As in Gilboa, Maccheroni, Marinacci, and Schmeidler \cite{GMMS}, we consider a
decision maker characterized by two binary relations: $\succsim^{\ast}$ and
$\succsim^{{\small \wedge}}$. The first binary relation is a Bewley
preference. It\ models the rankings for which the decision maker is sure. The
second binary relation is an uncertainty averse preference, as defined by
Cerreia-Vioglio, Maccheroni, Marinacci, and Montrucchio \cite{CMMM}. It models
the rankings that the decision maker expresses if he has to make a choice. We
assume that $\succsim^{{\small \wedge}}$ is a completion of $\succsim^{\ast}%
$.\ We identify axioms under which the set of probabilities and the utility
index representing $\succsim^{\ast}$ are the same as those representing
$\succsim^{{\small \wedge}}$. In this way, we show that Bewley preferences and
uncertainty averse preferences, two different approaches in modelling decision
making under Knightian uncertainty, are complementary. As a by-product, we
extend the main result of Gilboa, Maccheroni, Marinacci, and Schmeidler
\cite{GMMS}, who restrict their attention to maxmin expected utility completions.