For a fuzzy subset system ZL, the concepts of a ΔΓL-completion and a ZΓL-completion of a given fuzzy poset (X, e) are introduced and their universal properties are investigated. In this paper, we prove that: (1) the ΔΓL-completion ΔΓL (X) is a join-completion with the universal property; (2) the ZΓL-completion ZΓL (X) is the smallest ZL-complete fuzzy subposet of ΔΓL (X) in the case that ZL is fuzzy subset-hereditary. The results show that the Dedekind-MacNeille completion is a special case of the ZΓL-completion.
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