An　approach　called　hybrid　evidential　reasoning　is　proposed　based　on　the　extension　principle　to　deal　with　multiple　attribute　decision　making　under　uncertainty.　Heterogeneous　beliefs,　such　as　crisp　value,　interval　value　and　fuzzy　value,　on　the　same　problem　are　all　decomposed　into　interval　value　to　setup　a　uniform　belief　structure.　Interval　evidential　reasoning　is　used　to　work　out　the　interval　utility　of　the　alternative　for　each　membership　degrees,　and　the　utility　of　each　alternative　can　be　assembled　in　the　order　of　membership　degrees.　The　equation　of　fuzzy　centroid　is　reduced　and　used　to　calculate　the　belief　degree　of　quantitative　fuzzy　assessment　and　rank　the　fuzzy　utility　of　alternatives.　Finally,　an　example　is　examined　to　illustrate　the　effectiveness　and　feasibility　of　the　proposed　method.　Comparing　with　the　application　of　all　these　approaches　to　the　example,　the　results　show　that　the　proposed　approach　is　adaptable.　©,　2015,　Northeast　University.　All　right　reserved.