  In this paper, we have introduced the concept of $\left( \in ,\in \vee
q\right) $-fuzzy ideals in a right modular groupoid. We have discussed several
important features of a completely regular right modular groupoid by using the
$\left( \in ,\in \vee q\right) $-fuzzy left (right, two-sided) ideals, $\left(
\in ,\in \vee q\right) $-fuzzy (generalized) bi-ideals and $\left( \in ,\in
\vee q\right) $-fuzzy $(1,2)$-ideals. We have also used the concept of $\left(
\in ,\in \vee q_{k}\right) $-fuzzy left (right, two-sided) ideals, $\left( \in
,\in \vee q_{k}\right) $-fuzzy quasi-ideals $\left( \in ,\in \vee q_{k}\right)
$-fuzzy bi-ideals and $% \left( \in ,\in \vee q_{k}\right) $-fuzzy interior
ideals in completely regular right modular groupoid and proved that the $\left(
\in ,\in \vee q_{k}\right) $-fuzzy left (right, two-sided), $\left( \in ,\in
\vee q_{k}\right) $-fuzzy (generalized) bi-ideals, and $\left( \in ,\in \vee
q_{k}\right) $-fuzzy interior ideals coincide in a completely regular right
modular groupoid.
