. . . . . "From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto"@en . "Cintula, Petr" . . . "2"^^ . . "non-classical logics; formal fuzzy logic; formal fuzzy mathematics; high-order fuzzy logic"@en . "5" . "Fuzzy Sets and Systems" . . "Od fuzzy logiky k fuzzy matematice: metodologick\u00FD manifest"@cs . "642;646" . "[3D6EF1891739]" . "Od fuzzy logiky k fuzzy matematice: metodologick\u00FD manifest"@cs . . "The paper states the problem of fragmentation of contemporary fuzzy mathematics and the need of a unified methodology and formalism. We formulate several guidelines based on H\\'ajek's methodology in fuzzy logic, which enable us to follow closely the constructions and methods of classical mathematics recast in a fuzzy setting. As a particular solution we propose a three-layer architecture of fuzzy mathematics, with the layers of formal fuzzy logic, a foundational theory, and individual mathematical disciplines developed within its framework. The ground level of logic being sufficiently advanced, we focus on the foundational level; the theory we propose for the foundations of fuzzy mathematics can be characterized as Henkin-style higher-order fuzzy logic. Finally we give some hints on the further development of individual mathematical disciplines in the proposed framework, and proclaim it a research programme in formal fuzzy mathematics."@en . "5"^^ . "B\u011Bhounek, Libor" . . "From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto"@en . "From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto" . "The paper states the problem of fragmentation of contemporary fuzzy mathematics and the need of a unified methodology and formalism. We formulate several guidelines based on H\\'ajek's methodology in fuzzy logic, which enable us to follow closely the constructions and methods of classical mathematics recast in a fuzzy setting. As a particular solution we propose a three-layer architecture of fuzzy mathematics, with the layers of formal fuzzy logic, a foundational theory, and individual mathematical disciplines developed within its framework. The ground level of logic being sufficiently advanced, we focus on the foundational level; the theory we propose for the foundations of fuzzy mathematics can be characterized as Henkin-style higher-order fuzzy logic. Finally we give some hints on the further development of individual mathematical disciplines in the proposed framework, and proclaim it a research programme in formal fuzzy mathematics." . . "P(KJB100300502), Z(AV0Z10300504)" . "0165-0114" . . "476394" . "RIV/67985807:_____/06:00405623!RIV07-AV0-67985807" . . . "\u010Cl\u00E1nek konstatuje probl\u00E9m fragmentace soudob\u00E9 fuzzy matematiky a pot\u0159ebu jednotn\u00E9ho formalismu a metodologick\u00E9ho p\u0159\u00EDstupu. Formulujeme n\u011Bkolik obecn\u00FDch z\u00E1sad zalo\u017Een\u00FDch na H\u00E1jkov\u011B p\u0159\u00EDstupu k fuzzy logice, kter\u00E9 umo\u017En\u00ED pou\u017E\u00EDt zn\u00E1m\u00E9 klasick\u00E9 konstrukce a metody ve fuzzy matematice. Konkr\u00E9tn\u011B navrhneme troj-\u00FArov\u0148ovou architekturu fuzzy matematiky (logika, z\u00E1kladn\u00ED teorie a v n\u00ED budovan\u00E9 jednotliv\u00E9 matematick\u00E9 discipl\u00EDny). Jeliko\u017E vrstva logick\u00E1 je ji\u017E dostate\u010Dn\u011B propracov\u00E1na, zam\u011B\u0159\u00EDme se na vytvo\u0159en\u00ED z\u00E1kladn\u00ED teorie, k tomuto \u00FA\u010Delu navrhneme Henkinovskou fuzzy logiku vy\u0161\u0161\u00EDho \u0159\u00E1du. Na z\u00E1v\u011Br jsou nazna\u010Deny mo\u017Enosti dal\u0161\u00EDho v\u00FDvoje jednotliv\u00FDch discipl\u00EDn fuzzy matematiky v navr\u017Een\u00E9m formalismu a vyhl\u00E1\u0161en v\u00FDzkumn\u00FD program form\u00E1ln\u00ED fuzzy matematiky."@cs . . "RIV/67985807:_____/06:00405623" . . "From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto" . "2"^^ . "NL - Nizozemsko" . "157" . . .