Let　G　be　a　graph　with　order　n　and　G¯　be　its　complement.　In　1956,　Nordhaus　and　Gaddum　showed　that　2n⩽χ(G)+χ(G¯)⩽n+1　and　n⩽χ(G)χ(G¯)⩽(n+1)2/4,　where　χ(G)　and　χ(G¯)　are　the　chromatic　numbers　of　G　and　G¯,　respectively.　The　Nordhaus–Gaddum-type　problems　focus　on　the　sum　or　product　of　some　invariants　of　a　graph　and　its　complement.　In　this　paper,　we　introduce　an　edge-shift　operation　and　determine　the　extremal　hypergraphs,　which　attain　the　extremal　value　of　the　sum　of　spectral　radius　or　transversals　for　a　uniform　hypergraph　and　its　complement.　The　spectral　radius　is　the　maximal　absolute　value　of　eigenvalues　of　the　adjacency　tensor　of　a　hypergraph,　and　transversal　number　is　the　minimum　cardinality　of　a　vertex　subset,　which　has　a　nonempty　intersection　with　each　edge.　Furthermore,　we　also　discuss　some　relations　between　spectral　invariants　and　transversal　numbers　of　uniform　hypergraphs.　©　Operations　Research　Society　of　China,　Periodicals　Agency　of　Shanghai　University,　Science　Press,　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2025.