The　aim　of　this　paper　is　to　develop　a　new　Atanassov＇s　intuitionistic　fuzzy　(A-IF)　programming　method　to　solve　heterogeneous　multiattribute　group　decision-making　problems　with　A-IF　truth　degrees　in　which　there　are　several　types　of　attribute　values　such　as　A-IF　sets　(A-IFSs),　trapezoidal　fuzzy　numbers,　intervals,　and　real　numbers.　In　this　method,　preference　relations　in　comparisons　of　alternatives　with　hesitancy　degrees　are　expressed　by　A-IFSs.　Hereby,　A-IF　group　consistency　and　inconsistency　indices　are　defined　on　the　basis　of　preference　relations　between　alternatives.　To　estimate　the　fuzzy　ideal　solution　(IS)　and　weights,　a　new　A-IF　programming　model　is　constructed　on　the　concept　that　the　A-IF　group　inconsistency　index　should　be　minimized　and　must　be　not　larger　than　the　A-IF　group　consistency　index　by　some　fixed　A-IFS.　An　effective　method　is　developed　to　solve　the　new　derived　model.　The　distances　of　the　alternatives　to　the　fuzzy　IS　are　calculated　to　determine　their　ranking　order.　Moreover,　some　generalizations　or　specializations　of　the　derived　model　are　discussed.　Applicability　of　the　proposed　methodology　is　illustrated　with　a　real　supplier　selection　example.