In this paper, an ABC (Always Best Connected) supported QoS (Quality of Service) unicast routing scheme is proposed. In the proposed scheme, in order to overcome difficulties on accurately measuring network link parameter values and exactly expressing user QoS requirements, the knowledge of the fuzzy mathematics and probability theory is introduced, and the range is used to describe these parameters; both of the users utility and the network providers utility are computed, and gaming analysis is taken to deal with profits of both the user and the network provider; EDPGA (Elitist Distance-based Pareto Genetic Algorithm) is used to find the specific QoS unicast path with Pareto optimum under Nash Equilibrium among all parties utilities achieved or approached. While comparing with unicast routing scheme based on Dijkstra and the game theory based fuzzy unicast QoS routing scheme, simulation results show that this proposed scheme is both feasible and effective.