Fuzziness　is　inherent　in　decision　data　and　decision　making　process.　In　this　paper,　interval-valued　intuitionistic　fuzzy　(IVIF)　sets　are　used　to　capture　fuzziness　in　multiattribute　decision　making　(MADM)　problems.　The　purpose　of　this　paper　is　to　develop　a　methodology　for　solving　MADM　problems　with　both　ratings　of　alternatives　on　attributes　and　weights　being　expressed　with　IVIF　sets.　In　this　methodology,　a　weighted　absolute　distance　between　IF　sets　is　defined　using　weights　of　IF　sets.　Based　on　the　concept　of　the　relative　closeness　coefficients,　we　construct　a　pair　of　nonlinear　fractional　programming　models　which　can　be　transformed　into　two　simpler　auxiliary　linear　programming　models　being　used　to　calculate　the　relative　closeness　coefficient　intervals　of　alternatives　to　the　IVIF　positive　ideal　solution,　which　can　be　employed　to　generate　ranking　order　of　alternatives　based　on　the　concept　of　likelihood　of　interval　numbers.　The　proposed　method　is　illustrated　with　a　real　example.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.