This paper presents an integrated approach, of a multi-criteria decision-making framework and fuzzy multi-objective programming to optimize dispatching and rebalancing for Ride-sharing Autonomous Mobility-on-Demand (RAMoD) systems, whereby, a fleet of self-driving electric vehicles are coordinated to service on-demand travel requests and eventually allowing multiple passengers to share rides. Specifically, the fuzzy analytical hierarchy process and the Fuzzy technique for order of preference by similarity to ideal solution are first integrated in order to analyze customer preferences, prioritize their attitudes toward autonomous vehicles, and then to rank fleet vehicles according to these prioritizations. Next, leveraging the ranks of vehicles, we introduce a new Multi-Objective Possibilistic Linear Programming (MOPLP) model, considering realistic constraints and handling the uncertain nature of some critical data affecting RAMoD systems. Three conflicting goals are considered simultaneously which are (i) to minimize the lost customer requests, (ii) to minimize the total transportation cost and (iii) to improve customer satisfaction. This MOPLP model is converted to an equivalent crisp MOLP through applying appropriate strategies and the goal programming method is called to solve this MOLP and find an efficient compromise solution. Finally, the applicability and efficiency of the proposed approach are presented through an illustrative example. Collectively, this work provides a unified framework for controlling and analyzing RAMoD systems, which includes a wide range of modeling options (e.g., the inclusion of the uncertain future demand), and provides the first correlation between the dispatching and rebalancing decisions, and the process of analyzing customer preferences toward autonomous vehicles.