One　of　the　critical　activities　for　outsourcing　success　is　outsourcing　provider　selection,　which　may　be　regarded　as　a　type　of　fuzzy　heterogeneous　multiattribute　decision　making　(MADM)　problems　with　fuzzy　truth　degrees　and　incomplete　weight　information.　The　aim　of　this　paper　is　to　develop　a　new　fuzzy　linear　programming　method　for　solving　such　MADM　problems.　In　this　method,　the　decision　maker＇s　preferences　are　given　through　pair-wise　alternatives＇　comparisons　with　fuzzy　truth　degrees,　which　are　expressed　with　trapezoidal　fuzzy　numbers　(TrFNs).　Real　numbers,　intervals,　and　TrFNs　are　used　to　express　heterogeneous　decision　information.　Giving　the　fuzzy　positive　and　negative　ideal　solutions,　we　define　TrFN-type　fuzzy　consistency　and　inconsistency　indices　based　on　the　concept　of　the　relative　closeness　degrees.　The　attribute　weights　are　estimated　through　constructing　a　new　fuzzy　linear　programming　model,　which　is　solved　by　using　the　developed　fuzzy　linear　programming　method　with　TrFNs.　The　relative　closeness　degrees　of　alternatives　can　be　calculated　to　generate　their　ranking　order.　An　example　of　the　IT　outsourcing　provider　selection　problem　is　analyzed　to　demonstrate　the　implementation　process　and　applicability　of　the　method　proposed　in　this　paper.　(C)　2013　Elsevier　Ltd.　All　rights　reserved.