, p. [615]. http://geodesic.mathdoc.fr/item/KYB_2003__39_5_a8/