R-implications and the exchange principle: The case of border continuous t-norms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F13%3AA14016C4" target="_blank" >RIV/61988987:17610/13:A14016C4 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
R-implications and the exchange principle: The case of border continuous t-norms
Original language description
It is well-known that the residual of a left-continuous t-norm satisfies the exchange principle (EP). However, the left-continuity of a t-norm is only sufficient and not necessary, as many examples in the literature illustrate. In this work we study thenecessary and sufficient conditions on a t-norm for its residual to satisfy (EP). We present a complete characterization of two classes of t-norms whose residuals satisfy (EP), viz., t-norms that are border-continuous and those that have an ordinal sum representation. Based on the obtained results we characterize t-norms, whose residuals satisfy boththe exchange principle and the ordering property.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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