Ranking　of　triangular　intuitionistic　fuzzy　numbers　(TIFNs)　is　an　important　problem,　which　is　solved　by　the　value　and　ambiguity　based　ranking　method　developed　in　this　paper.　Firstly,　the　concept　of　TIFNs　is　introduced.　Arithmetic　operations　and　cut　sets　over　TIFNs　are　investigated.　Then,　the　values　and　ambiguities　of　the　membership　degree　and　the　non-membership　degree　for　TIFNs　are　defined　as　well　as　the　value-index　and　ambiguity-index.　Finally,　a　value　and　ambiguity　based　ranking　method　is　developed　and　applied　to　solve　multiattribute　decision　making　problems　in　which　the　ratings　of　alternatives　on　attributes　are　expressed　using　TIFNs.　A　numerical　example　is　examined　to　demonstrate　the　implementation　process　and　applicability　of　the　method　proposed　in　this　paper.　Furthermore,　comparison　analysis　of　the　proposed　method　is　conducted　to　show　its　advantages　over　other　similar　methods.