Cut systems in sets with similarity relations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F10%3AA1100WR6" target="_blank" >RIV/61988987:17610/10:A1100WR6 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
čeština
Original language name
Cut systems in sets with similarity relations
Original language description
The aim of the paper is to find some analogies between alpha-cuts systems in a classical fuzzy set theory and some nested systems of subsets defined in sets with similarity relations.We prove that any set A with similarity relation with values in complete residuated lattice can be uniquely defined by a special system of nested subsets in A x A. Using some nested systems we can also define fuzzy sets in sets with similarity relations and we show that these fuzzy sets correspond to fuzzy sets classicallydefined.
Czech name
Cut systems in sets with similarity relations
Czech description
The aim of the paper is to find some analogies between alpha-cuts systems in a classical fuzzy set theory and some nested systems of subsets defined in sets with similarity relations.We prove that any set A with similarity relation with values in complete residuated lattice can be uniquely defined by a special system of nested subsets in A x A. Using some nested systems we can also define fuzzy sets in sets with similarity relations and we show that these fuzzy sets correspond to fuzzy sets classicallydefined.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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