The　assumptions　of　strong　and　weak　disposability　for　undesirable　outputs　have　long　dominated　studies　of　data　envelopment　analysis　for　environmental　assessments.　Unfortunately,　these　assumptions　cannot　describe　the　diverse　technical　features　of　different　undesirable　outputs　during　the　actual　production　process.　Thus,　we　introduce　a　non-disposal　degree　to　develop　a　new　semi-disposability　assumption,　which　can　replace　the　assumptions　of　strong　and　weak　disposability　in　environmental　assessments.　This　assumption　ensures　that　decision　makers　can　address　undesirable　outputs　freely　within　the　scope　of　current　production　technology;　otherwise,　they　have　to　reduce　desirable　outputs　in　the　same　proportion　to　decrease　undesirable　outputs.　A　reference　point　comparison　method　is　proposed　for　determining　the　non-disposal　degree　from　an　objective　perspective.　The　assumption　of　semi-disposability　is　extended　to　uncertain　circumstances　by　using　the　interval　non-disposal　degree.　Finally,　two　empirical　examples　are　provided　to　illustrate　the　effectiveness　of　the　semi-disposability　assumption.　(C)　2017　Elsevier　B.V.　All　rights　reserved.