Convexity in Ordinal Data

  • Selma Strahringer
  • Rudolf Wille
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Convexity is a leading idea in data analysis, although it is mostly involved on an informal level; in particular, convexity in ordinal data has not been elaborated as a well defined tool. This paper presents a first discussion of convexity definitions in connection with examples of ordinal data. One result is that there is more than one definition of ordinal convexity which is meaningful for data analysis. Convexity in multi-varied ordinal data is analysed by methods of formal concept analysis. Some relation to Euclidean convexity is outlined.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Birkhoff, G. (1967): Lattice Theory. Third edition. Amer. Math. Soc., Providence, R. I.Google Scholar
  2. [2]
    Ganter, B., Wille, R. (1989): Conceptual Scaling. In: Roberts, F. (ed.): Applications of combinatorics and graph theory in the biological and social sciences. Springer Verlag, New York, 139–167.Google Scholar
  3. [3]
    Graham, R. L. (1978): Combinatorial Scheduling Theory. In: Steen, L. A. (ed.): Mathematics Today. Springer Verlag, New York, Heidelberg, Berlin, 183–211.Google Scholar
  4. [4]
    Grätzer, G. (1978): General Lattice Theory. Birkhäuser Verlag, Basel, Stuttgart.Google Scholar
  5. [5]
    Wille, R. (1982): Restructing lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.): Ordered Sets. Reidel, Dordrecht-Boston, 445–470.Google Scholar
  6. [6]
    Wille, R. (1988): Tensor products of complete lattices as closure systems. FB 4-Preprint 1123, TH Darmstadt.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • Selma Strahringer
    • 1
  • Rudolf Wille
    • 1
  1. 1.Forschungsgruppe Begriffsanalyse Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtGermany

Personalised recommendations