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In order to solve Group Decision Making (GDM) problems where the preference relations are provided by decision makers with incomplete linguistic labels, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the incomplete linguistic preference relation and then builds the corresponding optimization model. Subsequently, a programming model is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained according to the optimization result. A numerical example with incomplete linguistic preference relations is examined to illustrate and show the applicability of the proposed approach.