This　paper　investigates　a　method　to　deal　with　multiple　attribute　group　decision　making　(MAGDM)　problems　in　which　the　decision　makers＇　weights　are　expressed　as　crisp　numbers,　the　weights　of　attributes　are　unknown,　and　attribute　values　are　expressed　as　interval-valued　trapezoidal　intuitionistic　fuzzy　numbers　(IVTrIFNs).　Firstly,　some　new　aggregation　operators　are　proposed,　including　the　interval-valued　trapezoidal　intuitionistic　fuzzy　weighted　geometric　averaging　(IVTrIFWGA)　operator,　the　interval-valued　trapezoidal　intuitionistic　fuzzy　ordered　weighted　geometric　averaging(IVTrIFOWGA)　operator,　and　the　interval-valued　trapezoidal　intuitionistic　fuzzy　hybrid　geometric　averaging　(IVTrIFHGA)　operator.　Some　desirable　properties　of　these　operators　are　studied.　The　results　of　using　these　operators　for　aggregation　are　also　interval-valued　trapezoidal　intuitionistic　fuzzy　numbers.　Secondly,　a　fuzzy　cross-entropy　of　interval-valued　trapezoidal　intuitionistic　fuzzy　sets(IVTrIFSs)　is　defined,　based　on　which　a　new　mathematical　model　is　established　to　determine　the　weights　of　attributes.　Finally,　the　fuzzy　grey　relation　analysis　(GRA)　is　utilized　to　rank　decision　alternatives.　Numerical　examples　are　provided　to　demonstrate　the　effectiveness　of　the　proposed　multiple　attribute　group　decision　making　method　and　its　advantages　in　overcoming　the　defects　of　the　existing　methods.　©　2019　-　IOS　Press　and　the　authors.　All　rights　reserved.