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

被引：0

作者：

Horvath, Eszter K. ^{[1
]}

Radeleczki, Sandor ^{[2
]}

Seselja, Branimir ^{[3
]}

Tepavcevic, Andreja ^{[3
,4
]}

机构：

[1] Univ Szeged, Bolyai Inst, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary

[2] Univ Miskolc, Dept Anal, H-3515 Miskolc, Hungary

[3] Univ Novi Sad, Fac Sci, Dept Math & Informat, Novi Sad, Serbia

[4] Math Inst SANU, Belgrade, Serbia

来源：

MATHEMATICA SLOVACA | 2023年 / 73卷 / 03期

关键词：

Lattice-valued functions; formal context; concept lattice; Dedekind-MacNeille completion; cuts;

D O I：

10.1515/ms-2023-0043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：583 / 594

页数：12

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