In this paper, we investigate multiple attribute group decision making (MAGDM) problems where decision makers represent their evaluation of alternatives by trapezoidal fuzzy two-dimensional uncertain linguistic variable. To begin with, we introduce the definition, properties, expectation, operational laws of trapezoidal fuzzy two-dimensional linguistic information. Then, to improve the accuracy of decision making in some case where there are a sort of interrelationship among the attributes, we analyze partition Bonferroni mean (PBM) operator in trapezoidal fuzzy two-dimensional variable environment and develop two operators: trapezoidal fuzzy two-dimensional linguistic partitioned Bonferroni mean (TF2DLPBM) aggregation operator and trapezoidal fuzzy two-dimensional linguistic weighted partitioned Bonferroni mean (TF2DLWPBM) aggregation operator. Furthermore, we develop a novel method to solve MAGDM problems based on TF2DLWPBM aggregation operator. Finally, a practical example is presented to illustrate the effectiveness of this method and analyses the impact of different parameters on the results of decision-making.