This paper proposes an effective approach for the part-machine grouping(PMG) based on the non-binary part-machine incidence matrix in which real manufacturing factors such as the operation sequences with multiple visits to the same machine and production volumes of parts are incorporated and each entry represents actual moves due to different operation sequences. The proposed approach adopts Fuzzy ART neural network to quickly create the Initial part families and their machine cells. A new performance measure to evaluate and compare the goodness of non-binary block diagonal solution is suggested. To enhance the poor solution due to category proliferation inherent to most artificial neural networks, a supplementary procedure reassigning parts and machines is added. To show effectiveness of the proposed approach to large-size PMG problems, a psuedo-replicated clustering procedure is designed. Experimental results with intermediate to large-size data sets show effectiveness of the proposed approach.