Formulas for generators of R-implications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00328128" target="_blank" >RIV/68407700:21230/19:00328128 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.fss.2018.09.011" target="_blank" >https://doi.org/10.1016/j.fss.2018.09.011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2018.09.011" target="_blank" >10.1016/j.fss.2018.09.011</a>

Result language
angličtina
Original language name
Formulas for generators of R-implications
Original language description
We study implications on the unit interval. Like triangular norms and conorms, these implications also may have generators (additive or multiplicative). Although there are constructive proofs of the existence of generators of these operations, they rarely lead to closed formulas. Thus we lack a practical tool for computations of the generators. Recently we have shown that the generators of triangular norms can often be computed from the partial derivatives of the original operations. Here we apply a similar technique to R-implications. Some of the formulas have analogies for triangular norms, some do not. Besides, we show (and avoid) another potential problem of computation of generators of triangular norms, not mentioned before.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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