An Approach to Determining the Optimal Cell Number of Manufacturing Cell Formation

An approach to determining the optimal cell number of manufacturing cell formation is presented. Firstly, the difference of weighting exponent, cluster center and metrics how to have an impact upon the clustering results and membership function are studied. Secondly, a method to determine the optimal m value is given. Two-order partial derivative of the objective function for FCM is calculated, and the variational weighting exponent m is obtained that can prevent the parameter from being the unique value and play an important role in the process of fuzzy clustering. Moreover, in order to avoid a single validity index can not assess correctly, partition coefficient (PC), classification entropy (CE), Fukuyama and Sugeno (FS) and Xie and Beni (XB) are considered as multi-performance indexes to evaluate the cluster validity, and then an optimal number c is chosen based on these validity measures. Finally, test exampls are given to illustrate the validity of the proposed approach