The　aim　of　this　paper　is　to　develop　a　method　for　solving　multi-attribute　group　decision　making　(MAGDM)　problems　with　intuitionistic　uncertain　2-tuple　linguistic　(IU2TL)　variables　(IU2TLVs).　Firstly,　operational　laws　and　similarity　degrees　of　IU2TLVs　are　introduced.　Secondly,　a　new　aggregation　operator　called　IU2TL　continuous　chi-deviation　ordered　weighted　quasi-averaging　(IU2TLC-CDOWQA)　is　proposed.　Then,　to　deal　with　heterogeneous　relationships,　the　IU2TL　continuous　extend　Bonferroni　mean　(IU2TLC-EBM)　operator　is　developed,　and　hereby　a　method　for　MAGDM　problems　with　IU2TLVs　is　proposed.　Finally,　an　illustrated　example　and　comparing　analysis　show　that　the　proposed　method　is　practical　and　effective.