All

What are you looking for?

All
Projects
Results
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

On EMV-algebras

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597254" target="_blank" >RIV/61989592:15310/19:73597254 - isvavai.cz</a>

  • Result on the web

    <a href="https://www.sciencedirect.com/science/article/pii/S0165011419301447" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011419301447</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.fss.2019.02.013" target="_blank" >10.1016/j.fss.2019.02.013</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On EMV-algebras

  • Original language description

    The paper deals with an algebraic extension of MV-algebras based on the definition of generalized Boolean algebras. We introduce a new class of structures, not necessarily with a top element, which are called EMV-algebras, in a way that every EMV-algebra contains an MV-algebra. First, we present basic properties of EMV-algebras. We give some examples, introduce and investigate congruence relations, ideals and filters on these algebras. We establish a basic representation result saying that each EMV-algebra can be embedded into an EMV-algebra with top element and we characterize EMV-algebras either as structures which are termwise equivalent to MV-algebras or as maximal ideals of EMV-algebras with top element. We study the lattice of ideals of an EMV-algebra and prove that every EMV-algebra has at least one maximal ideal. We define an EMV-clan of fuzzy sets as a special EMV-algebra where all operations are defined by points. We show that any semisimple EMV-algebra is isomorphic to an EMV-clan of fuzzy functions on a set. The set of EMV-algebras is neither a variety nor a quasivariety, but rather a special class of EMV-algebras which we call a q-variety of EMV-algebras. We present an equational base for each proper q-subvariety of the q-variety of EMV-algebras. We establish categorical equivalencies among the category of proper EMV-algebras, the category of MV-algebras with a fixed special maximal ideal, and a special category of Abelian unital l-groups.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

    <a href="/en/project/GA15-15286S" target="_blank" >GA15-15286S: Algebraic, many-valued and quantum structures for uncertainty modelling</a><br>

  • Continuities

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

Others

  • Publication year

    2019

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    FUZZY SETS AND SYSTEMS

  • ISSN

    0165-0114

  • e-ISSN

  • Volume of the periodical

    373

  • Issue of the periodical within the volume

    OCT

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    33

  • Pages from-to

    116-148

  • UT code for WoS article

    000482585800007

  • EID of the result in the Scopus database

    2-s2.0-85061805905