Cross-efficiency　evaluation　(CEE)　is　an　effective　tool　for　ranking　decision-making　units　(DMUs).　The　traditional　data　envelopment　analysis　(DEA)　model　employs　self-evaluation　to　measure　the　performance　of　DMUs.　CEE,　as　an　extension　of　the　DEA,　includes　self-evaluation　and　peer-evaluation,　assessing　the　overall　performance　of　each　DMU　through　its　own　weights　and　the　weights　of　all　DMUs.　The　current　CEE,　however,　aggregates　self-evaluation　and　peer-evaluation　efficiencies　mostly　via　the　arithmetic　average,　which　underestimates　the　importance　of　self-evaluation　and　ignores　the　subjective　preferences　of　decision-makers　as　well.　To　address　this　deficiency,　considering　the　fairness　mentality　of　decision-makers,　this　paper　first　introduces　the　regret　theory　to　depict　the　regret　aversion　of　decision-makers,　and　proposes　the　fair　regret　cross-efficiency　aggregation　(FRCEA)　method　(Method　1).　Then　the　upper　and　lower　limits　of　the　fair　regret　interval　cross-efficiency　(FRICE)　are　calculated,　and　parameters　reflecting　the　preferences　of　decision-makers　are　introduced.　Next,　this　paper　puts　forth　a　consensus　cross-efficiency　aggregation　(CCEA)　method　(Method　2)　based　on　the　efficiency　expectations　of　DMUs　and　the　actual　aggregation　results.　By　creating　a　fair　evaluation　environment,　this　paper　aims　to　enable　all　DMUs　to　participate　in　the　efficiency　evaluation　and　accept　the　results,　reaching　a　final　consensus.　Finally,　the　effectiveness　and　rationality　of　the　methods　above　are　verified　after　evaluating　the　academic　research　efficiencies　of　13　prestigious　universities　in　China.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2025.