In the fierce global competition, cost, quality and customer satisfaction appears to be utmost significant. Flexible manufacturing systems (FMS) have a great potential in manufacturing both cost effective and customer based products. These systems bring us flexibility, but this flexibility accompanies cost and time. Thus, selecting suitable FMS necessitates excessive attention. The problem of FMS selection and evaluation becomes more difficult when facing multi FMSs selection problem. In this paper, we propose an integrated approach to find a suitable combination of FMSs in a multi FMSs decision making problem. Each FMS has several alternatives. Therefore, there are many possible solutions for this problem. We first identify the objective and subjective attributes. Second, Grey system theory is applied to deal with the incomplete and uncertain information of subjective data, and the objective data are extracted from simulation modelling. A goal-programming model is then utilized to formulate the problem and to assign priorities to the objectives. Finally, a genetic algorithm (FA) based model is applied to solve the combination problem, as the formulated problem is difficult to be solved. The model proposed in this paper determines the most appropriate FMSs combination and facilitates decision making of such a hard problem.