Carbon　emission　efficiency　is　the　key　to　measuring　the　overall　level　of　carbon　emissions.　Carbon　emissions　in　actual　production　activities　are　uncertain,　and　the　measurement　results　are　biased　from　the　perspective　of　direct　carbon　emissions.　Based　on　the　perspective　of　implied　emission　reduction　potential,　this　study　differentiates　the　carbon　emission　efficiency　and　emission　reduction　potential　of　different　disposability,　under　the　semi-disposability　hypothesis,　the　interval　number　E-DEA　model　of　the　undesirable　output　is　proposed.　Then　a　new　production　possibility　set　is　constructed　to　solve　the　overlapping　problem　of　interval　planning.　Finally,　the　proposed　method　is　applied　to　measure　the　emission　reduction　potential　of　30　provinces　in　China.　The　results　indicate　that　the　weak　disposability　hypothesis　always　underestimates　the　emission　reduction　potential.　The　strong　disposability　hypothesis　always　overestimates　the　emission　reduction　potential.　While　the　semi-disposability　hypothesis　can　evaluate　the　emission　reduction　potential　more　scientifically　and　reasonably,　taking　into　account　the　influence　of　different　technical　characteristics　or　the　managerial　capacity　of　decision-makers.　©　2023　Elsevier　Ltd