A comparative study of Tarski's fixed point theorems with the stress on commutative sets of L-fuzzy isotone maps with respect to transitivities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F20%3A63523358" target="_blank" >RIV/70883521:28140/20:63523358 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011418309588?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418309588?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2018.12.001" target="_blank" >10.1016/j.fss.2018.12.001</a>

Result language
angličtina
Original language name
A comparative study of Tarski's fixed point theorems with the stress on commutative sets of L-fuzzy isotone maps with respect to transitivities
Original language description
The paper deals mainly with a fuzzification of the classical Tarski's theorem for commutative sets of isotone maps (the so-called generalized theorem) in a sufficiently rich fuzzy setting on general structures called L-complete propelattices. Our concept enables a consistent analysis of the validity of single statements of the generalized Tarski's theorem in dependence on assumptions of relevant versions of transitivity (weak or strong). The notion of the L-complete propelattice was introduced in connection with the fuzzified more famous variant of Tarski's theorem for a single L-fuzzy isotone map, whose main part holds even without the assumption of any version of transitivity. These results are here extended also to the concept of the so-called L-fuzzy relatively isotone maps and then additionally compared to the results, which are achieved for the generalized theorem and which always need a relevant version of transitivity. Wherever it is possible, facts and differences between both the theorems are demonstrated by appropriate examples or counterexamples.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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