A function f : (X, μ ) → (Y, σ ) is said to be almost ( μ, σ ) - irresolute if f - 1 (V) ∈ so(X, μ ) for every regular semi-open set V of Y . In this paper the authors introduce and investigate almost ( μ , σ )- irresolute, quasi ( μ , σ )- irresolute on generalized topological space (X, μ ) into the topological space (Y, σ ) . Some characterizations and properties of such a type of functions are discussed