On approximations of Zadeh's extension principle

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F16%3AA160193C" target="_blank" >RIV/61988987:17610/16:A160193C - 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

On approximations of Zadeh's extension principle

Popis výsledku v původním jazyce

In this paper we provide several results concerning the approximation of Zadeh's extension of a given function. We provide several simple observations due to which we provide a general procedure allowing to approximate Zadeh's extension of any continuousmap. Among other things, we demonstrated that the technique of F-transform can also be used to approximate this extension. Further, we studied how the choice of the metric on the space of fuzzy sets (resp. fuzzy numbers) can affect the quality of the approximation, and we clarified that, in comparison to recent habits, the choice of the levelwise metric need not be the most appropriate one, and that the approximation process could be simplified. Our results are general in the sense that we mostly require nothing but the continuity of the original map.

Název v anglickém jazyce

On approximations of Zadeh's extension principle

Popis výsledku anglicky

In this paper we provide several results concerning the approximation of Zadeh's extension of a given function. We provide several simple observations due to which we provide a general procedure allowing to approximate Zadeh's extension of any continuousmap. Among other things, we demonstrated that the technique of F-transform can also be used to approximate this extension. Further, we studied how the choice of the metric on the space of fuzzy sets (resp. fuzzy numbers) can affect the quality of the approximation, and we clarified that, in comparison to recent habits, the choice of the levelwise metric need not be the most appropriate one, and that the approximation process could be simplified. Our results are general in the sense that we mostly require nothing but the continuity of the original map.

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/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

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Svazek periodika

283

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

26-39

Kód UT WoS článku

000365375000002

EID výsledku v databázi Scopus

2-s2.0-84947489973