Cross-efficiency　evaluation　methods　have　long　been　suggested　as　an　alternative　for　the　ranking　of　decision　making　units　(DMUs)　in　data　envelopment　analysis　(DEA).　Neutral　cross-efficiency　evaluation　methods　have　been　developed　in　a　way　that　is　only　concerned　with　their　own　interests　and　are　indifferent　to　other　DMUs.　This　paper　proposes　a　new　cross-efficiency　evaluation　method　in　which　each　DMU　has　a　neutral　attitude　to　its　peers.　This　is　done　by　introducing　an　ideal　virtual　frontier　(IVF)　and　an　anti-ideal　virtual　frontier　(AVF).　Unlike　current　neutral　cross-efficiency　evaluation　methods,　this　cross-efficiency　evaluation　method　determines　one　set　of　input　and　output　weights　for　each　DMU,　aiming　to　improve　the　DMU＇s　performance　by　taking　the　IVF　and　AVF　as　evaluation　criteria.　This　is　done　by　minimizing　the　deviation　of　a　DMU　from　the　IVF　and　maximizing　the　deviation　of　the　DMU　from　the　AVF.　As　a　result,　the　cross-efficiencies　measured　by　these　new　DEA　models　are　neutral　and　more　logical.　Numerical　examples　are　provided　to　illustrate　the　potential　applications　of　these　new　DEA　models　and　their　effectiveness　in　ranking　DMUs.　©　2019　Elsevier　Ltd