The　concept　of　an　intuitionistic　fuzzy　number　(IFN)　is　of　importance　for　quantifying　an　ill-known　quantity,　and　the　ranking　of　IFNs　is　a　very　difficult　problem.　The　aim　of　this　paper　is　to　introduce　the　concept　of　a　triangular　IFN　(TIFN)　as　a　special　case　of　the　IFN　and　develop　a　new　methodology　for　ranking　TIFNs.　Firstly　the　concepts　of　TIFNs　and　cut　sets　as　well　as　arithmetical　operations　are　introduced.　Then　the　values　and　ambiguities　of　the　membership　function　and　the　non-membership　function　for　a　TIFN　are　defined.　A　new　ranking　method　is　developed　on　the　basis　of　the　concept　of　a　ratio　of　the　value　index　to　the　ambiguity　index　and　applied　to　multiattribute　decision　making　problems　in　which　the　ratings　of　alternatives　on　attributes　are　expressed　with　TIFNs.　The　validity　and　applicability　of　the　proposed　method,　as　well　as　analysis　of　the　comparison　with　other　methods,　are　illustrated　with　a　real　example.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.