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A t-norm embedding theorem for fuzzy sets
Algebraic operations
Extension principle
Fuzzy convex sets
Embedding theorem
t-Norms
Mathematical morphology
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.
cris.lastimport.scopus | 2024-04-07T16:47:11Z | |
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.affiliation | Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej | pl |
dc.contributor.author | Bielawski, Jakub | pl |
dc.contributor.author | Tabor, Jacek - 132362 | pl |
dc.date.accessioned | 2014-07-24T11:06:07Z | |
dc.date.available | 2014-07-24T11:06:07Z | |
dc.date.issued | 2012 | pl |
dc.description.physical | 33-53 | pl |
dc.description.volume | 209 | pl |
dc.identifier.doi | 10.1016/j.fss.2012.06.004 | pl |
dc.identifier.eissn | 1872-6801 | pl |
dc.identifier.issn | 0165-0114 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/302 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights.licence | bez licencji | |
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.subtype | Article | pl |
dc.title | A t-norm embedding theorem for fuzzy sets | pl |
dc.title.journal | Fuzzy Sets and Systems | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |