Multiple　attribute　decision　analysis　(MADA)　problems　having　both　quantitative　and　qualitative　attributes　under　uncertainty　can　be　modeled　using　the　evidential　reasoning　(ER)　approach.　Several　types　of　uncertainties　such　as　ignorance　and　fuzziness　can　be　modeled　in　the　ER　framework.　In　this　paper,　the　ER　approach　will　be　extended　to　model　new　types　of　uncertainties　including　interval　belief　degrees　and　interval　data　that　could　be　incurred　in　decision　situations　such　as　group　decision　making.　The　Dempster-Shafer　(D-S)　theory　of　evidence　is　first　extended,　which　is　one　of　the　bases　of　the　ER　approach.　The　analytical　ER　algorithm　is　used　to　combine　all　evidence　simultaneously.　Two　pairs　of　nonlinear　optimization　models　are　constructed　to　estimate　the　upper　and　lower　bounds　of　the　combined　belief　degrees　and　to　compute　the　maximum　and　the　minimum　expected　utilities　of　each　alternative,　respectively.　Interval　data　are　equivalently　transformed　to　interval　belief　degrees　and　are　incorporated　into　the　nonlinear　optimization　models.　A　cargo　ship　selection　problem　is　examined　to　show　the　implementation　process　of　the　proposed　approach.　(c)　2005　Elsevier　B.V.　All　rights　reserved.