Cellular manufacturing attempts to identify concurrently part families requiring similar production processes and corresponding machine cells to manufacture those part families. Some authors have solved the problem using a fuzzy clustering approach based on the Fuzzy c-Means (FCM) algorithm. In this work we discuss the drawbacks of the application of FCM to this problem and we propose a new algorithm to overcome them. The modified FCM (MFCM) algorithm groups parts and machines concurrently and unlike FCM achieves a crisp assignment directly. We have also developed a computer program in order to test the comparative performance of MFCM, FCM and two heuristics (ZODIAC and GRAFICS) on a set of problems from the literature. MFCM outperforms the other methods although it requires longer computing times.