The concepts of I-R closed set,-set and α I N 5 -set are introduced via idealization. New decompositions of some weaker forms of continuity are obtained by using these sets.

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In this paper, we study the concept of soft sets which is introduced by Molodtsov [5] and the notion of soft continuity is introduced by Zorlutuna et al. [8]. We give the definition of (τ 1 , τ 2)-semi open soft (resp. (τ 1 , τ 2)-pre open soft, (τ 1 , τ 2)-α-open soft, (τ 1 , τ 2)-β-open soft) set via two soft topologies. We introduce mixed semi-soft (resp. mixed pre-soft, mixed α-soft, mixed β-soft) continuity between two soft topological spaces (X, τ 1 , A), (X, τ 2 , A) and a soft topological space (Y, τ, B). Also we prove that a function is mixed α-soft continuous if and only if it is both mixed pre-soft continuous and mixed semisoft continuous.