Show simple item record

Parcijalni operatori zatvaranjai primene u teoriji uređenih skupova

dc.contributor.advisorŠešelja, Branimir
dc.contributor.otherTepavčević, Andreja
dc.contributor.otherŠešelja, Branimir
dc.contributor.otherMarković, Petar
dc.contributor.otherKurilić, Miloš
dc.contributor.otherPantović, Jovanka
dc.creatorSlivková, Anna
dc.date.accessioned2018-12-19T17:10:28Z
dc.date.available2018-12-19T17:10:28Z
dc.date.available2020-07-03T13:41:01Z
dc.date.issued2018-06-06
dc.identifier.urihttps://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija152231663786690.pdf?controlNumber=(BISIS)107201&fileName=152231663786690.pdf&id=11110&source=NaRDuS&language=srsr
dc.identifier.urihttp://nardus.mpn.gov.rs/handle/123456789/10362
dc.identifier.urihttps://www.cris.uns.ac.rs/record.jsf?recordId=107201&source=NaRDuS&language=srsr
dc.identifier.urihttps://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije152231666146757.pdf?controlNumber=(BISIS)107201&fileName=152231666146757.pdf&id=11111&source=NaRDuS&language=srsr
dc.description.abstractIn this thesis we generalize the well-known connections between closure operators, closure systems and complete lattices. We introduce a special kind of a partial closure operator, named sharp partial closure operator, and show that each sharp partial closure operator uniquely corresponds to a partial closure  system. We further introduce a special kind of a partial clo-sure system, called principal partial closure system, and then prove the representation theorem for ordered sets with respect to the introduced partial closure operators and partial closure systems. Further, motivated by a well-known connection between matroids and geometric lattices, given that the notion of matroids can be naturally generalized to partial matroids (by dening them with respect to a partial closure operator instead of with respect to a closure operator), we dene geometric poset, and show that there is a same kind of connection between partial matroids and geometric posets as there is between matroids and geometric lattices. Furthermore, we then dene semimod-ular poset, and show that it is indeed a generalization of semi-modular lattices, and that there is a same kind of connection between semimodular and geometric posets as there is between semimodular and geometric lattices. Finally, we note that the dened notions can be applied to im-plicational systems, that have many applications in real world,particularly in big data analysis.en
dc.description.abstractU ovoj tezi uopštavamo dobro poznate veze između operatora zatvaranja, sistema zatvaranja i potpunih mreža. Uvodimo posebnu vrstu parcijalnog operatora zatvaranja, koji nazivamo oštar parcijalni operator zatvaranja, i pokazujemo da svaki oštar parcijalni operator zatvaranja jedinstveno korespondira parcijalnom sistemu zatvaranja. Dalje uvodimo posebnu vrstu parcijalnog sistema zatvaranja, nazvan glavni parcijalni sistem zatvaranja, a zatim dokazujemo teoremu reprezentacije za posete u odnosu na uvedene parcijalne operatore zatvaranja i parcijalne sisteme zatvaranja. Dalje, s obzirom na dobro poznatu vezu između matroida i geometrijskih mreža, a budući da se pojam matroida može na prirodan nacin uopštiti na parcijalne  matroide (definišući ih preko parcijalnih operatora zatvaranja umesto preko operatora  zatvaranja), definišemo geometrijske uređene skupove i pokazujemo da su povezani sa parcijalnim matroidima na isti način kao što su povezani i matroidi i  geometrijske mreže. Osim toga, definišemo polumodularne uređene skupove i pokazujemo da su oni zaista uopštenje polumodularnih mreža i da ista veza postoji  između polumodularnih i geometrijskih poseta kao što imamo između polumodularnih i geometrijskih mreža. Konačno, konstatujemo da definisani pojmovi  mogu biti primenjeni na implikacione sisteme, koji imaju veliku primenu u realnom svetu, posebno u analizi velikih podataka.sr
dc.languageen
dc.publisherУниверзитет у Новом Саду, Природно-математички факултетsr
dc.rightsopenAccessen
dc.sourceУниверзитет у Новом Садуsr
dc.subjectpartial closure operatoren
dc.subjectparcijalni operator zatvaranjasr
dc.subjectpartial closure systemen
dc.subjectpartial matroiden
dc.subjectsemimodularityen
dc.subjectgeometric poseten
dc.subjectparcijalni sistem zatvaranjasr
dc.subjectparcijalni matroidsr
dc.subjectpolumodularnostsr
dc.subjectgeometrijski posetsr
dc.titlePartial closure operators and applications in ordered set theoryen
dc.title.alternativeParcijalni operatori zatvaranjai primene u teoriji uređenih skupovasr
dc.typedoctoralThesissr
dc.rights.licenseBY-NC
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/37549/IzvestajKomisije.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/37548/Disertacija.pdf


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record