In　data　envelopment　analysis,　the　existing　methods　for　measuring　the　relative　efficiencies　of　decision　making　units　(DMUs)　are　to　compare　DMUs　relative　to　the　best　or　the　worst　of　all　DMUs.　In　this　paper,　we　consider　both　the　best　DMU　and　the　worst　DMU　as　the　reference　DMUs　and　propose　the　normalized　efficiency.　Further,　from　the　optimistic　and　pessimistic　viewpoints,　we　construct　two　DEA　models　to　obtain　the　upper　and　lower　bounds　of　the　normalized　efficiency　and　then　achieve　an　interval　efficiency　evaluation　to　rank　all　DMUs　completely.　Finally,　two　examples　are　presented　to　illustrate　the　performance　of　the　interval　efficiency　evaluation.　©　2018　Elsevier　Ltd