MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA15015U3" target="_blank" >RIV/61988987:17610/14:A15015U3 - 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
MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers
Original language description
The existing arithmetics of fuzzy numbers, usually stemming from the ?-cut arithmetic, do not preserve some of the important properties of the standard arithmetics of real numbers. We present a novel framework for arithmetics of extensional fuzzy numbersthat more or less preserves all the important (algebraic) properties of the arithmetic of real numbers and thus seems to be an important seed for further investigations on this topic. The investigation leads to novel algebraic structures - MI-algebras (MI-monoids, MI-groups, MI-fields) - that abstract the discussed properties. The main idea of these structures is based on a set of ?pseudoidentities? that complements the only commonly used identity element in a monoid/group structure.
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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