About: Cut Systems in Omega-sets and Reflections

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let $\Omega$ be a complete residuated lattice. Let $\Setr$ be the category of sets with similarity relations with values in $\Omega$ (called $\Omega$-sets), which is an analogy of the category of classical sets with relations as morphisms. A cut system in an $\Omega$-set $(A,\delta)$ in the category $\Setr$ is a system $(C_{\alpha})_{\alpha\in\Omega}$, where $C_{\alpha}$ are subsets in $A\times\Omega$ with some special properties. It is well known that in the category $\Setr$, there is a close relation between cut systems in an $\Omega$-set on one hand and fuzzy sets in the same $\Omega$-set, on the other hand. Moreover, there exists an extension procedure such that any system $(C_{\alpha})_{\alpha}$ of subsets from $A\times\Omega$ can be extended onto a cut system $(\overline{C_{\alpha}})_{\alpha}$. In the paper we prove that the extension procedure is, in some sense, the best possible. Let $\Omega$ be a complete residuated lattice. Let $\Setr$ be the category of sets with similarity relations with values in $\Omega$ (called $\Omega$-sets), which is an analogy of the category of classical sets with relations as morphisms. A cut system in an $\Omega$-set $(A,\delta)$ in the category $\Setr$ is a system $(C_{\alpha})_{\alpha\in\Omega}$, where $C_{\alpha}$ are subsets in $A\times\Omega$ with some special properties. It is well known that in the category $\Setr$, there is a close relation between cut systems in an $\Omega$-set on one hand and fuzzy sets in the same $\Omega$-set, on the other hand. Moreover, there exists an extension procedure such that any system $(C_{\alpha})_{\alpha}$ of subsets from $A\times\Omega$ can be extended onto a cut system $(\overline{C_{\alpha}})_{\alpha}$. In the paper we prove that the extension procedure is, in some sense, the best possible. (en)
Title	Cut Systems in Omega-sets and Reflections Cut Systems in Omega-sets and Reflections (en)
skos:prefLabel	Cut Systems in Omega-sets and Reflections Cut Systems in Omega-sets and Reflections (en)
skos:notation	RIV/61988987:17610/12:A13014WP!RIV13-MSM-17610___
http://linked.open...avai/predkladatel	Centrum excelence IT4Innovations, divize OU, Ústav pro výzkum a aplikace fuzzy modelování
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0070)
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Močkoř, Jiří
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ostravská univerzita v Ostravě / Centrum excelence IT4Innovations, divize OU, Ústav pro výzkum a aplikace fuzzy modelování
http://linked.open...dnocenehoVysledku	129309
http://linked.open...ai/riv/idVysledku	RIV/61988987:17610/12:A13014WP
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	residuated lattice; set with similarity relation; fuzzy set; cut system; reflective category (en)
http://linked.open.../riv/klicoveSlovo	fuzzy set cut system reflective category set with similarity relation residuated lattice
http://linked.open...ontrolniKodProRIV	[72623C4642E9]
http://linked.open...v/mistoKonaniAkce	Istanbul
http://linked.open...i/riv/mistoVydani	New Jersey-London-Singapore-Beijing
http://linked.open...i/riv/nazevZdroje	Uncertainty Modeling in Knowledge Engineering and Decision Making
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	IT4Innovations Centre of Excellence
http://linked.open...UplatneniVysledku	2012
http://linked.open...iv/tvurceVysledku	Močkoř, Jiří
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2012-08-27 (xsd:date)
number of pages	6 (xsd:int)
http://purl.org/ne...btex#hasPublisher	World Scientific
https://schema.org/isbn	978-981-4417-73-0
http://localhost/t...ganizacniJednotka	17610
is http://linked.open...avai/riv/vysledek of	Cut Systems in Omega-sets and Reflections

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