\begin{tikzpicture}
\umlemptyclass{A1}
\umlassoc[arg=x, mult=1, pos=0.6, angle1=-90, angle2=-140, loopsize=2cm]{A1}{A1}
\umlassoc[arg=y, mult=1..*, pos=0.6, angle1=-90, angle2=-140, loopsize=4cm]{A1}{A1}
\umlassoc[arg=z, mult=0..*, pos=0.8, angle1=-90, angle2=0, loopsize=2cm]{A1}{A1}
\end{tikzpicture}