The　convexity　of　meta-frontier　is　a　debated　topic　in　data　envelopment　analysis　(DEA).　This　paper　claims　that　meta-frontier　is　a　non-convex　hull,　but　the　production　activities　between　the　non-convex　meta-frontier　and　the　convex　traditional　production　frontier　may　be　feasible.　Therefore,　technology　compatibility　is　defined　to　explain　this　feasibility,　and　a　modified　DEA　model　is　constructed　to　evaluate　the　efficiency　of　decision-making　units　with　technology　heterogeneity　and　technology　compatibility.　Sequentially,　two　new　meta-frontier　DEA　frameworks　are　constructed　to　evaluate　and　decompose　efficiency,　thereby　revealing　the　impact　of　technology　heterogeneity　and　technology　compatibility　on　efficiency.　In　addition,　a　series　of　discussions　are　presented　to　analyze　these　two　new　frameworks.