  We show that the class of all aggregation functions on $[0,1]$ can be
generated as a composition of infinitary sup-operation $\bigvee$ acting on sets
with cardinality not exceeding $\mathfrak{c}$, $b$-medians $\mathsf{Med}_b$,
$b\in[0,1[$, and unary aggregation functions $1_{]0,1]}$ and $1_{[a,1]}$, $a\in
]0,1]$. Moreover, we show that we cannot relax the cardinality of argument sets
for suprema to be countable, thus showing a kind of minimality of the
introduced generating set. As a by product, generating sets for fuzzy
connectives, such as fuzzy unions, fuzzy intersections and fuzzy implications
are obtained, too.
