Abstract
Although ordinal data occur in high frequency, a structure theory for ordinal data exists only in fragments. For a systematic development of such a theory, we propose a basic notion of ordinal structures (ordinal contexts). Since interpretations of data are always based on concepts and their relations, we assign to each ordinal structure a canonical conceptual structure modelled by methods of formal concept analysis. This allows, in particular, to develop a substantial theory of ordinal dimensionality. The theoretical results are demonstrated by examples.
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References
BERGE, C. (1989), Hypergraphs: Combinatorics of Finite Sets, North-Holland, Amsterdam, New York, Oxford, Tokyo.
BIRKHOFF, G. (1967), Lattice Theory, 3rd ed., Amer. Math. Soc., Providence, R. I.
BRÜGGEMANN, R., and HALFON, E. (1990), Ranking analysis of contaminated sites along the shores of Lake Ontario, submitted to Canadian Journal of Fisheries and Aquatic Sciences.
COOMBS, C.H. (1964), A Theory of Data, Wiley, New York.
DILWORTH, R.P. (1950), A decomposition theorem for partially ordered sets, Ann. of Math., (2) 51, 161–166.
GANTER, B., and WILLE, R. (1989), Conceptual Scaling, in: Applications of combinatorics and graph theory to the biological and social sciences, ed. F. Roberts; Springer, New York, 139–167.
GANTER, B., and WILLE, R. (1991), Formale Begriffsanalyse,BI-Wissenschaftsverlag (to appear).
KRANTZ, D.H., LUCE, R.D., SUPPES, P., and TVERSKY, A. (1971), Foundations of Measurement, Vol. I, Academic Press, New York.
PFANZAGL, J. (1968) Theory of Measurement, Physica-Verlag, Würzburg-Wien.
ROBERTS, F.S. (1979), Measurement Theory, Addison-Wesley, Reading, Mass.
STRAHRINGER, S., and WILLE, R. (1991), Convexity in Ordinal Data, in: Classification, Data Analysis, and Knowledge Organization, eds. H.H. Bock and P. Ihm, Springer, Berlin-Heidelberg, 113–120.
WAGNER, H. (1973), Begriff, Handbuch philosophischer Grundbegriffe,Kösel, München, 191–209.
WILLE, R. (1982), Restructing lattice theory: an approach based on hierarchies of concepts, in: Ordered Sets, ed. I. Rival, Reidel, Dordrecht-Boston, 445–470.
WILLE, R. (1984), Liniendiagramme hierarchischer Begriffssysteme, in: Anwendungen der Klas- sifikation: Datenanalyse und numerische Klassifikation, ed. H.H. Bock, Indeks Verlag, Frankfurt, 32–51; engl. translation: Line diagrams of hierarchical concept systems, Int. Classif., 11, 77–86.
WILLE, R. (1985), Finite distributive lattices as concept lattices, Atti Inc. Logica Mathematica, 2, 635–648.
WILLE, R., and WILLE, U. (1989), On the controversy over Huntington’s equations: When are such equations meaningful?, FB4-Preprint 1245, TH Darmstadt.
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© 1992 Springer-Verlag Berlin · Heidelberg
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Strahringer, S., Wille, R. (1992). Towards a Structure Theory for Ordinal Data. In: Schader, M. (eds) Analyzing and Modeling Data and Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46757-8_14
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DOI: https://doi.org/10.1007/978-3-642-46757-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54708-2
Online ISBN: 978-3-642-46757-8
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