This　paper　introduces　two　virtual　decision　making　units　(DMUs)　called　ideal　DMIJ　(IDMU)　and　anti-ideal　DMIJ　(ADMU)　into　the　data　envelopment　analysis　(DEA).　The　resultant　DEA　models　are,　respectively,　referred　to　as　the　data　envelopment　analysis　with　ideal　and　anti-ideal　decision　making　units.　One　evaluates　DMUs　from　the　viewpoint　of　the　best　possible　relative　efficiency,　while　the　other　evaluates　them　from　the　perspective　of　the　worst　possible　relative　efficiency.　The　two　distinctive　efficiencies　are　combined　to　form　a　comprehensive　index　called　the　relative　closeness　(RC)　to　the　IDMU　just　like　the　well-known　TOPSIS　approach　in　multiple　attribute　decision　making　(MADM).　The　RC　index　is　then　used　as　the　evidence　of　overall　assessment　of　each　DMIJ,　based　on　which　an　overall　ranking　for　all　the　DMUs　can　be　obtained.　Two　numerical　examples　are　provided　to　illustrate　the　applications　of　the　proposed　DEA　models　and　the　RC　index.　(c)　2005　Elsevier　Inc.　All　rights　reserved.