Data　envelopment　analysis　(DEA)　is　a　widely　used　approach　for　evaluating　the　relative　efficiency　of　decision-making　units　(DMUs)　in　multiple-input　and　multiple-output　situations.　Although　traditional　DEA　models　use　precise　input–output　data,　real-world　problems　often　involve　mixed　uncertainties,　including　fuzziness　and　stochasticity.　This　paper　focuses　on　dealing　with　situations　where　inputs　and　outputs　have　both　fuzzy　and　stochastic　characteristics,　using　DEA　models　for　efficiency　evaluation.　Through　the　integration　of　the　α-level　approach　and　chance-constrained　programming,　novel　DEA　models　with　fuzzy　stochastic　variables　(FSVs)　are　proposed,　and　deterministic　equivalent　interval　DEA　models　with　linear　constraints　are　provided　to　address　this　problem.　The　main　contributions　and　advantages　of　the　proposed　model　over　existing　DEA　models　with　FSVs　are　fourfold:　(1)　linear　and　always-feasible　models　are　proposed;　(2)　a　fixed　and　uniform　production　boundary　(i.e.,　the　same　set　of　constraints)　is　used　to　measure　the　efficiency　of　DMUs　with　fuzzy　stochastic　input　and　output;　(3)　the　obtained　results　can　distinguish　between　efficient　and　inefficient　DMUs;　(4)　Equivalent　interval　DEA　models　were　obtained　to　provide　a　more　comprehensive　assessment　of　the　efficiency　of　the　DMUs.　Finally,　a　numerical　example　is　presented　to　demonstrate　the　applicability　of　the　proposed　models　and　the　feasibility　of　the　obtained　solutions.　©　The　Author(s)　under　exclusive　licence　to　Taiwan　Fuzzy　Systems　Association　2024.