Context Comparison and Conceptual Measurability

  • Bernhard Ganter
  • Rudolf Wille


Maps between concept lattices that can be used for structure comparison are above all the complete homomorphisms. In Section 3.2 we have worked out the connection between compatible subcontexts and complete congruences, i.e., the kernels of complete homomorphisms. A further approach consists in coupling the lattice homomorphisms with context homomorphisms. In this connection, it seems reasonable to use pairs of maps, i.e., to map the objects and the attributes separately. Those pairs can be treated like maps. We do so without further ado and write, for instance,
$$(\alpha ,\beta ):(G,M,I) \to (H,N,J),$$
if we mean a pair of maps \( \alpha :G \to H,\beta :M \to N, \) using the usual notations for maps by analogy. This does not present any problems, since in the case that \( G \cap M = + H \cap N \) we can replace such a pair of maps (α,β) by the map
$$\alpha \cup \beta :G\dot \cup M \to H\dot \cup N$$


Concept Lattice Attribute Concept Object Concept Galois Connection Lattice Homomorphism 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Bernhard Ganter
    • 1
  • Rudolf Wille
    • 2
  1. 1.Institut für Algebra, Fakultät für Mathematik und NaturwissenschaftenTechnische Universität DresdenDresdenGermany
  2. 2.Arbeitsgruppe Allgemeine Algebra Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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