One　of　the　critical　activities　for　bilateral　matching　decision　is　matching　accuracy,　which　may　be　regarded　as　a　type　of　bilateral　matching　decision　problem　with　heterogeneous　information　and　attribute　association.　This　paper　aims　to　develop　a　new　fuzzy　linear　programming　method　to　address　such　problems.　In　the　proposed　method,　the　multiple　attributes　are　expressed　as　exact　numbers,　interval　numbers,　triangular　fuzzy　numbers,　intuitionistic　fuzzy　numbers,　linguistic　terms,　and　neutrosophic　numbers.　Firstly,　the　distance　of　heterogeneous　data　and　fuzzy　measures　are　introduced;　meanwhile,　heterogeneous　information　attribute　weights　are　calculated　based　on　the　Choquet　integral.　Then　based　on　the　psychological　characteristics　of　matching　participants＇　loss　avoidance　and　superiority　maximization,　the　lexicographical　method　is　used　to　solve　the　multi-objective　linear　programming　model　to　obtain　the　optimal　bilateral　transaction　matching　pair.　Finally,　an　example　of　second-hand　housing　online　rental-sales　matching　problems　is　analyzed　to　demonstrate　the　implementation　process　and　applicability　of　the　method　proposed　in　this　paper.