Due　to　various　uncertain　factors,　sometimes　it　is　difficult　to　obtain　accurate　data.　In　comparison,　interval-valued　data　can　better　represent　uncertain　information.　However,　most　of　the　existing　theoretical　researches　on　Extended　Belief　Rule-Based　(EBRB)　system　are　aimed　at　real-valued　data　and　lack　methods　applied　to　interval-valued　data.　Based　on　the　theory　of　interval　evidence　reasoning,　this　paper　proposes　a　new　method　of　constructing　and　reasoning　for　interval-valued　EBRB　systems.　This　model　can　not　only　be　applied　to　interval-valued　data　but　also　real-valued　data.　And　after　analyzing　the　problems　of　the　conventional　EBRB　similarity　formula,　we　use　the　method　of　normalized　Euclidean　distance.　In　addition,　because　of　the　ignorance　of　attribute　weights　by　conventional　methods,　this　paper　combines　mutual　information　methods　to　determine　attribute　weights.　Some　case　studies　about　interval-valued　datasets　and　real-valued　datasets　are　provided　in　the　last.　The　experimental　results　have　proven　the　feasibility　and　efficiency　of　the　proposed　method.　©　2021,　Springer　Nature　Switzerland　AG.