We introduce the notion of interval-valued fuzzy bi-ideals
with respect to $t$-norm $T^*$ and $s$-norm $S^*$ and investigate
some of the properties. The homomorphism image and inverse image
are investigated. In particular, by the congruence relations on
semigroups, new interval valued intuitionistic $(S^*, T^*)$-fuzzy
bi-ideals are constructed.