Affiliations: [a] School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Songjiang, Shanghai, PR China | [b] School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Songjiang, Shanghai, PR China | [c] Fuzhou Teachers’ College, East China University of Technology, Fuzhou, Jiangxi, PR China
Correspondence:
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Corresponding authors. Shuhua Su, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Songjiang, Shanghai 201620, PR China. E-mail: [email protected] and Shuqun Yang, School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Songjiang, Shanghai 201620, PR China. E-mail: [email protected].
Abstract: 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.
