In　this　paper,　we　investigate　the　problem　of　minimizing　the　ratio　of　normalized　non-negative　monotone　non-submodular　set　function　f　and　normalized　non-negative　monotone　set　function　g.　We　take　advantage　of　the　greedy　technique　and　get　a　performance　guarantee　depending　on　the　generalized　curvature　and　inverse　generalized　curvature　of　f,　as　well　as　the　submodularity　ratio　of　g.　Our　results　generalize　the　works　of　Bai　et　al.　(Algorithms　for　optimizing　the　ratio　of　submodular　functions.　In:　Proceedings　of　the　33rd　International　Conference　on　Machine　Learning,　2016)　and　Qian　et　al.　(Optimizing　ratio　of　monotone　set　functions.　In:　Proceedings　of　the　26th　International　Joint　Conference　on　Artificial　Intelligence,　2017).　©　2019,　Operations　Research　Society　of　China,　Periodicals　Agency　of　Shanghai　University,　Science　Press,　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.