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Cut Systems in Omega-sets and Reflections

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F12%3AA13014WP" target="_blank" >RIV/61988987:17610/12:A13014WP - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Cut Systems in Omega-sets and Reflections

  • Original language description

    Let $Omega$ be a complete residuated lattice. Let $Setr$ be the category of sets with similarity relations with values in $Omega$ (called $Omega$-sets), which is an analogy of the category of classical sets with relations as morphisms. A cut system in an $Omega$-set $(A,delta)$ in the category $Setr$ is a system $(C_{alpha})_{alphainOmega}$, where $C_{alpha}$ are subsets in $AtimesOmega$ with some special properties. It is well known that in the category $Setr$, there is a close relationbetween cut systems in an $Omega$-set on one hand and fuzzy sets in the same $Omega$-set, on the other hand. Moreover, there exists an extension procedure such that any system $(C_{alpha})_{alpha}$ of subsets from $AtimesOmega$ can be extended ontoa cut system $(overline{C_{alpha}})_{alpha}$. In the paper we prove that the extension procedure is, in some sense, the best possible.

  • 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

    2012

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

    Uncertainty Modeling in Knowledge Engineering and Decision Making

  • ISBN

    978-981-4417-73-0

  • ISSN

  • e-ISSN

  • Number of pages

    6

  • Pages from-to

    586-591

  • Publisher name

    World Scientific

  • Place of publication

    New Jersey-London-Singapore-Beijing

  • Event location

    Istanbul

  • Event date

    Aug 27, 2012

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article