  We define a variant of the Young integration on some kinds of self-similar
sets which are called cellular self-similar sets. This variant is an analogue
of the Young integration defined on the unit interval. We give the criteria of
the variant on cellular self-similar sets, and also show that the variant is a
cyclic 1-cocycle of the algebra of complex-valued H\"older continuous functions
on the cellular self-similar sets. This suggests that the cocycle is a variant
of currents.
