This paper presents a new multi-objective fuzzy mathematical model for the cellular manufacturing system (CMS) design and its solution methodology. The aim of the proposed model is to handle two important problems of CMS design called cell formation and exceptional elements simultaneously in fuzzy environment. The objective functions of the model are minimization of the cost of exceptional element elimination, minimization of the number of outer cell operations and maximization of the utilized machine capacity. The fuzziness stems from model parameters which are part demand, machine capacity and the exceptional elements' elimination costs. To illustrate the model, an example problem with fuzzy extension is adopted from literature and computational results are obtained by using the two-phased solution procedure proposed by Arıkan and Güngör [F. Arıkan, Z. Güngör, A two-phased approach for multi-objective programming problems with fuzzy coefficients, Information Science 177 (2007), 5191-5202]. The approach is performed to reach simultaneous optimal solutions for all objective functions. The model solutions are investigated by using well-known performance measures and also three problem-specific performance measures are proposed. The model is capable of expressing vagueness of all the system parameters and gives the decision-maker (DM) alternative decision plans for different grades of precision.