Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402LNQ" target="_blank" >RIV/61988987:17610/23:A2402LNQ - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011423002592" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011423002592</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2023.108614" target="_blank" >10.1016/j.fss.2023.108614</a>

Result language
angličtina
Original language name
Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I
Original language description
The continuous completions of conditionally cancellative pre-t-norms defined in the regions linked to the characterization of (S,N)-implications when Sis a continuous t-conorm and Nis a fuzzy negation with one point of discontinuity are determined. The results have been divided in two parts. In this first part we provide three main results: we determine the existence and expression of the additive generator of a cancellative pre-t-norm known above a level curve and, using this result as a basis, we provide the continuous completions of pre-t-norms determined in regions of the type [0,1]^2(0,a)^2 or [0,1]^2(a,1)^2with a ∈ (0,1). It is highlighted that, differently from the cancellative case where all the results provide unique continuous completions, in the analogous situations in the conditionally cancellative case the corresponding continuous completions might not be unique. This fact causes more complex results for the remaining regions, which are discussed in the second paper of this study.
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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