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

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dc.title A comparative study of Tarski's fixed point theorems with the stress on commutative sets of L-fuzzy isotone maps with respect to transitivities en
dc.contributor.author Včelař, František
dc.contributor.author Pátíková, Zuzana
dc.relation.ispartof Fuzzy Sets and Systems
dc.identifier.issn 0165-0114 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued 2020
utb.relation.volume 382
dc.citation.spage 29
dc.citation.epage 56
dc.type article
dc.language.iso en
dc.publisher Elsevier B.V.
dc.identifier.doi 10.1016/j.fss.2018.12.001
dc.relation.uri https://www.sciencedirect.com/science/article/pii/S0165011418309588
dc.subject Fuzzy relation en
dc.subject Fixed point en
dc.subject Complete lattice en
dc.subject L-fuzzy isotone map en
dc.subject Commutative set of maps en
dc.subject Relatively isotone map en
dc.subject Transitivity (weak or strong) en
dc.description.abstract 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. © 2018 Elsevier B.V. en
utb.faculty Faculty of Applied Informatics
dc.identifier.uri http://hdl.handle.net/10563/1009530
utb.identifier.obdid 43880360
utb.identifier.scopus 2-s2.0-85057611714
utb.identifier.wok 000508214700002
utb.identifier.coden FSSYD
utb.source j-scopus
dc.date.accessioned 2020-01-24T13:28:08Z
dc.date.available 2020-01-24T13:28:08Z
utb.ou Department of Mathematics
utb.contributor.internalauthor Včelař, František
utb.contributor.internalauthor Pátíková, Zuzana
utb.fulltext.affiliation František Včelař ∗, Zuzana Pátíková Department of Mathematics, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín, 76005, Czech Republic
utb.fulltext.dates Received 9 January 2017 received in revised form 3 October 2018 accepted 2 December 2018 Available online 4 December 2018
utb.wos.affiliation [Vcelar, Frantisek; Patikova, Zuzana] Tomas Bata Univ Zlin, Fac Appl Informat, Dept Math, Nad Stranemi 4511, Zlin 76005, Czech Republic
utb.scopus.affiliation Department of Mathematics, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín, 76005, Czech Republic
utb.fulltext.faculty Faculty of Applied Informatics
utb.fulltext.faculty Faculty of Applied Informatics
utb.fulltext.ou Department of Mathematics
utb.fulltext.ou Department of Mathematics
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