Generation of continuous T-norms through latticial operations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402I2V" target="_blank" >RIV/61988987:17610/23:A2402I2V - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S016501142200392X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016501142200392X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2022.09.005" target="_blank" >10.1016/j.fss.2022.09.005</a>

Result language
angličtina
Original language name
Generation of continuous T-norms through latticial operations
Original language description
It is well known that the usual point-wise ordering over the set of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations on the set of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set . As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations on the set , two binary operations on the set of continuous t-norms are proposed and showed that the discussed structure is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them.
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
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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