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The paper deals with optimal determination of the cutting parameters in multipass machining operations. A new optimization approach is proposed which uses a possibilistic formulation of the classical optimization problem and optimizes the resulting possibilistic model using a genetic algorithm. The proposed approach makes it possible to find the optimal value of all the cutting parameters, including the depth of cut, in just one step. A numerical example is provided to compare the performance of the proposed method with other recent methods proposed in the literature. Furthermore, fuzzy data must be used in the formulation of the optimization problem and therefore a fuzzy possibilistic approach is suggested. Solution of the proposed fuzzy possibilistic optimization problem has been approached by using fuzzy modalities and genetic algorithms.