|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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