In this paper, the notions of (concave) (L, M)-fuzzy interior operators are introduced. It
is proved that the category of (L, M)-fuzzy concave spaces and the category of concave
(L, M)-fuzzy interior spaces is isomorphic, and there is aGalois correspondence between the
category of (L, M)-fuzzy concave spaces and the category of (L, M)-fuzzy interior spaces. In
addition, (L, M)-fuzzy hull operators proposed by Sayed et al. (Filomat 33(13):4151–4163,
2019) are further studied. Particularly, some results in Sayed et al. (2019) are corrected.