Considering　various　situations　and　characteristics　of　supply　chain　management,　we　regard　the　outsourcing　provider　selection　as　a　type　of　fuzzy　inhomogenous　multiattribute　group　decision　making　(MAGDM)　problems　with　fuzzy　alternatives＇　comparisons　and　incomplete　weight　information.　Hereby　we　focus　on　developing　a　new　fuzzy　linear　programming　method　for　solving　such　MAGDM　problems.　In　this　method,　the　decision　makers＇　preferences　are　given　through　pair-wise　alternatives＇　comparisons　with　fuzzy　truth　degrees　represented　as　trapezoidal　fuzzy　numbers　(TrFNs).　Intuitionistic　fuzzy　sets,　TrFNs,　intervals　and　real　numbers　are　used　to　express　the　inhomogenous　decision　information.　Under　the　condition　that　the　fuzzy　positive　ideal　solution　(PIS)　and　fuzzy　negative　ideal　solution　(NIS)　are　known,　the　fuzzy　consistency　and　inconsistency　indices　are　defined　on　the　basis　of　the　relative　closeness　degrees　and　expressed　with　TrFNs.　The　attribute　weights　are　estimated　through　constructing　a　new　fuzzy　linear　programming　model,　which　is　solved　by　the　developed　method　of　fuzzy　linear　programming　with　TrFNs.　Through　solving　the　constructed　linear　goal　programming　model,　we　obtain　the　collective　comprehensive　relative　closeness　degrees　of　alternatives　to　the　fuzzy　PIS,　which　are　used　to　rank　the　alternatives.　The　effectiveness　of　the　proposed　method　is　verified　with　an　example　of　IT　outsourcing　provider　selection.　©　2014　Elsevier　B.V.　All　rights　reserved.