Evidential　reasoning　(ER)　is　one　of　the　important　approaches　used　to　solve　multi-attribute　decision　analysis　(MADA)　problems　under　uncertainty,　involving　both　quantitative　and　qualitative　attributes.　The　ER　approach　provides　a　distributed　modeling　framework　fusing　several　types　of　uncertain　and　incomplete　information,　including　ignorance　and　vagueness,　to　work　out　the　optimum　alternative　rationally.　In　this　paper,　we　review　the　original　ER　algorithm　and　recursive　interval　evidential　reasoning　(IER)　algorithm　and　derive　a　general　analytical　algorithm　for　IER,　thus　enabling　an　aggregation　of　attributes’　assessments　in　an　explicit　manner.　Then,　a　more　complicated　uncertain　occasion　is　investigated,　where　it　is　possible　to　conduct　evaluation　assessments,　including　quantitative　data,　belief　degrees,　grades,　and　weights,　in　the　form　of　an　interval.　A　pair　of　nonlinear　optimization　models　based　on　the　new　algorithm　is　established　to　solve　this　problem　under　interval　uncertainty,　and　the　maximum　and　minimum　expected　utilities　of　each　alternative　are　calculated　and　ranked　accordingly.　Additionally,　we　prove　that　the　original　ER　and　recursive　IER　algorithms　are　special　cases　of　the　new　algorithm.　Finally,　a　numerical　example　is　used　to　demonstrate　the　steps　involved　in　the　proposed　approach.　©　2016　Elsevier　B.V.