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.