On a representation of t-norms on bounded meet semilattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402FNK" target="_blank" >RIV/61988987:17610/23:A2402FNK - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0020025523000270" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0020025523000270</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ins.2023.01.027" target="_blank" >10.1016/j.ins.2023.01.027</a>

Result language
angličtina
Original language name
On a representation of t-norms on bounded meet semilattices
Original language description
We investigate how and when a t-norm on a bounded meet semilattice can be represented by a t-norm on its sub-semilattice and a collection of interior operators. We present such a representation using a novel notion of consistent triplet consisting of a t-norm, a commutative semigroup of interior operators, and a meet semilattice of symmetric lower sets. Furthermore, we study a related problem of extension of a t-norm from a sub-semilattice to the whole semilattice given a consistent triplet. This gives us a new construction method for t-norms on bounded semilattices that covers several known methods. Our results are illustrated by numerous examples.
Czech name
—
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/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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