A new concurrent cell formation method for solving a Cell Formation (CF) problem in a Cellular Manufacturing System (CMS) is developed and proposed in this research. To solve such problem, conventionally a facility planner needs to classify parts into families and group machines into cells, respectively. However, existing methods for solving the CF problem are difficult and complicated. Moreover, efficient solutions of some of those methods are not guarantee. So, the efficient method based on two important performance measures, called Exceptional Elements (EE) and the Void Elements (VE) of a perfect grouping, are developed. Preemptive Fuzzy Goal Programming (P-FGP) is applied to these two performance measures for finding the efficient solution. The problems of grouping part family and machine cells can be simultaneously easily solved. Moreover, machines and parts grouping can also be adjustable to find preferred solutions by use of P-FGP. The numerical examples existed in the literatures are shown to demonstrate the efficiency of the proposed model over the conventional method.