On a new classification of triangular norms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2502I2X" target="_blank" >RIV/61988987:17610/23:A2502I2X - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011422003748" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422003748</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2022.09.002" target="_blank" >10.1016/j.fss.2022.09.002</a>

Result language
angličtina
Original language name
On a new classification of triangular norms
Original language description
In this paper, we introduce the notion of (k)-triangular norms and present a new classification of triangular norms (t-norms for short) splitting the set T of all t-norms into an infinite countable partition {T1⁎,T2⁎,…}∪{T⁎}. From the four basic t-norms, the minimum TM is the unique member of T1⁎, the drastic product TD belongs to T2⁎, the product TP and also the Łukasiewicz t-norm TL are members of T⁎. We show that t-norms from Tk⁎ are always (k+1)-contractive, but not vice-versa. We also provide some necessary and some sufficient conditions for t-norms to be (proper) (k)-t-norms. In the end, we give several examples and construction methods for t-norms belonging to particular classes of the proposed partition or to the set Tk=⋃i=1kTi⁎.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10100 - 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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