In this paper, we introduce the notion of (Î,Î Vqk)- fuzzy subnear-ring which is a generalization of (Î,Î Vq)-fuzzy subnear-ring. We have given examples which are (Î,Î Vqk)-fuzzy ideals but they are not (Î,Î Vq)-fuzzy ideals. We have also introduced the notions of (Î,Î Vqk)-fuzzy quasi-ideals and (Î,Î Vqk)-fuzzy bi-ideals of near-ring. We have characterized (Î,Î Vqk)-fuzzy quasi-ideals and (Î,Î Vqk)-fuzzy bi-ideals of near-rings.