Mathematicae General Algebra and Applications 22(2) (2002)
CLASSIFICATION SYSTEMS AND THEIR LATTICE
Institute of Mathematics, University of Miskolc
3515 Miskolc-Egyetemváros, Hungary
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
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