In　real-world　applications,　apart　from　being　precise-valued　or　interval-valued,　belief　structure　measurements　can　also　be　discrete-valued.　However,　problems　relating　to　the　combination　of　discrete-valued　belief　structures　have　not　been　resolved.　Therefore,　in　the　research　presented　in　this　paper,　we　explore　the　counterintuitive　behavior　associated　with　the　combination　of　discrete　evidence　and　extend　the　concept　of　evidential　reasoning　(ER)　to　evidential　reasoning　with　a　discrete　structure　in　order　to　serve　as　the　theoretical　basis　and　as　technical　support　for　the　fusion　of　discrete　information.　This　method　offers　an　approach　to　the　normalization　of　discrete　evidence,　provides　a　means　of　objectively　determining　the　weight　of　discrete　evidence,　and　optimizes　the　combination　of　discrete　evidence　based　on　evidential　reasoning.　The　results　of　various　examples　show　that　the　method　not　only　offers　an　effective　solution　to　the　combination　of　non-conflicting　discrete　evidence,　but　it　also　overcomes　the　counterintuitive　results　of　combining　internally　or　externally　conflicting　evidence.　©　2017　Elsevier　B.V.