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Statements

Subject Item
n2:RIV%2F61988987%3A17610%2F14%3AA15014WR%21RIV15-MSM-17610___
rdf:type
n15:Vysledek skos:Concept
dcterms:description
It is well known that any fuzzy set $X$ in a classical set $A$ with values in a complete (residuated) lattice $\Omega$ can be identified with a system of $\alpha$-cuts $X_{\alpha}$, $\alpha\in\Omega$. In this paper we are interested in relationships between sets of fuzzy sets and sets of f-cuts in an $\Omega$-set $(A,\delta)$ in corresponding categories $\Set$ and $\Setr$, endowed with binary operations extended either from binary operations in the lattice $\Omega$, or from binary operations defined on a set $A$ by the generalized Zadeh's extension principle. We prove that the final binary structures are (under some conditions) isomorphic. It is well known that any fuzzy set $X$ in a classical set $A$ with values in a complete (residuated) lattice $\Omega$ can be identified with a system of $\alpha$-cuts $X_{\alpha}$, $\alpha\in\Omega$. In this paper we are interested in relationships between sets of fuzzy sets and sets of f-cuts in an $\Omega$-set $(A,\delta)$ in corresponding categories $\Set$ and $\Setr$, endowed with binary operations extended either from binary operations in the lattice $\Omega$, or from binary operations defined on a set $A$ by the generalized Zadeh's extension principle. We prove that the final binary structures are (under some conditions) isomorphic.
dcterms:title
Isomorphisms and functors of fuzzy sets and cut systems Isomorphisms and functors of fuzzy sets and cut systems
skos:prefLabel
Isomorphisms and functors of fuzzy sets and cut systems Isomorphisms and functors of fuzzy sets and cut systems
skos:notation
RIV/61988987:17610/14:A15014WR!RIV15-MSM-17610___
n3:aktivita
n12:P
n3:aktivity
P(ED1.1.00/02.0070)
n3:cisloPeriodika
July 2014
n3:dodaniDat
n8:2015
n3:domaciTvurceVysledku
n13:3240002
n3:druhVysledku
n10:J
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
22963
n3:idVysledku
RIV/61988987:17610/14:A15014WR
n3:jazykVysledku
n16:eng
n3:klicovaSlova
residuated lattice; set with similarity relation; fuzzy set; cut system
n3:klicoveSlovo
n11:fuzzy%20set n11:set%20with%20similarity%20relation n11:cut%20system n11:residuated%20lattice
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[934182247704]
n3:nazevZdroje
SOFT COMPUT
n3:obor
n9:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n17:ED1.1.00%2F02.0070
n3:rokUplatneniVysledku
n8:2014
n3:svazekPeriodika
18
n3:tvurceVysledku
Močkoř, Jiří
n3:wos
000337282700001
s:issn
1432-7643
s:numberOfPages
9
n6:organizacniJednotka
17610