This　paper　studies　how　to　conduct　efficiency　assessment　using　data　envelopment　analysis　(DEA)　in　interval　and/or　fuzzy　input-output　environments.　A　new　pair　of　interval　DEA　models　is　constructed　on　the　basis　of　interval　arithmetic,　which　differs　from　the　existing　DEA　models　handling　interval　data　in　that　the　former　is　a　linear　CCR　model　without　the　need　of　extra　variable　alternations　and　uses　a　fixed　and　unified　production　frontier　(i.e.　the　same　constraint　set)　to　measure　the　efficiencies　of　decision-making　units　(DMUs)　with　interval　input　and　output　data,　while　the　latter　is　usually　a　nonlinear　optimization　problem　with　the　need　of　extra　variable　alternations　or　scale　transformations　and　utilizes　variable　production　frontiers　(i.e.　different　constraint　sets)　to　measure　interval　efficiencies.　Ordinal　preference　information　and　fuzzy　data　are　converted　into　interval　data　through　the　estimation　of　permissible　intervals　and　a-level　sets,　respectively,　and　are　incorporated　into　the　interval　DEA　models.　The　proposed　interval　DEA　models　are　developed　for　measuring　the　lower　and　upper　bounds　of　the　best　relative　efficiency　of　each　DMU　with　interval　input　and　output　data,　which　are　different　from　the　interval　formed　by　the　worst　and　the　best　relative　efficiencies　of　each　DMU.　A　minimax　regret-based　approach　(MRA)　is　introduced　to　compare　and　rank　the　efficiency　intervals　of　DMUs.　Two　numerical　examples　are　provided　to　show　the　applications　of　the　proposed　interval　DEA　models　and　the　preference　ranking　approach.　(c)　2005　Elsevier　B.V.　All　rights　reserved.