Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Completion of ordered structures by cuts of fuzzy sets: An overview
Journal: Fuzzy Sets and Systems
Volume: 136
Issue: 1
First page: 1
Last page: 19
Issue Date: 16-May-2003
Rank: M22
ISSN: 0165-0114
DOI: 10.1016/S0165-0114(02)00365-2
Abstract: 
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.
Keywords: Algebra | Canonical representation | Completion | Cut | Fuzzy set | Partially ordered set
Publisher: Elsevier
Project: Serbian Ministry of Science and Technology, Grant No. 1227

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