A Functional Approach to Cardinality of Finite Fuzzy Sets
The result's identifiers
Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A Functional Approach to Cardinality of Finite Fuzzy Sets
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
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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Number of pages
10
Pages from-to
234-243
Publisher name
Springer
Place of publication
Heidelberg
Event location
Montpellier, Francie
Event date
Jul 15, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000345122900024