To　address　the　problem　of　multi-attribute　matching　decision-making,　in　which　both　the　attributes　and　attribute　weights　are　interval-value　intuitionistic　fuzzy　numbers　(IVIFNs),　we　propose　an　approach　for　matching　decision-making.　Based　on　the　definition　of　weighted　absolute　distance　for　IVIFNs,　we　develop　fractional　programming　models　to　realize　an　optimal　degree　of　matching　between　two-sided　agents,　using　the　order　preference　technique　of　similarity　to　reach　an　ideal　solution.　Via　Charnes　and　Cooper　transformations,　we　transform　these　nonlinear　models　into　linear　programming　models.　Then,　by　solving　these　models,　we　obtain　intervalvalue　matrices　for　the　degree　of　matching.　In　addition,　we　develop　a　double-objective　interval　optimization　model　that　maximizes　the　degree　of　matching　on　both　sides.　Using　the　linear　weighted　method,　we　convert　these　models　into　a　single-objective　optimization　model.　Matching　results　can　then　be　reached　by　solving　this　model.　An　example　analysis　illustrates　the　validity　and　feasibility　of　the　proposed　method.