Muirhead　mean　(MM)　is　a　well-known　aggregation　operator　which　can　consider　interrelationships　among　any　number　of　arguments　assigned　by　a　variable　vector.　Besides,　it　is　a　universal　operator　since　it　can　contain　other　general　operators　by　assigning　some　special　parameter　values.　However,　the　MM　can　only　process　the　crisp　numbers.　Inspired　by　the　MM＇　advantages,　the　aim　of　this　paper　is　to　extend　MM　to　process　the　intuitionistic　fuzzy　numbers　(IFNs)　and　then　to　solve　the　multi-attribute　group　decision　making　(MAGDM)　problems.　Firstly,　we　develop　some　intuitionistic　fuzzy　Muirhead　mean　(IFMM)　operators　by　extending　MM　to　intuitionistic　fuzzy　information.　Then,　we　prove　some　properties　and　discuss　some　special　cases　with　respect　to　the　parameter　vector.　Moreover,　we　present　two　new　methods　to　deal　with　MAGDM　problems　with　the　intuitionistic　fuzzy　information　based　on　the　proposed　MM　operators.　Finally,　we　verify　the　validity　and　reliability　of　our　methods　by　using　an　application　example,　and　analyze　the　advantages　of　our　methods　by　comparing　with　other　existing　methods.