Completion of ordered structures by cuts of fuzzy sets: an overview

Authors:
Branimir Šešelja;Andreja Tepavčević
Affiliations:
Technical Faculty, Department of Mathematics, Institute of Mathematics, University of Novi Sad, Trg D. Obradovic´a 4, 21000 Novi Sad, Yugoslavia;Technical Faculty, Department of Mathematics, Institute of Mathematics, University of Novi Sad, Trg D. Obradovic´a 4, 21000 Novi Sad, Yugoslavia
Venue:
Fuzzy Sets and Systems - Logic and algebra
Year:
2003

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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.