Inverse　data　envelopment　analysis　(DEA),　which　is　an　effective　tool　for　determining　inputs　and　outputs,　is　commonly　applied　in　areas　such　as　output　prediction,　resource　allocation,　and　target　setting.　However,　existing　inverse　DEA　methods　typically　assume　precise　and　deterministic　data,　which　limits　applicability　in　uncertain　production　environments,　particularly　when　both　random　and　fuzzy　environments　are　present.　This　study　introduces　a　novel　inverse　DEA　approach　for　optimizing　inputs　and　outputs　in　mixed　uncertainty　environments.　The　proposed　model　allows　decision-makers　to　achieve　target　efficiency　and　meet　various　input/output　targets　under　different　production　scale　assumptions.　First,　a　new　optimality　principle　for　multi-objective　fuzzy　random　problems　is　presented　and　the　necessary　theoretical　conditions　for　input/output　calculations　are　derived.　Second,　an　equivalent　linear　model　is　introduced　to　solve　the　inverse　DEA　problem　with　fuzzy　random　variables,　thereby　overcoming　the　challenges　associated　with　nonlinear　programming.　Notably,　the　proposed　model　offers　enhanced　flexibility　as　it　does　not　rely　on　specific　fuzzy　numbers　or　predefined　assumptions　regarding　random　distributions.　Finally,　the　effectiveness　of　the　model　is　validated　through　numerical　examples　and　a　case　study,　demonstrating　its　practical　application　in　complex　decision-making　scenarios.