Decompositions of new classes of functions

In this paper, αIN5-sets, SIN5 -sets, PIN5-sets, βIN5-sets are introduced via idealization. Using these sets, new classes of generalizations of non-continuous functions are obtained and some of their properties are given. Also, decompositions of strongly α − I-continuity, strongly α-pre-I-irresoluteness, I-irresoluteness and strongly semi-β − I-irresoluteness are established.