Fuzzy complete lattices

In this paper, based on L-fuzzy posets previously introduced by the third author, L-fuzzy complete lattices are defined, which are generalizations of usual complete lattices and coincide with Wagner's complete and cocomplete Ω-categories enriched over the frame L, and are consequently a special kind of complete Ω-lattices defined by Lai and Zhang. However, Tarski fixed-point theorem for the L-fuzzy complete lattices is proved in a different way from that by Lai and Zhang. Furthermore, some fuzzy powerset operators are suggested, they are not only generalizations of ordinary powerset operators, but also generalizations of L-valued Zadeh powerset operators, and their properties are discussed.