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

共 50 条

[31] Algebraic Study of Lattice-Valued Logic and Lattice-Valued Modal Logic
Maruyama, Yoshihiro
LOGIC AND ITS APPLICATIONS, 2009, 5378 : 170 - 184
[32] SOME PROBLEMS ON THE LATTICE-VALUED LOWER SEMICONTINUOUS FUNCTIONS
LI, YM
CHINESE SCIENCE BULLETIN, 1992, 37 (14): : 1228 - 1229
[33] Locally sensitive lattice-valued possibilistic entropy functions
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou vezí 2, 182 07 Prague 8, Czech Republic
Neural Network World, 2008, 6 (469-488)
[34] Cut approach to invariance groups of lattice-valued functions
Horvath, Eszter K.
Seselja, Branimir
Tepavcevic, Andreja
SOFT COMPUTING, 2017, 21 (04) : 853 - 859
[35] Lattice-valued finite state machines and lattice-valued transformation semigroups
Gomez, M.
Lizasoain, I.
Moreno, C.
FUZZY SETS AND SYSTEMS, 2012, 208 : 1 - 21
[36] Lattice-Valued Interval Operators and Its Induced Lattice-Valued Convex Structures
Pang, Bin
Xiu, Zhen-Yu
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2018, 26 (03) : 1525 - 1534
[37] Lattice-valued continuous convergence is induced by a lattice-valued uniform convergence structure
Jaeger, Gunther
FUZZY SETS AND SYSTEMS, 2006, 157 (20) : 2715 - 2724
[38] Lattice-valued betweenness relations and its induced lattice-valued convex structures
Shi, Yi
Shi, Fu-Gui
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2019, 37 (06) : 8523 - 8533
[39] On the aspects of enriched lattice-valued topological groups and closure of lattice-valued subgroups
Ahsanullah, T. M. G.
Al-Thukair, Fawzi
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2021, 14 (03): : 949 - 968
[40] Decision Making with Uncertainty Information Based on Lattice-Valued Fuzzy Concept Lattice
Yang, Li
Xu, Yang
JOURNAL OF UNIVERSAL COMPUTER SCIENCE, 2010, 16 (01) : 159 - 177

← 1 2 3 4 5 →