The　aim　of　this　paper　is　to　propose　a　satisfactory　degree　method　by　using　nonlinear　programming　for　solving　multi　attribute　decision　making　(MADM)　problems　in　which　ratings　of　alternatives　on　attributes　is　expressed　via　interval-valued　intuitionistic　fuzzy　(IVIF)　sets　and　preference　information　on　attributes　is　incomplete.　Concretely,　a　nonlinear　programming　model　is　firstly　explored　to　determine　the　satisfactory　degree　which　is　the　ratio　of　the　square　of　the　weight　Euclidean　distance　between　an　alternative　and　the　IVIF　negative　ideal　solution　(IVIFNIS)　to　the　sum　of　the　square　of　the　weight　Euclidean　distance　between　the　IVIF　negative　ideal　solution　(IVIFNIS)　and　the　IVIF　positive　ideal　solution　(IVIFPIS).　Another　nonlinear　programming　model　is　also　developed　to　obtain　satisfactory　intuitionistic　fuzzy　sets,　and　then　the　general　satisfactory　degrees　of　the　satisfactory　intuitionistic　fuzzy　sets　are　used　to　generate　the　ranking　order　of　the　alternatives.　Finally,　a　real　example　is　employed　to　verify　the　applicability　of　the　proposed　approach　and　illustrate　its　practicality　and　effectiveness.