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This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theoryfor star bodies. An Orlicz $\varphi$-radial addition of two or more star bodiesis proposed and related dual Orlicz-Brunn-Minkowski inequality is established.Based on a linear Orlicz $\varphi$-radial addition of two star bodies, wederive a formula for the Orlicz $L_{\phi}$-dual mixed volume. Moreover, a dualOrlicz-Minkowski inequality for the Orlicz $L_{\phi}$-dual mixed volume, a dualOrlicz isoperimetric inequality for the Orlicz $L_{\phi}$-dual surface area anda dual Orlicz-Urysohn inequality for the Orlicz $L_{\phi}$-harmonic mean radiusare proved.

Dual Orlicz-Brunn-Minkowski theory: Orlicz $\varphi$-radial addition, Orlicz $L_{\phi}$-dual mixed volume and related inequalities