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  • The paper introduces a simple, yet powerful axiomatization of Zadeh's notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism. In this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed; however, we also demonstrate how to add structure to the universe of discourse within our framework.
  • The paper introduces a simple, yet powerful axiomatization of Zadeh's notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism. In this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed; however, we also demonstrate how to add structure to the universe of discourse within our framework. (en)
  • V článku je zavedena jednoduchá, ale silná axiomatizace Zadehova pojmu fuzzy množiny, založená na formální fuzzy logice. Předložený formalismus je dostatečně bohatý na to, aby se mohl stát formálním základem značné části fuzzy matematiky. Jeho podstatou je elementární teorie fuzzy množin, vybudovaná jako dvousortová teorie prvního řádu nad fuzzy logikou; ta je dále zobecněna na jednoduchou teorii typů. Ukazujeme redukci této elementární teorie fuzzy množin na fuzzy výrokový počet a obecnou metodu fuzzifikace klasických matematických teorií v našem formalismu. V článku se omezujeme na ty množinové relace a operace, jež jsou definovatelné bez odkazu na strukturu universa objektů; ukazujeme však také, jak dodatečnou strukturu universa diskursu v našem formalismu definovat. (cs)
Title
  • Fuzzy Class Theory
  • Fuzzy Class Theory (en)
  • Teorie fuzzy tříd (cs)
skos:prefLabel
  • Fuzzy Class Theory
  • Fuzzy Class Theory (en)
  • Teorie fuzzy tříd (cs)
skos:notation
  • RIV/67985807:_____/05:00405252!RIV06-AV0-67985807
http://linked.open.../vavai/riv/strany
  • 34;55
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(IAA1030004), P(OC 274.001), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika
  • -
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
  • 522305
http://linked.open...ai/riv/idVysledku
  • RIV/67985807:_____/05:00405252
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • formal fuzzy logic; fuzzy set; foundations of fuzzy mathematics; LPi logic; higher-order fuzzy logic; fuzzy type theory; multi-sorted fuzzy logic (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [9B7154580855]
http://linked.open...i/riv/nazevZdroje
  • Fuzzy Sets and Systems
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
  • 154
http://linked.open...iv/tvurceVysledku
  • Běhounek, Libor
  • Cintula, Petr
http://linked.open...n/vavai/riv/zamer
issn
  • 0165-0114
number of pages
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