  This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A
radial Orlicz addition of two or more star sets is proposed and a corresponding
dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz
linear combination of two star sets, a formula for the dual Orlicz mixed volume
is derived and a corresponding dual Orlicz-Minkowski inequality proved. The
inequalities proved yield as special cases the precise duals of the conjectured
log-Brunn-Minkowski and log-Minkowski inequalities of B\"{o}r\"{o}czky, Lutwak,
Yang, and Zhang. A new addition of star sets called radial $M$-addition is also
introduced and shown to relate to the radial Orlicz addition.
