# Characterizations of right modular groupoids by $(\in, \in \vee q_{k})$-fuzzy ideals

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.