Owing　to　more　vague　concepts　frequently　represented　in　decision　data,　intuitionistic　fuzzy　sets　(IFSs)　are　more　fliexibly　used　to　model　real-life　decision　situations.　At　the　same　time,　with　ever　increasing　complexity　in　many　decision　situations　in　reality,　there　are　often　some　challenges　for　a　decision　maker　to　provide　complete　attribute　preference　information,　i.e.,　the　weights　may　be　completely　unknown　or　partially　known.　The　aim　of　this　paper　is　to　develop　an　effiective　method　for　solving　intuitionistic　fuzzy　multi-attribute　decision　making　(MADM)　problems　with　incomplete　weight　information.　In　this　method,　ratings　of　alternatives　on　attributes　are　expressed　with　IFSs.　The　multi-objective　programming　models　are　established　to　calculate　unknown　weights　by　using　weight　information　partially　known　a　priori.　The　derived　minimum　weighted　Minkowski　distance　power　models　are　used　to　determine　the　unknown　weights　and　to　generate　the　ranking　order　of　the　alternatives　simultaneously.　The　proposed　models　are　easily　extended　to　intuitionistic　fuzzy　MADM　problems　with　different　weight　information　structures.　An　example　of　the　supplier　selection　problem　is　examined　to　demonstrate　applicability　and　flexibility　of　the　proposed　models　and　method.