In traditional cell-formation problems, it is assumed that each part is developed on a single machine. However, in many realistic situations, the suitability of alternative machines for developing the same part feature is frequently vague. Therefore, the fuzzy relation is ideally suited to represent this vague and uncertain cell-formation problem. Furthermore, part-machine family formation problems are usually NP-complete. In this study, a genetic algorithm (GA) is used to deal with the problem. The aim of this study is to design a GA-based algorithm to solve the part-machine family formation problem in a fuzzy environment. The results of computational tests presented are very promising.