Copyright © 2012 Hongping Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of the category of L-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions of L-posets and provide an equivalent description for them.