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  • 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. (en)
Title
  • Isomorphisms and functors of fuzzy sets and cut systems
  • Isomorphisms and functors of fuzzy sets and cut systems (en)
skos:prefLabel
  • Isomorphisms and functors of fuzzy sets and cut systems
  • Isomorphisms and functors of fuzzy sets and cut systems (en)
skos:notation
  • RIV/61988987:17610/14:A15014WR!RIV15-MSM-17610___
http://linked.open...avai/riv/aktivita
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  • P(ED1.1.00/02.0070)
http://linked.open...iv/cisloPeriodika
  • July 2014
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  • 22963
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  • RIV/61988987:17610/14:A15014WR
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  • residuated lattice; set with similarity relation; fuzzy set; cut system (en)
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  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [934182247704]
http://linked.open...i/riv/nazevZdroje
  • SOFT COMPUT
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  • 18
http://linked.open...iv/tvurceVysledku
  • Močkoř, Jiří
http://linked.open...ain/vavai/riv/wos
  • 000337282700001
issn
  • 1432-7643
number of pages
http://localhost/t...ganizacniJednotka
  • 17610
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