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 Belohlavek's completely lattice L-ordered sets is discussed.