In this paper, a mixed-integer non-linear programming model has been proposed to design an integrated cellular manufacturing system with type-2 fuzzy parameters. The integrated cellular manufacturing system consists of the following elements: cell formation, cellular layout and operator and tool assignment. One of the important features of the proposed model is considering total expected cost criteria to operator assignment. Tool costs, inter and intra cell movement costs and machine constant costs are type-2 fuzzy variables. In order to defuzzification of parameters the critical value (CV)-based reduction method is used to reduce type-2 fuzzy variables into type-1 fuzzy variables and finally the centroid defuzzification method defuzzifies fuzzy costs to crisp numbers of the costs. Furthermore, to solve a small-sized numerical example, the Branch and Bound algorithm with the Lingo software has been used. Because of NP-hardness of the model for large-sized problems and no exist benchmark to validate the performance of the proposed model, three tuned meta-heuristic algorithms (i.e., particle swarm optimization, differential evolution and fire fly) are presented too. The results show that the particle swarm optimization algorithm has better statistically performances in most problems.
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