On the connection between many-valued contexts and general geometric structures
- 67 Downloads
We study the connection between certain many-valued contexts and general geometric structures. The known one-to-one correspondence between attribute-complete many-valued contexts and complete affine ordered sets is used to extend the investigation to π-lattices, class geometries, and lattices with classification systems. π-lattices are identified as a subclass of complete affine ordered sets, which exhibit an intimate relation to concept lattices closely tied to the corresponding context. Class geometries can be related to complete affine ordered sets using residuated mappings and the notion of a weak parallelism. Lattices with specific sets of classification systems allow for some sort of “reverse conceptual scaling”.
KeywordsMany-valued contexts Affine ordered sets (Concept) lattices General geometric structures Conceptual scaling
Mathematics Subject Classification (2010)06
Unable to display preview. Download preview PDF.
- 2.Ganter, B., Wille, R.: Conceptual scaling. In: Roberts, F. (ed.) Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, pp. 139–167. Springer, Berlin, Heidelberg, New York (1989)Google Scholar
- 7.Kaiser, T.B.: Connecting many-valued contexts to general geometric structures. In: Conference Proceedings Concept Lattices and Applications (CLA08). Olomouc (2008)Google Scholar
- 8.Kaiser, T.B.: From Data Tables to General Geometric Structures. Dissertation, Shaker, Aachen (2008)Google Scholar
- 10.Körei, A., Radeleczki S.: Box elements in a concept lattice. In: Ganter, B., Kwuida, L. (eds.) Contributions to ICFCA 2006, pp. 41–55. Verlag Allgemeine Wissenschaft (2006)Google Scholar
- 13.Vogt, F., Wachter, C., Wille, R.: Data analysis based on a conceptual file. In: Bock, H.H., Ihm, P. (eds.) Classification, Data Analysis and Knowledge Organization, pp. 131–142. Springer, Berlin, Heidelberg (1991)Google Scholar