A Functional Approach to Cardinality of Finite Fuzzy Sets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA1501B7F" target="_blank" >RIV/61988987:17610/14:A1501B7F - 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

A Functional Approach to Cardinality of Finite Fuzzy Sets

Popis výsledku v původním jazyce

In this contribution, we present a functional approach to the cardinality of finite fuzzy sets, it means an approach based on one-to-one correspondences between fuzzy sets. In contrast to one fixed universe of discourse used for all fuzzy sets, our theory is developed within a class of fuzzy sets which universes of discourse are countable sets, and finite fuzzy sets are introduced as fuzzy sets with finite supports. We propose some basic operations with fuzzy sets as well as two constructions - fuzzy power set and fuzzy exponentiation. To express the fact that two finite fuzzy sets have approximately the same cardinality we propose the concept of graded equipollence. Using this concept we provide graded versions of several well-known statements, including the Cantor-Bernstein theorem and the Cantor theorem.

Název v anglickém jazyce

A Functional Approach to Cardinality of Finite Fuzzy Sets

Popis výsledku anglicky

In this contribution, we present a functional approach to the cardinality of finite fuzzy sets, it means an approach based on one-to-one correspondences between fuzzy sets. In contrast to one fixed universe of discourse used for all fuzzy sets, our theory is developed within a class of fuzzy sets which universes of discourse are countable sets, and finite fuzzy sets are introduced as fuzzy sets with finite supports. We propose some basic operations with fuzzy sets as well as two constructions - fuzzy power set and fuzzy exponentiation. To express the fact that two finite fuzzy sets have approximately the same cardinality we propose the concept of graded equipollence. Using this concept we provide graded versions of several well-known statements, including the Cantor-Bernstein theorem and the Cantor theorem.

Druh

D - Stať ve sborníku

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

2014

Kód důvěrnosti údajů

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

Název statě ve sborníku

Information Processing and Management of Uncertainty in Knowledge-Based Systems

ISBN

978-3-319-08854-9

ISSN

1865-0929

e-ISSN

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Počet stran výsledku

10

Strana od-do

234-243

Název nakladatele

Springer

Místo vydání

Heidelberg

Místo konání akce

Montpellier, Francie

Datum konání akce

15. 7. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000345122900024