The　order　relation　of　fuzzy　number　is　important　in　decision　making　and　optimization　modeling,　and　ranking　fuzzy　numbers　is　difficult　in　nature.　Ranking　trapezoidal　intuitionistic　fuzzy　numbers　(TrIFNs)　is　more　difficult　due　to　the　fact　that　the　TrIFNs　are　a　generalization　of　the　fuzzy　numbers.　The　aim　of　this　paper　is　to　develop　a　new　methodology　for　ranking　TrIFNs.　We　define　the　value-index　and　ambiguity-index　based　on　the　value　and　ambiguity　of　the　membership　and　non-membership　functions,　and　then　propose　a　difference-index　based　ranking　method,　which　is　applied　to　multiattribute　decision　making　(MADM)　problems.　The　proposed　method　is　compared　to　show　its　advantages　and　applicability.　©　2015,　Association　for　Scientific　Research.　All　rights　reserved.