A Note on Cuts of Lattice-Valued Functions and Concept Lattices-Reference-Cited by-同舟云学术

A Note on Cuts of Lattice-Valued Functions and Concept Lattices

Published:2023-06-01 Issue:3 Volume:73 Page:583-594
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Horváth Eszter K.¹,Radeleczki Sándor²,Šešelja Branimir³,Tepavčević Andreja⁴

Affiliation:

1. * Bolyai Institute, University of Szeged , Aradi vértanúk tere 1 , Szeged , HUNGARY

2. ** Department of Analysis, University of Miskolc , Miskolc-Egyetemváros , HUNGARY

3. *** Department of Mathematics and Informatics, University of Novi Sad, Faculty of Sciences , Novi Sad , SERBIA

4. **** Department of Mathematics and Informatics, University of Novi Sad, Faculty of Sciences, Novi Sad, Mathematical Institute SANU , Belgrade , SERBIA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0043/pdf

Reference18 articles.

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2. Ganter, B.—Wille, R.: Formal Concept Analysis, Mathematical Foundations, Springer, 1999.

3. Goguen, J. A.: L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145–174.

4. Horváth, E. K.—Radeleczki, S.—Šešelja, B.—Tepavčević, A.: Cuts of poset-valued functions in the framework of residuated maps, Fuzzy Sets and Systems 397 (2020), 28–40.

5. Horváth, E. K.—Šešelja, B.—Tepavčević, A.: Isotone lattice-valued Boolean functions and cuts, Acta Sci. Math. Szeged 81 (2015), 375–80.