Abstract
The notion of an affine ordered set is specialized to that of a complete affine ordered set, which can be linked to attribute-complete many-valued contexts and is categorically equivalent to the notion of a closed system of equivalence relations (SER). This specialization step enables us to give conditions under which the complete affine ordered set can be interpreted as the set of congruence classes labeled with the congruence relation they stem from yielding a coordinatization theorem for affine ordered sets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davey, B.A., Priestly, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Berlin – Heidelberg – New York (1999)
Ihringer, Th.: Allgemeine Algebra. Teubner, Stuttgart (1993)
Kaiser, T.B.: Representation of Data Contexts and Their Concept Lattices in General Geometric Spaces. In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS 2005. LNCS (LNAI), vol. 3596, pp. 195–208. Springer, Heidelberg (2005)
Kaiser, T.B., Schmidt, S.E.: Geometry of Data Tables. In: Eklund, P.W. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 222–235. Springer, Heidelberg (2004)
Pawlak, Z.: Rough Sets - Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht – Boston – London (1991)
Pratt, V.R.: Chu spaces and their interpretation as concurrent objects. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 392–405. Springer, Heidelberg (1995)
Wille, R.: Kongruenzklassengeometrien. Springer, Berlin – Heidelberg – New York (1970)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaiser, T.B. (2008). Closure Systems of Equivalence Relations and Their Labeled Class Geometries. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds) Concept Lattices and Their Applications. CLA 2006. Lecture Notes in Computer Science(), vol 4923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78921-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-78921-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78920-8
Online ISBN: 978-3-540-78921-5
eBook Packages: Computer ScienceComputer Science (R0)