Heterogeneous　multiattribute　group　decision　making　(MAGDM)　problems　which　involve　multi-granularity　linguistic　labels,　fuzzy　numbers,　interval　numbers　and　real　numbers　are　very　complex　and　important　in　practical　applications　of　decision　making　theory.　Hitherto,　there　exists　no　general　theoretical　inducement　for　solving　such　problems.　The　purpose　of　this　paper　is　to　develop　a　systematic　methodology　for　solving　the　heterogeneous　MAGDM　problems　by　introducing　the　multiattribute　ranking　index　based　on　the　particular　measure　of　closeness　to　the　positive　ideal　solution　(PIS)　and　using　the　weighted　Minkowski　distance　to　measure　differences　between　each　alternative　and　the　PIS　as　well　as　the　negative　ideal　solution　(NIS).　The　proposed　methodology　is　shown　to　have　some　advantages　over　the　fuzzy　TOPSIS.　Validity　and　applicability　of　the　methodology　proposed　in　this　paper　is　illustrated　with　a　real　example　of　the　missile　weapon　system　selection　problem.　©　2010　Elsevier　Ltd.　All　rights　reserved.