Selecting　a　suitable　outsourcing　provider　is　one　of　the　most　critical　activities　in　supply　chain　management.　In　this　paper,　a　new　fuzzy　linear　programming　method　is　proposed　to　select　outsourcing　providers　by　formulating　it　as　a　fuzzy　inhomogeneous　multi-attribute　decision　making　(MADM)　problems　with　fuzzy　truth　degrees　and　incomplete　weight　information.　In　this　method,　the　decision　maker＇s　preferences　are　represented　as　trapezoidal　fuzzy　numbers　(TrFNs),　which　obtained　through　pair-wise　comparisons　of　alternatives.　Based　on　the　fuzzy　positive　ideal　solution　(FPIS)　and　fuzzy　negative　ideal　solution　(FNIS),　the　fuzzy　consistency　and　inconsistency　indices　are　defined　by　the　relative　closeness　degrees　in　TrFNs.　The　attribute　weights　are　estimated　by　solving　the　proposed　fuzzy　linear　programming.　And　then　the　selection　ranking　is　determined　by　the　comprehensive　relative　closeness　degree　of　each　alternative　to　the　FPIS.　An　industrial　IT　outsourcing　provider　selection　example　is　analyzed　to　demonstrate　the　implementation　process　of　this　method.　©　International　Journal　of　Industrial　Engineering.