Flipping and cyclic shifting of binary aggregation functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F09%3AA0900TWQ" target="_blank" >RIV/61988987:17610/09:A0900TWQ - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Flipping and cyclic shifting of binary aggregation functions
Original language description
We introduce two types of transformations of random variables, called flipping and cyclic shifting. As these transformations preserve monotonicity at the level of univariate cumulative distribution functions, they can be used to develop corresponding coordinate-wise transformations of binary aggregation functions. We lay bare the admissibility of these transformations, i.e. the necessary and sufficient conditions under which they result in a binary aggregation function. We investigate which additional properties, such as the 1-Lipschitz property and 2-increasingness, entail these admissibility conditions. Moreover, we point out which of these properties are preserved under flipping and/or cyclic shifting. Interestingly, quasi-copulas remain quasi-copulas under flipping, while copulas remain copulas under flipping as well as under cyclic shifting.
Czech name
Pretáčacie a otáčacie binárne agregačné funkcie
Czech description
Zavádzame dva typy transformácií nahodných premenných, a na ich základe navrhujeme dva typy transformácií binárnych agregačných funkcií. Zároveň sledujeme správanie sa transformovaných agregačných funkcií so špeciálnymi vlastnosťami, ako sú 1-Lispchitzovskosť či 2-rastúcosť.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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