Heterogeneous　multi-attribute　case　retrieval　is　a　crucial　step　in　generating　emergency　alternatives　during　the　course　of　emergency　decision　making　(EDM)　by　referring　to　historical　cases.　This　paper　develops　a　heterogeneous　multi-attribute　case　retrieval　method　for　EDM　that　considers　five　attribute　formats:　crisp　numbers,　interval　numbers,　intuitionistic　fuzzy　numbers,　single-valued　neutrosophic　numbers　(SvNNs),　and　interval-valued　neutrosophic　numbers　(IvNNs).　First,　we　propose　a　similarity　measurement　of　IvNNs　and　calculate　the　attribute　similarities　for　the　five　attribute　formats.　The　attribute　weights　are　established　using　an　optimal　model.　Next,　the　case　similarities　are　calculated　and　the　set　of　the　similar　historical　cases　is　constructed.　Furthermore,　the　evaluated　information　based　on　heterogeneous　multi-attribute　from　similar　historical　cases　is　provided,　and　the　calculation　method　for　the　evaluation　of　utility　based　on　TODIM　(an　acronym　for　interactive　and　multi-criteria　decision-making　in　Portugese)　is　proposed.　The　most　suitable　historical　case　is　determined　based　on　the　case　similarity　and　the　evaluated　utility.　From　this,　the　emergency　alternative　is　generated.　Finally,　we　demonstrate　the　efficacy　of　the　proposed　method　with　a　case　study　and　conduct　comparisons　against　the　performance　of　existing　methods　to　assess　the　validity　and　superiority　of　the　proposed　method.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.