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Subject Item
n2:RIV%2F67985807%3A_____%2F05%3A00405252%21RIV06-AV0-67985807
rdf:type
n13:Vysledek skos:Concept
dcterms:description
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. 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. 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.
dcterms:title
Fuzzy Class Theory Teorie fuzzy tříd Fuzzy Class Theory
skos:prefLabel
Fuzzy Class Theory Teorie fuzzy tříd Fuzzy Class Theory
skos:notation
RIV/67985807:_____/05:00405252!RIV06-AV0-67985807
n4:strany
34;55
n4:aktivita
n12:Z n12:P
n4:aktivity
P(IAA1030004), P(OC 274.001), Z(AV0Z10300504)
n4:cisloPeriodika
-
n4:dodaniDat
n11:2006
n4:domaciTvurceVysledku
n8:1134426 n8:1922688
n4:druhVysledku
n16:J
n4:duvernostUdaju
n15:S
n4:entitaPredkladatele
n14:predkladatel
n4:idSjednocenehoVysledku
522305
n4:idVysledku
RIV/67985807:_____/05:00405252
n4:jazykVysledku
n18:eng
n4:klicovaSlova
formal fuzzy logic; fuzzy set; foundations of fuzzy mathematics; LPi logic; higher-order fuzzy logic; fuzzy type theory; multi-sorted fuzzy logic
n4:klicoveSlovo
n7:fuzzy%20type%20theory n7:LPi%20logic n7:formal%20fuzzy%20logic n7:foundations%20of%20fuzzy%20mathematics n7:higher-order%20fuzzy%20logic n7:fuzzy%20set n7:multi-sorted%20fuzzy%20logic
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[9B7154580855]
n4:nazevZdroje
Fuzzy Sets and Systems
n4:obor
n10:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
2
n4:projekt
n9:OC%20274.001 n9:IAA1030004
n4:rokUplatneniVysledku
n11:2005
n4:svazekPeriodika
154
n4:tvurceVysledku
Cintula, Petr Běhounek, Libor
n4:zamer
n17:AV0Z10300504
s:issn
0165-0114
s:numberOfPages
22