Authors: Horváth, Eszter K.
Radeleczki, Sándor
Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Computer Science 
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
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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