Isomorphisms and functors of fuzzy sets and cut systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA15014WR" target="_blank" >RIV/61988987:17610/14:A15014WR - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Isomorphisms and functors of fuzzy sets and cut systems
Original language 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 $X_{alpha}$, $alphainOmega$. 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 ona set $A$ by the generalized Zadeh's extension principle. We prove that the final binary structures are (under some conditions) isomorphic.
Czech name
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Czech description
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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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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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