Three-way　decision　(TWD)　theory　provides　us　with　a　new　perspective　and　methodology　to　improve　the　flexibility　of　traditional　multiple　criteria　decision-making　(MCDM)　methods.　However,　the　construction　of　TWD　theory　under　uncertain　environment　is　still　a　serious　challenge.　In　light　of　this,　this　paper　proposes　a　novel　interval-valued　TWD　theory　for　solving　MCDM　problems　under　uncertain　environment.　First,　several　rules　are　defined　to　calculate　the　interval-valued　thresholds　under　multiple　criteria　environment.　Afterwards,　on　the　basis　of　interval-valued　Technique　for　Order　Preference　by　Similarity　to　Ideal　Solution　(TOPSIS)　method,　a　new　approach　is　developed　to　calculate　the　interval-valued　conditional　probability　of　each　alternative.　Then,　a　new　information　transformation　and　fusion　mechanism　in　the　framework　of　evidential　reasoning　algorithm　is　established　to　conduct　the　interval-valued　thresholds　under　multiple　criteria　into　overall　interval-valued　thresholds.　Finally,　according　to　the　overall　interval-valued　thresholds　and　interval-valued　conditional　probabilities,　several　new　decision　rules　for　objects　under　different　decision　situations　are　provided　to　generate　the　classifications　and　rankings　of　alternatives.　To　illustrate　the　feasibility　of　the　proposed　method,　an　application　about　purchasing　green　vehicles　is　performed.　Further　detailed　discussions　and　comparisons　with　other　methods　are　also　conducted　to　show　the　effectiveness　and　superiority　of　the　current　proposal.　©　2022　Elsevier　B.V.