The　aim　of　this　paper　is　to　develop　a　new　methodology　for　solving　fuzzy　multi-attribute　group　decision　making　problems　with　non-homogeneous　information,　including　multi-granular　linguistic　term　sets,　fuzzy　numbers,　interval　values　and　real　numbers.　In　this　methodology,　different　distances　are　defined　to　measure　differences　between　alternatives　and　the　ideal　solution　as　well　as　the　negative　ideal　solution.　A　relative　closeness　method　is　developed　by　introducing　the　multi-attribute　ranking　index　based　on　the　particular　measure　of　closeness　to　the　IS.　The　proposed　method　determines　a　compromise　solution　for　the　group,　providing　a　maximum　＇group　utility＇　for　the　＇majority＇　and　a　minimum　of　an　individual　regret　for　the　＇opponent＇.　The　implementation　process,　effectiveness　and　feasibility　of　the　method　proposed　in　this　paper　are　illustrated　with　a　real　example　of　the　missile　weapon　system　design　project　selection.　©　2010　Springer　Science+Business　Media,　LLC.