Efficiency　assessment　by　using　data　envelopment　analysis　(DEA)　in　interval　environment　is　studied.　Two　parameters　with　regard　to　the　input　and　output　are　introduced　to　characterize　the　variability　of　the　production　possibility　sets.　The　extended　production　facets　with　different　production　possibility　sets　are　determined.　The　inclusion　relation　between　different　extended　production　facets　is　discussed,　and　self-evaluation　models　are　constructed　to　calculate　the　interval　efficiency　of　the　decision-making　units　(DMUs)　with　the　optimal　production　facet.　By　setting　self-evaluation　as　a　target,　the　aggressive　and　benevolent　cross-efficiency　models　are　established　based　on　the　likelihood　between　the　values　of　self-evaluation　and　peer　evaluation.　The　analysis　of　the　models　yields　the　interval　cross-efficiency　matrices　and　the　weight　allocation　method　that　is　more　advantageous　to　the　DMU　for　aggregating　the　interval　cross-efficiency　matrices.　An　example　is　used　to　illustrate　the　applications　of　the　models.　©　2017　-　IOS　Press　and　the　authors.　All　rights　reserved.