It has been proved that there is no optimal online scheduler for uniform parallel machines. Despite its non- optimality, EDF is an appropriate algorithm to use in such environments. However, its performance significantly drops in overloaded situations. Moreover, EDF produces a relatively large number of migrations which may prove unacceptable for use on some parallel machines. In this paper a new algorithm based on fuzzy logic for scheduling soft real-time tasks on uniform multiprocessors is presented. The performance of this algorithm is then compared with that of EDF algorithm. It is shown that our proposed approach not only demonstrates a performance close to that of EDF in non- overloaded conditions but also has supremacy over EDF in overloaded situations in many aspects. Furthermore, it imposes much less overhead on the system.