L-fuzzy interiors and L-fuzzy closures

In this paper, we introduce new definitions of L-fuzzy neighborhood systems, L-fuzzy interior operators and L-fuzzy closure operators. Three characterizations of the category L-FTOP of L-fuzzy topological spaces and their L-fuzzy continuous mappings are presented by means of the category L-FNS of L-fuzzy neighborhood spaces and their continuous mappings, the category L-FIS of L-fuzzy interior spaces and their L-fuzzy continuous mappings, and the category L-FCS of L-fuzzy closure spaces and their L-fuzzy continuous mappings.