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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

  • DOI - Digital Object Identifier

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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • 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