The　intuitionistic　fuzzy　(IF)　set　characterized　by　two　functions　was　a　generalization　of　the　fuzzy　set.　In　this　paper,　we　investigate　multiattribute　decision　making　(MADM)　problems　with　ratings　of　alternatives　being　expressed　using　IF　sets　and　attribute　weights　given　as　real　numbers.　Firstly,　the　generalized　ordered　weighted　averaging　(GOWA)　operators　introduced　by　Yager　[Yager,　R.　(2004).　Generalized　OWA　aggregation　operators.　Fuzzy　Optimization　and　Decision　Making,　3,　93-107]　are　extended　to　aggregate　IF　sets.　Secondly,　MADM　problems　with　IF　sets　are　formulated　through　transforming　the　ratings　of　alternatives　on　both　qualitative　and　quantitative　attributes　into　IF　sets　in　a　unified　way.　The　method　and　procedure　based　on　the　extended　GOWA　operators　are　developed　to　solve　the　MADM　problems　with　IF　sets.　Finally,　the　effectiveness　and　practicability　of　the　proposed　method　are　illustrated　with　a　numerical　example.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.