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Completion of ordered structures by cuts of fuzzy sets: An overview. (English) Zbl 1020.06005

Summary: The aim of the paper is to present a role of fuzzy sets in the theory of ordered structures. Main algebraic properties of cuts of fuzzy sets are given, and a completion of partially ordered sets to complete lattices is described. It turns out that this completion is equivalent with the famous Dedekind-MacNeille completion, but the algorithm presented here is much simpler.

MSC:

06B23 Complete lattices, completions
03E72 Theory of fuzzy sets, etc.
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