Cellular manufacturing consists in decomposing the system into a number of manufacturing cells, each one dedicated to the processing of a family of similar part types. Most neural networks approaches proposed to solve the part-machine grouping problem are based on the competitive learning paradigm or some of its variants (ART, SOFM). In this paper we use a cell formation approach that has two steps: either machines are grouped first and then parts are assigned or viceversa. The first step is modelled as a grouping problem using weighted similarity coefficients that are an extension of the commonly used Jaccard similarity coefficients. The resulting quadratic programming problem is solved using a Hopfield-Tank neural network. The second step is a straightforward LP assignment problem. The performance of the proposed approach is benchmarked against Simulated Annealing and Tabu Search-based approaches, a Maximum Spanning Tree heuristic and a Self-Organizing Neural Network.