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Due to the uncertainty of decision environment and difference of decision makers’ cultural and knowledge background, actual group decision making problems are usually with multi-granularity uncertain linguistic information and incomplete weight information. In this paper, we focus on dealing with multi-granularity uncertain linguistic group decision making problems with incomplete weight information. In the proposed method, uncertain linguistic evaluation information of each decision maker is transformed to trapezoidal fuzzy numbers, and then two optimization models are established to minimize the deviation between each decision maker’s evaluation and the group’s collective evaluation on each alternative. By solving the established optimization models, the collective evaluation of the alternatives can be denoted by trapezoidal fuzzy numbers. After that, the closeness coefficient of each alternative can be …