|Authors:||Horváth, Eszter K.
Mathematical Institute of the Serbian Academy of Sciences and Arts
|Title:||A Note on Cuts of Lattice-Valued Functions and Concept Lattices||Journal:||Mathematica Slovaca||Volume:||73||Issue:||3||First page:||583||Last page:||594||Issue Date:||2023||Rank:||~M21||ISSN:||0139-9918||DOI:||10.1515/ms-2023-0043||Abstract:||
Motivated by applications of lattice-valued functions (lattice-valued fuzzy sets) in the theory of ordered structures, we investigate a special kind of posets and lattices induced by these mappings. As a framework, we use the Formal Concept Analysis in which these ordered structures can be naturally observed. We characterize the lattice of cut sets and the Dedekind-MacNeille completion of the set of images of a lattice valued function by suitable concept lattices and we give necessary and sufficient conditions under which these lattices coincide. In addition, we give conditions under which the lattice of cuts is completely distributive.
|Keywords:||concept lattice | cuts | Dedekind-MacNeille completion | formal context | Lattice-valued functions||Publisher:||De Gruyter|
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