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In this article, we introduce the concept of (∈, ∈ ∨q δ k )-fuzzy (generalized) bi-ideal, (∈, ∈ ∨q δ k )-fuzzy (1, 2)-ideal, (∈, ∈ ∨q δ k )-fuzzy quasi-ideal in semigroups. We show that each (∈, ∈ ∨q δ k )-fuzzy quasiideal is an (∈, ∈ ∨q δ k )-fuzzy bi-ideal and each (∈, ∈ ∨q δ k )-fuzzy left (right) ideal is an (∈, ∈ ∨q δ k )-fuzzy quasi-ideal but the converses are not true in general.