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dc.contributor.authorJardón, Daniel
dc.contributor.authorSánchez, Iván
dc.contributor.authorSanchis López, Manuel
dc.date.accessioned2019-01-28T11:09:57Z
dc.date.available2019-01-28T11:09:57Z
dc.date.issued2018-10-29
dc.identifier.citationJARDÓN, Daniel; SÁNCHEZ, Iván; SANCHIS LÓPEZ, Manuel (2018). Some questions about Zadeh's extension on metric spaces.Fuzzy Sets and Systems, online 29 October 2018ca_CA
dc.identifier.urihttp://hdl.handle.net/10234/180217
dc.description.abstractFor a continuous function f on a Hausdorff space X , we prove that [ ̂ f(u) ] α = f(u α ) for each u ∈ F (X) and α ∈[ 0 , 1 ] , where ̂ f is the Zadeh’s extension of f . By means of this result, some results on (locally) compact spaces and the Zadeh’s extension are generalized. Given a metric space (X, d) , we introduce Skorokhod’s metric d 0 on the set F (X) of the family of all upper semicontinuous fuzzy sets u : X →[ 0 , 1 ] with compact support and such that u − 1 ( 1 ) is non-empty. We show that if f : (X, d) → (X, d) is a continuous function, then its Zadeh’s extension ̂ f to ( F (X), d 0 ) is also continuous and that (X, d) is separable if and only if ( F (X), d 0 ) is separable. We also present a fuzzy version of the so-called Hutchinson operator, a valuable tool in fractal theory.ca_CA
dc.format.extent10 p.ca_CA
dc.language.isoengca_CA
dc.publisherElsevierca_CA
dc.relation.isPartOfFuzzy Sets and Systems, online 29 October 2018ca_CA
dc.subjectFuzzy numberca_CA
dc.subjectSkorokhod metricca_CA
dc.subjectZadeh’s extensionca_CA
dc.subjectSeparabilityca_CA
dc.subjectSemiflowca_CA
dc.subjectHutchinson operatorca_CA
dc.subjectContractionca_CA
dc.titleSome questions about Zadeh's extension on metric spacesca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.1016/j.fss.2018.10.019
dc.rights.accessRightsinfo:eu-repo/semantics/restrictedAccessca_CA
dc.relation.publisherVersionhttps://www.sciencedirect.com/science/article/pii/S0165011418308194ca_CA
dc.type.versioninfo:eu-repo/semantics/publishedVersionca_CA


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