Advertisement

Vague Groups

  • Jordi Recasens
Chapter
  • 371 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 260)

Abstract

In the crisp case, if (G, ∘ ) is a set with an operation ∘ : G ×GG and ~ is an equivalence relation on G, then ∘ is compatible with ~ if and only if

$$ a \sim a' \ {\rm and} \ b \sim b' \ {\rm implies} \ a \circ b \sim a' \circ b'. $$
In this case, an operation \(\tilde{\circ}\) can be defined on \(\overline{G}=G/\sim\) by
$$ \overline{a} \tilde{\circ} \overline{b}=\overline{a \circ b} $$
where \(\overline{a}\) and \(\overline{b}\) are the equivalence classes of a and b with respect to ~.

Demirci generalized this idea to the fuzzy framework by introducing the concept of vague algebra, which basically consists of fuzzy operations compatible with given indistinguishability operators [37].

Keywords

Normal Subgroup Fuzzy Number Indistinguishability Operator Identity Element Quotient Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jordi Recasens

    There are no affiliations available

    Personalised recommendations