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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

The paper deals mainly with a fuzzification of the classical Tarski&apos;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&apos;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&apos;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.

Název v anglickém jazyce

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

Popis výsledku anglicky

The paper deals mainly with a fuzzification of the classical Tarski&apos;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&apos;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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

382

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

27

Strana od-do

29-56

Kód UT WoS článku

000508214700002

EID výsledku v databázi Scopus

2-s2.0-85057611714