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 $(\in ,\in \vee q)$-fuzzy left (right, two-sided) ideals, $\left( \in ,\in \vee q\right) $-fuzzy(generalized)bi-idealsand$\left( \in ,\in \vee q\right) $-fuzzy$(1,2)$-ideals\mathrm{.}Wehavealsousedtheconceptof$\left( \in ,\in \vee q_{k}\right) $-fuzzyleft(right,two-sided)ideals,$\left( \in ,\in \vee q_{k}\right) $-fuzzyquasi-ideals$\left( \in ,\in \vee q_{k}\right) $-fuzzybi-idealsand$% \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) $-fuzzyleft(right,two-sided),$\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.