Material implications in lattice effect algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73583864" target="_blank" >RIV/61989592:15310/18:73583864 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0020025517311702" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0020025517311702</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ins.2017.12.049" target="_blank" >10.1016/j.ins.2017.12.049</a>

Result language
angličtina
Original language name
Material implications in lattice effect algebras
Original language description
In this paper we show that it is not acceptable using the minimal conditions of implication introduced for orthomodular lattices as minimal conditions of a good implication for lattice effect algebras. Hence, we first define the concept of a partial t-norm on bounded lattices. Then we obtain the concept of a pt-implication on bounded involutive lattices by introducing some conditions using partial t-norms. Furthermore, we conclude that the Sasaki arrow which is a very important implication in lattice effect algebras is the best pt-implication on them. Finally, applying the Sasaki arrow, we construct a fuzzy implication on a lattice effect algebra and also we prove that it is a weak pt-implication as well.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-15286S" target="_blank" >GA15-15286S: Algebraic, many-valued and quantum structures for uncertainty modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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