A t-norm embedding theorem for fuzzy sets

2012
journal article
article
dc.abstract.enIt 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.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowejpl
dc.contributor.authorBielawski, Jakubpl
dc.contributor.authorTabor, Jacek - 132362 pl
dc.date.accessioned2014-07-24T11:06:07Z
dc.date.available2014-07-24T11:06:07Z
dc.date.issued2012pl
dc.description.physical33-53pl
dc.description.volume209pl
dc.identifier.doi10.1016/j.fss.2012.06.004pl
dc.identifier.eissn1872-6801pl
dc.identifier.issn0165-0114pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/302
dc.languageengpl
dc.language.containerengpl
dc.rights.licencebez licencji
dc.subject.enAlgebraic operationspl
dc.subject.enExtension principlepl
dc.subject.enFuzzy convex setspl
dc.subject.enEmbedding theorempl
dc.subject.ent-Normspl
dc.subject.enMathematical morphologypl
dc.subtypeArticlepl
dc.titleA t-norm embedding theorem for fuzzy setspl
dc.title.journalFuzzy Sets and Systemspl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
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.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.authorpl
Bielawski, Jakub
dc.contributor.authorpl
Tabor, Jacek - 132362
dc.date.accessioned
2014-07-24T11:06:07Z
dc.date.available
2014-07-24T11:06:07Z
dc.date.issuedpl
2012
dc.description.physicalpl
33-53
dc.description.volumepl
209
dc.identifier.doipl
10.1016/j.fss.2012.06.004
dc.identifier.eissnpl
1872-6801
dc.identifier.issnpl
0165-0114
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/302
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights.licence
bez licencji
dc.subject.enpl
Algebraic operations
dc.subject.enpl
Extension principle
dc.subject.enpl
Fuzzy convex sets
dc.subject.enpl
Embedding theorem
dc.subject.enpl
t-Norms
dc.subject.enpl
Mathematical morphology
dc.subtypepl
Article
dc.titlepl
A t-norm embedding theorem for fuzzy sets
dc.title.journalpl
Fuzzy Sets and Systems
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

* The migration of download and view statistics prior to the date of April 8, 2024 is in progress.

Views
19
Views per month
Views per city
Chandler
5
Philadelphia
3
Ashburn
2
Wroclaw
2
Dublin
1
Krakow
1

No access

No Thumbnail Available