Considering　the　hesitancy　degrees　on　pair-wise　comparisons　of　alternatives　as　interval-valued　intuitionistic　fuzzy　(IVIF)　sets　(IVIFSs),　we　develop　a　new　fuzzy　mathematical　programming　method　for　solving　heterogeneous　multiattribute　decision-making　problems　based　on　the　Linear　Programming　Technique　for　Multidimensional　Analysis　of　Preference.　In　this　method,　IVIFSs,　intuitionistic　fuzzy　sets　(IFSs),　trapezoidal　fuzzy　numbers,　linguistic　variables,　intervals　and　real　numbers　are　used　to　represent　multiple　types　of　attribute　values　and　the　attribute　weights　are　not　completely　known.　The　preference　relations　between　alternatives　given　by　decision　maker　are　expressed　with　IVIFSs　of　ordered　pairs　of　alternatives.　The　consistency　and　inconsistency　indices　are　defined　as　IVIFSs　on　the　basis　of　comparisons　of　alternatives　with　IVIF　truth　degrees.　The　attribute　weights　and　fuzzy　ideal　solution　(FIS)　are　estimated　through　constructing　a　fuzzy　mathematical　programming　model,　which　is　solved　by　the　technically　developed　method　of　IVIF　mathematical　programming.　Hereby　the　distances　of　alternatives　to　the　FIS　are　computed　to　rank　the　alternatives.　Some　generalization　and　discussion　on　the　constructed　IVIF　mathematical　programming　model　are　also　presented.　A　green　supplier　selection　example　is　provided　to　illustrate　the　effectiveness　of　the　proposed　model　and　method.　The　comparison　analyses　verify　the　superiorities　of　the　proposed　method.　(C)　2015　Elsevier　Inc.　All　rights　reserved.