Strong fuzzy compact sets and ultra-fuzzy compact sets in L-topological spaces

In this paper, Lowenʹs strong fuzzy compactness and ultra-fuzzy compactness of I-topological spaces are extended to L-subsets, for L—a complete lattice. The properties of strong fuzzy compact L-subsets and ultra-fuzzy compact L-subsets are studied in detail here, and comparisons between these notions as well as the notion of N-compactness are shown.