In　the　actual　efficiency　evaluation　process,　it　frequently　occurs　that　the　quantitative　input　and　output　data　of　each　decision-making　unit　is　difficult　to　obtain　due　to　the　limitation　in　data　measurement　and　the　absence　of　prior　information.　Instead,　the　form　of　judgment　information　can　be　selected　to　express　the　input–output　state　of　the　evaluated　decision-making　units　compared　with　the　reference　level.　Traditional　cross-efficiency　evaluation　methods　do　not　involve　this　case　and　cannot　be　well　used　in　this　situation.　Based　on　the　above　problems,　a　multiplicative　cross-efficiency　evaluation　model　with　judgmental　information　is　constructed,　and　the　optimal　adjustment　model　is　provided　by　introducing　deviation　variables　to　deal　with　the　inconsistent　issue　of　data　features.　In　addition,　for　the　case　of　multiple　optimal　solutions,　the　maximizing　and　minimizing　secondary　objective　models　of　the　multiplicative　cross-efficiency　are　established　respectively　to　reasonably　identify　the　corresponding　optimal　weights.　Simultaneously,　in　order　to　effectively　depict　the　interaction　between　decision-making　units,　the　characteristic　functions　of　JM-cross　efficiency　cooperative　game　and　the　multiplicative　Shapley　value　are　established　based　on　benevolent　and　aggressive　cross-efficiency　matrices.　Moreover,　in　order　to　avoid　the　extreme　ranking　results　that　are　oriented　by　high　impact　decision-making　units,　a　series　of　optimization　coordination　models　are　developed,　and　an　optimal　efficiency　ranking　vector　generation　method　with　strong　applicability　and　decision　flexibility　is　proposed.　The　optimal　efficiency　ranking　vector　not　only　creates　a　precise　match　with　the　given　Shapley　index　of　the　multiplicative　cross-efficiency　game,　but　also　bounds　between　the　minimum　and　the　maximum　average　efficiency.　Finally,　the　validity　and　rationality　of　the　discussed　models　are　illustrated　by　a　concrete　example.　©　2023　Elsevier　Ltd