About: Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Up to our best knowledge, distinct so far existing arithmetics of fuzzy numbers, usually stemming from the Zadeh's extensional principle, do not preserve some of the important properties of the standard arithmetics of classical (real) numbers. Obviously, although we cannot expect that a generalization of standard arithmetic will preserve precisely all its properties however, at least the most important ones should be preserved. We present a novel framework of arithmetics of extensional fuzzy numbers that preserves more or less 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 suggested approach arithmetics of extensional fuzzy numbers is demonstrated on many examples and besides the algebraic properties, it is also shown that it carries some desirable practical properties. Up to our best knowledge, distinct so far existing arithmetics of fuzzy numbers, usually stemming from the Zadeh's extensional principle, do not preserve some of the important properties of the standard arithmetics of classical (real) numbers. Obviously, although we cannot expect that a generalization of standard arithmetic will preserve precisely all its properties however, at least the most important ones should be preserved. We present a novel framework of arithmetics of extensional fuzzy numbers that preserves more or less 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 suggested approach arithmetics of extensional fuzzy numbers is demonstrated on many examples and besides the algebraic properties, it is also shown that it carries some desirable practical properties. (en)
Title	Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction (en)
skos:prefLabel	Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction (en)
skos:notation	RIV/61988987:17610/12:A13014MH!RIV13-MSM-17610___
http://linked.open...avai/predkladatel	Centrum excelence IT4Innovations, divize OU, Ústav pro výzkum a aplikace fuzzy modelování
http://linked.open...avai/riv/aktivita	O
http://linked.open...avai/riv/aktivity	O
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Štěpnička, Martin Holčapek, Michal
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ostravská univerzita v Ostravě / Centrum excelence IT4Innovations, divize OU, Ústav pro výzkum a aplikace fuzzy modelování
http://linked.open...dnocenehoVysledku	123654
http://linked.open...ai/riv/idVysledku	RIV/61988987:17610/12:A13014MH
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	fuzzy numbers; arithmetic; field; group; MI-group; Mi-field (en)
http://linked.open.../riv/klicoveSlovo	arithmetic fuzzy numbers MI-group Mi-field field group
http://linked.open...ontrolniKodProRIV	[D1B0B404C281]
http://linked.open...v/mistoKonaniAkce	Brisbane
http://linked.open...i/riv/nazevZdroje	Proc. of FUZZ-IEEE 2012
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...iv/tvurceVysledku	Holčapek, Michal Štěpnička, Martin
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000309188200211
http://linked.open.../riv/zahajeniAkce	2012-01-01 (xsd:date)
number of pages	8 (xsd:int)
http://purl.org/ne...btex#hasPublisher	IEEE
https://schema.org/isbn	978-1-4673-1506-7
http://localhost/t...ganizacniJednotka	17610
is http://linked.open...avai/riv/vysledek of	Arithmetics of Extensional Fuzzy Numbers -- Part I: Introduction

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