The　aim　of　this　paper　is　to　propose　some　novel　multiple　attribute　group　decision　making　(MAGDM)　methods　to　deal　with　MAGDM　problems　in　which　the　attributes　are　interactive　in　the　form　of　interval-valued　hesitant　uncertain　linguistic　numbers　(IVHULNs).　Firstly,　some　new　aggregation　operators　for　IVHULNs　based　on　Bonferroni　mean　(BM)　are　proposed,　which　are　the　interval-valued　hesitant　uncertain　linguistic　BM　(IVHULBM)　operator,　the　normalized　weighted　IVHULBM　(NWIVHULBM)　operator,　the　interval-valued　hesitant　uncertain　linguistic　geometric　BM　(IVHULGBM)　operator　and　the　normalized　weighted　IVHULGBM　(NWIVHULGBM)　operator.　The　advantages　of　the　proposed　operators　are　that　it　cannot　only　effectively　aggregate　IVHULNs,　but　it　can　also　consider　the　interactive　characteristics　among　attributes.　At　the　same　time,　some　special　cases　of　these　operators　are　discussed.　Then,　this　paper　demonstrates　that　these　presented　operators　are　able　to　meet　four　desirable　properties,　which　are　reducibility,　idempotency,　monotonicity,　and　boundedness.　Moreover,　to　solve　MAGDM　problems,　two　approaches　on　the　basis　of　the　NWIVHULBM　and　NWIVHULGBM　operators　are　put　forward.　Finally,　the　proposed　methods　are　applied　to　a　decision　making　problem　regarding　online　service　quality　evaluation.　It　provides　us　with　a　useful　way　for　MAGDM　with　IVHULNs.