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A t-norm embedding theorem for fuzzy sets

A t-norm embedding theorem for fuzzy sets

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dc.contributor.author Bielawski, Jakub pl
dc.contributor.author Tabor, Jacek [SAP11017416] pl
dc.date.accessioned 2014-07-24T11:06:07Z
dc.date.available 2014-07-24T11:06:07Z
dc.date.issued 2012 pl
dc.identifier.issn 0165-0114 pl
dc.identifier.uri http://ruj.uj.edu.pl/xmlui/handle/item/302
dc.language eng pl
dc.title A t-norm embedding theorem for fuzzy sets pl
dc.type JournalArticle pl
dc.description.physical 33-53 pl
dc.abstract.en It is well-known that the class of upper semicontinuous normal convex fuzzy sets with compact supports can be embedded isometrically as a complete convex cone in a Banach space. We prove an analogous result for a subclass of fuzzy sets that is free from the normality limitation by exchanging the standard algebraic operations on fuzzy sets with operations based on strict t-norms. This allows us to investigate a new notion of fuzzy convexity that we call T-convexity. We show that the class of upper semicontinuous fuzzy T-convex sets with nonempty compact supports can be embedded as a closed convex cone in a Banach space. This implies that fuzzy T-convex sets satisfy the cancellation law. We discuss a possible application of the embedding theorem in mathematical morphology. pl
dc.subject.en Algebraic operations pl
dc.subject.en Extension principle pl
dc.subject.en Fuzzy convex sets pl
dc.subject.en Embedding theorem pl
dc.subject.en t-Norms pl
dc.subject.en Mathematical morphology pl
dc.description.volume 209 pl
dc.identifier.doi 10.1016/j.fss.2012.06.004 pl
dc.identifier.eissn 1872-6801 pl
dc.title.journal Fuzzy Sets and Systems pl
dc.language.container eng pl
dc.affiliation Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej pl
dc.subtype Article pl
dc.rights.original bez licencji pl
.pointsMNiSW [2012 A]: 40


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