Because　of　the　complexity　of　interval-valued　intuitionistic　fuzzy　set,　there　are　few　literatures　investigating　the　additive　consistency　of　the　interval-valued　intuitionistic　preference　relation.　This　paper　proposes　a　group　decision　making　approach　with　interval-valued　intuitionistic　preference　relations.　Firstly,　two　additive　reciprocal　fuzzy　preference　relations　and　two　fuzzy　non-preferred　relations　are　obtained　by　dividing　an　interval-valued　intuitionistic　preference　relation　in　order　to　avoid　the　operations　of　interval-valued　intuitionistic　fuzzy　numbers.　Here,　the　fuzzy　non-preferred　relation　is　interpreted　as　the　non-preferred　intensity　of　one　alternative　over　another　one.　Moreover,　the　rational　concept　of　additive　consistency　of　interval-valued　intuitionistic　preference　relation　is　defined.　Secondly,　optimizing　models　to　derive　priority　weight　vector　from　interval-valued　intuitionistic　preference　relation　are　constructed.　In　particular,　the　priority　weight　vector　is　in　terms　of　interval-valued　intuitionistic　fuzzy　numbers,　which　is　rational　under　the　interval-valued　intuitionistic　fuzzy　environment.　Thirdly,　an　extended　approach　to　address　group　decision　making　(GDM)　problems　is　proposed.　Each　individual　expert＇s　consistency　index　is　applied　to　measure　his/her　degree　of　importance.　Finally,　an　illustrative　example　of　supplier　selection　is　provided　to　illustrate　the　proposed　approach　addressing　GDM　problems.　The　feasibility　to　derive　priority　weight　vector　in　terms　of　interval-valued　intuitionistic　fuzzy　numbers　using　the　developed　approach　is　verified.　And　the　proposed　approach　is　compared　with　the　other　conventional　existing　ones　to　show　its　advantages.