Vague Groups

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


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].


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.


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© Springer-Verlag Berlin Heidelberg 2010

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  • Jordi Recasens

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