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Algorithms and Order pp 33–58Cite as

Lattices in Data Analysis: How to Draw Them with a Computer

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Part of the book series: NATO ASI Series ((ASIC,volume 255))

Abstract

There is a growing demand for lattice diagrams in concept analysis and for this computer programs are needed. The diagrams should not only reflect the structure of the concept lattices but also unfold views for interpreting the data. Therefore different methods of decomposing and representing concept lattices are discussed to clarify how computer programs can be designed for drawing such lattices. Examples are given too.

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References

  1. B. Banaschewski: Hüllensysteme und Erweiterungen von Quasi-Ordnungen. Z. Math. Logik Grundlagen Math. 2 (1956), 117–130.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Bouchet: Etude combinatoire des ordonnes finis. Applications. Thèse de Doctorat d’Etat. Univ. Sci. et Méd., Grenoble 1971.

    Google Scholar 

  3. O. Cogis: La dimension Ferrers des graph orientés. Thèse de Doctorat d’Etat. Univ. P. et M. Curie, Paris 1980.

    Google Scholar 

  4. J. Czyzowicz, A. Pelc, I. Rival: Drawing orders with few slopes. Preprint TR-87–12, Univ. of Ottawa 1987.

    Google Scholar 

  5. V. Duquenne: What can lattices do for experimental designs? Math. Soc. Sci. 11 (1986), 243–281.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Encarnacao, L. Messina, G. Rahmstorf: Systemkonfigurationen als Gegenstand der Wissensrepräsentation. Lecture at the IBM-Workshop “Wissensrepräsentation in Expertensystemen”, Herrenberg 1987.

    Google Scholar 

  7. K. Ferber, H. Jürgensen: A programme for the drawing of lattices. In: J. Leech (ed.): Computational problems in abstract algebra. Pergamon, Oxford & New York 1969, 83–87.

    Google Scholar 

  8. B. Ganter: Algorithmen zur Formalen Begriffsanalyse. In: B. Ganter, R. Wille, K.E. Wolff: Beiträge zur Begriffsanalyse. B.I. Wissenschaftsverlag, Mannheim 1987.

    Google Scholar 

  9. B. Ganter, J. Stahl, R. Wille: Conceptual measurement and many-valued contexts. In: W. Gaul, M. Schader (eds.): Classification as a tool of research. North-Holland, Amsterdam 1986, 169–176.

    Google Scholar 

  10. H. Jürgensen, J. Loewer: Drawing Hasse diagrams of partially ordered sets. In: G. Kalmbach: Orthomodular Lattices. Academic Press, London 1983, 331–345.

    Google Scholar 

  11. P. Luksch: Zur Konstruktion endlicher modularer Verbände, die von Ketten frei erzeugt sind. Diplomarbeit, FB Mathematik, TH Darmstadt 1984.

    Google Scholar 

  12. P. Luksch, M. Skorsky, R. Wille: On drawing concept lattices with a computer. In: W. Gaul, M. Schader (eds.): Classification as a tool of research. North-Holland, Amsterdam 1986, 269–274.

    Google Scholar 

  13. P. Luksch, R. Wille: Substitution decomposition of concept lattices. In: J. Czermak, G. Eigenthaler, H.K. Kaiser, W.B. Müller, W. Nöbauer (eds.): Contributions to general algebra 5. Hölder-Pichler-Tempsky, Wien 1987, 213–220.

    Google Scholar 

  14. P. Luksch, R. Wille: Formal concept analysis of paired comparisons. In: H.H. Bock (ed.): Classification and related methods of data analysis. North-Holland, Amsterdam (to appear).

    Google Scholar 

  15. M. Lutz: Computergraphik von Begriffsverbänden. Forschungs- und Arbeitsbericht, FG Graphisch-Interaktive Systeme, GRIS 87–1, TH Darmstadt 1987.

    Google Scholar 

  16. J. Riguet: Les relations de Ferrers. C.R. Acad. Sci. Paris 232 (1951), 1729–1730.

    MathSciNet  MATH  Google Scholar 

  17. J. Schmidt: Zur Kennzeichnung der Dedekind-MacNeilleschen Hülle einer geordneten Menge. Arch. Math. 7 (1956), 241–249.

    Article  MATH  Google Scholar 

  18. M. Skorsky: Handbuch für Benutzer und Programmierer des Programmpakets ANACONDA. FB Mathematik, TH Darmstadt 1986.

    Google Scholar 

  19. N. Spangenberg, K.E. Wolff: Conceptual GRID-evaluation. In: H.H. Bock (ed.): Classification and related methods of data analysis. North-Holland, Amsterdam (to appear).

    Google Scholar 

  20. J. Stephan: Liniendiagramme von Verbänden. Diplomarbeit, FB Mathematik, TH Darmstadt 1987.

    Google Scholar 

  21. H. Wagner: Begriff. In: Handbuch philosophischer Grundbegriffe. Kösel, München 1973, 191–209.

    Google Scholar 

  22. R. Wille: Subdirekte Produkte vollständiger Verbände. J. reine angew. Math. 283/284 (1976), 53–70.

    Article  MathSciNet  Google Scholar 

  23. R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.): Ordered sets. Reidel, Dordrecht-Boston 1982, 445–470

    Google Scholar 

  24. R. Wille: Subdirect decomposition of concept lattices. Algebra Universalis 17 (1983), 275–287.

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Wille: Complete tolerance relations of concept lattices. In: G. Eigenthaler, H.K. Kaiser, W.B. Müller, W. Nöbauer (eds.): Contributions to general algebra 3. Hölder-Pichler-Tempsky, Wien 1985, 397–415.

    Google Scholar 

  26. R. Wille: Tensorial decomposition of concept lattices. Order 2 (1985), 81–95

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Wille: Liniendiagramme hierarchischer Begriffssysteme. In: H.H. Bock (ed.): Anwendungen der Klassifikation: Datenanalyse und numerische Klassifikation. INDEKS Verlag, Frankfurt 1984, 77–86;

    Google Scholar 

  28. R. Wille: Line diagrams of hierarchical concept systems (engl. transl.). International Classification 11 (1984), 77–86.

    Google Scholar 

  29. R. Wille: Finite distributive lattices as concept lattices. Atti Inc. Logica Matematica (Siena) 2 (1985), 635–648.

    Google Scholar 

  30. R. Wille: Subdirect product construction of concept lattices. Discrete Mathematics 63 (1987), 305–313.

    Article  MathSciNet  MATH  Google Scholar 

  31. R. Wille: Bedeutungen von Begriffsverbänden. In: B. Ganter, R. Wille, K.E. Wolff (eds.): Beiträge zur Begriffsanalyse. B.I.-Wissenschaftsverlag, Mannheim 1987.

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule, D-6100, Darmstadt, Germany

    Rudolf Wille

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  1. Rudolf Wille
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Editors and Affiliations

  1. Departments of Computer Science and Mathematics, University of Ottawa, Ottawa, Canada

    Ivan Rival

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© 1989 Kluwer Academic Publishers

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Wille, R. (1989). Lattices in Data Analysis: How to Draw Them with a Computer. In: Rival, I. (eds) Algorithms and Order. NATO ASI Series, vol 255. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2639-4_2

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  • DOI: https://doi.org/10.1007/978-94-009-2639-4_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7691-3

  • Online ISBN: 978-94-009-2639-4

  • eBook Packages: Springer Book Archive

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