At present, methods for solving the manufacturing cell formation with the assignment of duplicated machines contain many steps. Firstly, part families and machine cells are determined. Then, the incidence matrix of the cell formation is reconsidered for machine duplications to reduce the interaction between cells with the restriction of cost. These ways are difficult and complicated. Besides, consideration of machine setup cost should be done simultaneously with the decision making. In this paper, an effective lexicographic fuzzy multi-objective optimization model for manufacturing cell formation with a setup cost constrained of machine duplication is presented. Based on the perfect grouping concept, two crucial performance measures called exceptional elements and void elements are utilized in the proposed model. Lexicographic fuzzy goal programming is applied to solve this multi-objective model with setup cost constraint. So, the decision maker can easily solve the manufacturing cell formation and control the setup cost of machine duplication, simultaneously.