In this paper, we propose a novel three-phase fuzzy approach to optimize dispatching and rebalancing for Ride-sharing Autonomous Mobility-on-Demand (RAMoD) systems, consisting of self-driving vehicles, which provide on-demand transportation service, and allowing several customers to share the same vehicle at the same time. We first introduce a new multi-objective possibilistic linear programming (MOPLP) model for the problem of dispatching and rebalancing in RAMoD systems considering the imprecise nature of the customer requests as well as two conflicting objectives simultaneously, namely, improving customer satisfaction and minimizing transportation costs. Then, after transforming this possibilistic programming model into an equivalent crisp multi-objective linear programming (MOLP) model, the Goal Programming (GP) approach is used to provide an efficient compromise solution. Finally, computational results show the practicality and tractability of the proposed model as well as the solution methodology.