Interval-valued　intuitionistic　fuzzy　(IVIF)　sets　are　useful　to　deal　with　fuzziness　inherent　in　decision　data　and　decision-making　processes.　The　aim　of　this　paper　is　to　develop　a　nonlinear-programming　methodology　that　is　based　on　the　technique　for　order　preference　by　similarity　to　ideal　solution　to　solve　multiattribute　decision-making　(MADM)　problems　with　both　ratings　of　alternatives　on　attributes　and　weights　of　attributes　expressed　with　IVIF　sets.　In　this　methodology,　nonlinear-programming　models　are　constructed　on　the　basis　of　the　concepts　of　the　relative-closeness　coefficient　and　the　weighted-Euclidean　distance.　Simpler　auxiliary　nonlinear-programming　models　are　further　deduced　to　calculate　relative-closeness　of　IF　sets　of　alternatives　to　the　IVIF-positive　ideal　solution,　which　can　be　used　to　generate　the　ranking　order　of　alternatives.　The　proposed　methodology　is　validated　and　compared　with　other　similar　methods.　A　real　example　is　examined　to　demonstrate　the　applicability　and　validity　of　the　methodology　proposed　in　this　paper.