Multiattribute　decision　making　(MADM)　with　multiple　formats　of　information,　which　is　called　heterogeneous　MADM　for　short,　is　very　complex　and　interesting　in　applications.　The　purpose　of　this　paper　is　to　extend　the　Linear　Programming　Technique　for　Multidimensional　Analysis　of　Preference　(LINMAP)　for　solving　heterogeneous　MADM　problems　which　involve　intuitionistic　fuzzy　(IF)　sets　(IFSs),　trapezoidal　fuzzy　numbers　(TrFNs),　intervals　and　real　numbers.　In　this　method,　DM＇s　preference　is　given　through　pair-wise　comparisons　of　alternatives　with　hesitation　degrees　which　are　represented　as　IFSs.　The　IF　consistency　and　inconsistency　indices　are　defined　on　the　basis　of　pair-wise　comparisons　of　alternatives.　Each　alternative　is　assessed　on　the　basis　of　its　distance　to　a　fuzzy　ideal　solution　(FIS)　unknown　a　priori.　Based　on　the　defined　IF　consistency　and　inconsistency　indices,　we　construct　a　new　fuzzy　mathematical　programming　model,　which　is　solved　by　the　developed　method　of　fuzzy　mathematical　programming　with　IFSs.　Once　the　FIS　and　the　attribute　weights　are　obtained,　we　can　calculate　the　distances　of　all　alternatives　to　the　FIS,　which　are　used　to　determine　the　ranking　order　of　the　alternatives.　A　supplier　selection　example　is　presented　to　demonstrate　the　validity　and　applicability　of　the　proposed　method.　(C)　2012　Elsevier　Ltd.　All　rights　reserved.