ArticleOriginal scientific text
Title
Classification systems and their lattice
Authors 1
Affiliations
- Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary
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
Bibliography
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Pages:
167-181
Main language of publication
English
Received
2002-10-03
Published
2002
DOI: 10.7151/dmgaa.1056
Exact and natural sciences