The Dedekind–MacNeille completions for fuzzy posets

In this paper, the Dedekind–MacNeille completion for an L-fuzzy poset, previously introduced by the authors, is built and characterized, which generalizes the Dedekind–MacNeille completion for an ordinary poset. The relationship between the L-fuzzy complete lattices defined by the authors and Bělohlávekʹs completely lattice L-ordered sets is discussed.