In　this　paper,　the　concept　of　interval　difference　is　firstly　defined.　Then,　an　interval　difference　based　evidential　reasoning　approach　is　proposed　to　analyze　multiple　attribute　decision　making　problems　in　three　situations,　including　(1)　unknown　attribute　weights　and　utilities　of　assessment　grades,　(2)　unknown　attribute　weights,　and　(3)　unknown　utilities　of　assessment　grades.　Three　optimization　models　are　constructed　to　identify　potentially　optimal　alternatives　in　the　three　situations.　For　each　potentially　optimal　alternative,　three　pairs　of　optimization　problems　are　constructed　to　generate　the　optimized　intervals　of　attribute　weights　and　utilities　of　assessment　grades　or　one　of　them.　By　using　the　optimized　intervals,　the　interval　difference　of　potentially　optimal　alternatives　is　calculated　and　used　to　generate　their　rank-order.　This　process　is　repeated　until　all　alternatives　are　identified　as　potentially　optimal　alternatives.　A　complete　rank-order　of　all　alternatives　is　then　generated.　The　performance　of　six　executive　cars　is　assessed　using　the　proposed　approach　to　demonstrate　its　applicability　and　validity.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.