Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 167-181
doi: 10.7151/dmgaa.1056

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CLASSIFICATION SYSTEMS AND THEIR LATTICE

Sándor Radeleczki

Institute of Mathematics, University of Miskolc
3515 Miskolc-Egyetemváros, Hungary
e-mail: matradi@gold.uni-miskolc.hu

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.

Keywords: concept lattice, CJ-generated complete lattice, atomistic complete lattice, (independent) classification system, classification lattice, box lattice.

2000 AMS Mathematics Subject Classification: Primary 06B05, 06B15; Secondary 06B23.

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Received 3 October 2002