About: MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers     Goto   Sponge   NotDistinct   Permalink

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  • 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 numbers that 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.
  • 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 numbers that 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. (en)
Title
  • MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers
  • MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers (en)
skos:prefLabel
  • MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers
  • MI-algebras: a new framework for arithmetics of (extensional) fuzzy numbers (en)
skos:notation
  • RIV/61988987:17610/14:A15015U3!RIV15-MSM-17610___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(ED1.1.00/02.0070)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 29124
http://linked.open...ai/riv/idVysledku
  • RIV/61988987:17610/14:A15015U3
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Fuzzy numbers; Arithmetics of fuzzy numbers; MI-monoid; MI-group; MI-field (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [BDF79BF3D5AC]
http://linked.open...i/riv/nazevZdroje
  • FUZZY SET SYST
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 257
http://linked.open...iv/tvurceVysledku
  • Holčapek, Michal
  • Štěpnička, Martin
http://linked.open...ain/vavai/riv/wos
  • 000344424600007
issn
  • 0165-0114
number of pages
http://localhost/t...ganizacniJednotka
  • 17610
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