Group　decision-making　(GDM)　is　essential　as　it　recognizes　the　inherent　complexity　of　many　decision　scenarios,　which　frequently　require　the　collective　wisdom　and　knowledge　of　multiple　decision-makers　(DMs)　to　be　effectively　resolved.　The　proposed　method　aims　to　develop　fuzzy　data　envelopment　analysis　(DEA)　cross-efficiency　models　tailored　to　address　GDM　challenges,　wherein　attribute　values　are　provided　by　DMs　using　hesitant　fuzzy　linguistic　term　sets　(HFLTSs).　For　this　purpose,　we　initially　transform　HFLTSs　into　their　corresponding　fuzzy　envelopes,　defined　as　trapezoidal　fuzzy　numbers　(TrFNs).　This　conversion　strategy　effectively　minimizes　the　loss　in　assessments　based　on　HFLTSs　while　retaining　the　inherent　ambiguity　of　the　original　information.　Building　upon　this　foundation,　we　develop　fuzzy　cross-efficiency　models　by　leveraging　the　alpha-level　sets　of　fuzzy　envelopes.　These　models　are　designed　to　handle　fuzzy　input　and　output　variables　under　various　alpha-level　sets,　which　are　capable　of　considering　all　possible　attribute　values　for　each　alternative.　Following　this,　we　implement　a　maximum　consensus　model　using　fuzzy　cross-efficiency　to　assign　weights　to　DMs.　These　weights　facilitate　the　aggregation　of　individual　fuzzy　cross-efficiency　intervals　obtained　from　DMs＇　assessments　into　collective　ones,　which　serve　to　rank　alternatives.　Finally,　we　showcase　the　effectiveness　and　superiority　of　our　proposal　through　numerical　validation　and　comparative　analysis.