  Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$,
with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd,
then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq
t(T) \leq 2t(S)+1$. On the other hand, if $t(T)$ is even, there exists such $T$
if and only if $S$ is almost symmetric and different from $\mathbb{N}$; in this
case the type of $S$ is the number of even pseudo-Frobenius numbers of $T$.
Moreover, we construct these families of semigroups using the numerical
duplication with respect to a relative ideal.
