In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches.