This paper describes a fuzzy rule-based assembly algorithm for precision parts mating. The difficulties in divising reliable assembly strategies result from the complexity and the uncertainties of the assembly process and its environments such as imperfect knowledge of the parts being assembled as well as the limitations of the assembly devices performing the assembly. To cope with these problems, we present a new assembly algorithm using fuzzy set theory. This algorithm allows us to represent the uncertainty by using the fuzzy membership function and achieving nonlinear mapping from measured force/torque signals to corrective motions. The performance of the proposed assembly method is evaluated through a series of experiments. Experimental results show that the proposed method can be effectively used for chamferless and precision parts mating.