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For <i>L</i> a complete co-residuated lattice and <i>R</i> an <i>L</i>-fuzzy relation, an <i>L</i>-fuzzy upper approximation operator based on co-implication adjoint with <i>L</i> is constructed and discussed. It is proved that, when <i>L</i> is regular, the new approximation operator is the dual operator of the Qiao–Hu <i>L</i>-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the <i>L</i>-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean <i>L</i>-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.