Classification systems and their lattice
Discussiones Mathematicae - General Algebra and Applications (2002)
- Volume: 22, Issue: 2, page 167-181
- ISSN: 1509-9415
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topSándor Radeleczki. "Classification systems and their lattice." Discussiones Mathematicae - General Algebra and Applications 22.2 (2002): 167-181. <http://eudml.org/doc/287635>.
@article{SándorRadeleczki2002,
abstract = {We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.},
author = {Sándor Radeleczki},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {concept lattice; CJ-generated complete lattice; atomistic complete lattice; (independent) classification system; classification lattice; box lattice; classification system},
language = {eng},
number = {2},
pages = {167-181},
title = {Classification systems and their lattice},
url = {http://eudml.org/doc/287635},
volume = {22},
year = {2002},
}
TY - JOUR
AU - Sándor Radeleczki
TI - Classification systems and their lattice
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 2
SP - 167
EP - 181
AB - We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.
LA - eng
KW - concept lattice; CJ-generated complete lattice; atomistic complete lattice; (independent) classification system; classification lattice; box lattice; classification system
UR - http://eudml.org/doc/287635
ER -
References
top- [1] R. Beazer, Pseudocomplemented algebras with Boolean congruence lattices, J. Austral. Math. Soc. 26 (1978), 163-168. Zbl0389.06004
- [2] B. Ganter and R. Wille, Formal Concept Analysis. Mathematical Foundations, Springer-Verlag, Berlin 1999. Zbl0909.06001
- [3] S. Radeleczki, Concept lattices and their application in Group Technology (Hungarian), 'Proceedings of International Computer Science Conference: microCAD'98 (Miskolc, 1998)', University of Miskolc 1999, 3-8.
- [4] S. Radeleczki, Classification systems and the decomposition of a lattice into direct products, Math. Notes (Miskolc) 1 (2000), 145-156. Zbl1062.06008
- [5] E.T. Schmidt, A Survey on Congruence Lattice Representations, Teubner-texte zur Math., Band 42, Leipzig 1982.
- [6] M. Stern, Semimodular Lattices. Theory and Applications, Cambridge University Press, Cambridge 1999. Zbl0957.06008
- [7] R. Wille, Subdirect decomposition of concept lattices, Algebra Universalis 17 (1983), 275-287. Zbl0539.06006
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