Extremal Lipschitz continuous aggregation functions with a given diagonal section

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73590121" target="_blank" >RIV/61989592:15310/18:73590121 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011418300022" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418300022</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2017.12.014" target="_blank" >10.1016/j.fss.2017.12.014</a>

Result language
angličtina
Original language name
Extremal Lipschitz continuous aggregation functions with a given diagonal section
Original language description
In this paper we study the smallest and the greatest M-Lipschitz continuous n-ary aggregation functions with a given diagonal section. We show that several properties that were studied for the smallest and the greatest 1-Lipschitz continuous binary aggregation functions with a given diagonal section extend naturally to higher dimensions while considering different Lipschitz constants. Just as in the binary case, we show that the smallest n-quasi-copula with a given diagonal section coincides with the smallest 1-Lipschitz n-ary aggregation function with that diagonal section. Additionally, we show that the smallest n-quasi-copula with a given diagonal section, called the Bertino n-quasi-copula, is supermodular for any n >= 2.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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