Od fuzzy logiky k fuzzy matematice: metodologický manifest

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F06%3A00405623" target="_blank" >RIV/67985807:_____/06:00405623 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/KJB100300502" target="_blank" >KJB100300502: Formální teorie matematických struktur s vágností</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2006

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

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Svazek periodika

157

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

5

Strana od-do

642-646

Kód UT WoS článku

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EID výsledku v databázi Scopus

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