Applying sociality-aware (SA) device-to-device (D2D) user equipment (UE)-to-network (UE-NW) relay can help to improve UEs' accessibility to the network, thus increasing the network coverage and capacity. In this context, one key issue is the design of the relay helper UE (HUE) selection procedure. However, few existing studies jointly consider the diverse impacts from various design criteria on the performance of HUE selection. In this paper, the sociality-aware D2D UE-NW relay selection (RS) issue is formulated as a constrained multi-objective binary integer linear programming (MOBILP) problem, which can be solved by the proposed SA-D2D-RS method. Specifically, the new solution jointly exploits the fuzzy analytic hierarchy process (FAHP) and the entropy weight generation method that provides both subjective and objective preferences in decision making. Simulation results validate the superiority of the proposed scheme through realistic social data traces, and demonstrate its high access ratio as well as system throughput.