"Fuzzy Class Theory"@en . "2"^^ . "Fuzzy Class Theory" . "0165-0114" . . "2"^^ . "Teorie fuzzy t\u0159\u00EDd"@cs . "formal fuzzy logic; fuzzy set; foundations of fuzzy mathematics; LPi logic; higher-order fuzzy logic; fuzzy type theory; multi-sorted fuzzy logic"@en . . . . "RIV/67985807:_____/05:00405252!RIV06-AV0-67985807" . . "Cintula, Petr" . "-" . "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 \u010Dl\u00E1nku je zavedena jednoduch\u00E1, ale siln\u00E1 axiomatizace Zadehova pojmu fuzzy mno\u017Einy, zalo\u017Een\u00E1 na form\u00E1ln\u00ED fuzzy logice. P\u0159edlo\u017Een\u00FD formalismus je dostate\u010Dn\u011B bohat\u00FD na to, aby se mohl st\u00E1t form\u00E1ln\u00EDm z\u00E1kladem zna\u010Dn\u00E9 \u010D\u00E1sti fuzzy matematiky. Jeho podstatou je element\u00E1rn\u00ED teorie fuzzy mno\u017Ein, vybudovan\u00E1 jako dvousortov\u00E1 teorie prvn\u00EDho \u0159\u00E1du nad fuzzy logikou; ta je d\u00E1le zobecn\u011Bna na jednoduchou teorii typ\u016F. Ukazujeme redukci t\u00E9to element\u00E1rn\u00ED teorie fuzzy mno\u017Ein na fuzzy v\u00FDrokov\u00FD po\u010Det a obecnou metodu fuzzifikace klasick\u00FDch matematick\u00FDch teori\u00ED v na\u0161em formalismu. V \u010Dl\u00E1nku se omezujeme na ty mno\u017Einov\u00E9 relace a operace, je\u017E jsou definovateln\u00E9 bez odkazu na strukturu universa objekt\u016F; ukazujeme v\u0161ak tak\u00E9, jak dodate\u010Dnou strukturu universa diskursu v na\u0161em formalismu definovat."@cs . . "522305" . "[9B7154580855]" . . "P(IAA1030004), P(OC 274.001), Z(AV0Z10300504)" . . . "B\u011Bhounek, Libor" . . . . "Teorie fuzzy t\u0159\u00EDd"@cs . . . "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." . "Fuzzy Sets and Systems" . "RIV/67985807:_____/05:00405252" . "Fuzzy Class Theory"@en . "34;55" . "22"^^ . . . "154" . "NL - Nizozemsko" . "Fuzzy Class Theory" . . . . . .