  In this paper, we propose a doxastic extension $BL^+$ of Lukasiewicz logic
which is sound and complete relative to the introduced corresponding semantics.
Also, we equip our doxastic Lukasiewicz logic $BL^+$ with public announcement
and propose the logic $DL$. As an application, we model a fuzzy version of
muddy children puzzle with public announcement using $DL$. Finally, we define a
translation between $DL$ and $BL^+$, and prove the soundness and completeness
theorems for D L
