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Modeling Approaches for Median Relations

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Models, Methods and Decision Support for Management

Abstract

In the recent past, different tools have been developed for a more problem-oriented approach to modeling which, in turn, might shorten the problem-solving process itself. For a problem example from qualitative data analysis—determining a median relation—it is illustrated how different modeling/optimizing environments (AMPL, OPL, LPL) as well as a developer environment (ECLiPSe) support a more natural problem formulation. In this context, a brief outline of the programming paradigm of constraint logic programming is given.

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References

  • Aggoun, A., Chan, D., Dufresne, P., Falvey, E., Grant, H., Herold, A., Macartney, G., Meier, M., Miller, D., Mudambi, S., Novello, S., Perez, B., van Rossum, E., Schimpf, J., Shen, K., Tsahageas, P. A., and de Villeneuve, D. H. (1999). ECLiPSe user manual release 4.2. Technical report, IC-Parc, Centre for Planning and Resource Control, Imperial College of Science, Technology and Medicine, London SW7 2AZ.

    Google Scholar 

  • Arditti, D. (1982). Un nouvel algorithme de recherche d’un ordre induit par des comparaisons par paires. Note technique NT/PAA/TIM/MTI/ 811, Centre National d’Études des Télécommunications, Issy-les-Moulineaux, France.

    Google Scholar 

  • Barbut, M. (1961). Médiane, distributivité, éloignements.Publica tions du Centre de Mathématique Sociale, E. P. H. E., 6e section, Paris. (Mathématiques et Sciences humaines, vol. 18 (1980), no. 70 (Été), pp. 531).

    Google Scholar 

  • Barthélemy, J. P. and Monjardet, B. (1981). The median procedure in cluster analysis and social choice theory. Mathematical Social Sciences, 1(3), 235–267.

    Article  Google Scholar 

  • Barthélemy, J. P. and Monjardet, B. (1988). The median procedure in data analysis: New results and open problems. In Bock (1988), pages 309–316.

    Google Scholar 

  • Bock, H. H., editor (1988). Classification and Related Methods of Data Analysis. First Conference of the International Federation of Classification Societies, Rheinisch-Westfälische Technische Hochschule Aachen, June 29 — July 1, 1987. North-Holland, Amsterdam.

    Google Scholar 

  • Brailsford, S. C., Potts, C. N., and Smith, B. M. (1999). Constraint satisfaction problems: Algorithms and applications. European Journal of Operational Research, 119 557–581.

    Article  Google Scholar 

  • Breitinger, S. and Lock, H. C. R. (1995). Using constraint logic programming for industrial scheduling problems. In C. Beierle and L. Plumer, editors, Logic Programming: Formal Methods and Practical Applications, pages 273–299. Elsevier, Amsterdam.

    Google Scholar 

  • de Amorim, S. G., Barthélemy, J.-P., and Ribeiro, C. C. (1992). Clustering and clique partitioning: Simulated annealing and tabu search approaches. Journal of Classification, 9(1), 17–41.

    Article  Google Scholar 

  • de Cani, J. S. (1969). Maximum likelihood paired comparison ranking by linear programming Biometrika, 56(3), 537–545.

    Article  Google Scholar 

  • de Condorcet, M. J. A. N. C. (1785). Essai sur l’Application de l’Analyse it la Probabilité des Décisions Rendues ¨¤ la Pluralité des Voix. Paris. (Reprint Chelsea Publ. 6, New York, 1974).

    Google Scholar 

  • Fourer, R., Gay, D. M., and Kernighan, B. W. (1993). AMPL: A Modeling Language for Mathematical Programming. Duxbury Press/Wadsworth Publishing Company, Belmont, CA.

    Google Scholar 

  • Frühwirth, T. and Abdennadher, S. (1997). Constraint-Programmierung: Grundlagen und Anwendungen. Springer-Lehrbuch. Springer-Verlag, Berlin Heidelberg New York.

    Book  Google Scholar 

  • Goltz, H.-J. and Matzke, D. (1999). University timetabling using constraint logic programming In G. Gupta, editor, Practical Aspects of Declarative Languages, volume 1551 of Lecture Notes in Computer Science, pages 320–334. Springer-Verlag, Berlin Heidelberg New York.

    Google Scholar 

  • Grötschel, M. and Wakabayashi, Y. (1987). A cutting plane algorithm for a clustering problem. Report 9, Institut für Mathematik, Universität Augsburg, Memminger Straße 6, D-8900 Augsburg.

    Google Scholar 

  • Grötschel, M., Jünger, M., and Reinelt, G. (1982). A cutting plane algorithm for the linear ordering problem. WP 82219-OR, Institut für Operations Research, Universität Bonn.

    Google Scholar 

  • Guerinik, N. and van Caneghem, M. (1995). Solving crew scheduling problems by constraint programming. In Montanari and Rossi (1995), pages 481–498.

    Google Scholar 

  • Hürlimann, T. (1998). Reference manual for the LPL modeling language (version 4.30). Working paper, Institute of Informatics, University of Fribourg, site Regina Mundi, rue de Faucigny 2, CH-1700 Fribourg.

    Google Scholar 

  • Jaffar, J. and Maher, M. J. (1987). Constraint logic programming: A survey. Journal of Logic Programming, (19, 20), 503–573.

    Google Scholar 

  • Kanal, L. and Kumar, V. (1988). Search in Artificial Intelligence. Springer-Verlag, New York, Berlin, Heidelberg.

    Book  Google Scholar 

  • Kemeny, J. G. (1959). Mathematics without numbers. Daedalus, 88 577–591.

    Google Scholar 

  • Kowalski, R. (1979). Algorithm = logic + control. Communications of the ACM, 22(7), 424–436.

    Article  Google Scholar 

  • Marcotorchino, J. F. and Michaud, P. (1979). Optimisation en analyse ordinale des données, volume 4 of Statistiques et décisions économiques. Masson, Paris.

    Google Scholar 

  • Marriott, K. and Stuckey, P. J. (1998). Programming with constraints: An introduction. MIT Press, Cambridge, MA.

    Google Scholar 

  • Montanari, U. and Rossi, F., editors (1995). Principles and Practice of Constraint Programming — CP’95, volume 976 of Lecture Notes in Computer Science. Springer-Verlag, Berling-Heidelberg-New York.

    Google Scholar 

  • Rautenberg, W. (1996). Einführung in die mathematische Logik. Vieweg, Braunschweig.

    Google Scholar 

  • Régnier, S. (1965). Sur quelques aspects mathématiques des problèmes de classification automatique. International Computer Centre Bulletin, 4 175–191. Reprint in Mathématiques et Sciences humaines, vol. 21 (1983), no. 82, pp. 13–29.

    Google Scholar 

  • Schader, M. (1981). Scharfe und unscharfe Klassifikation qualitativer Daten, volume 65 of Mathematical systems in economics. Verlagsgruppe Athenäum Hain Scriptor Hanstein, Königsteim/Ts.

    Google Scholar 

  • Schader, M. and Tüshaus, U. (1986). Subgradient methods for analyzing qualitative data. In W. Gaul and M. Schader, editors, Classification as a Tool of Research, Karlsruhe, pages 397–403. North-Holland, Amsterdam.

    Google Scholar 

  • Sterling, L. and Shapiro, E. (1994). The Art of PROLOG: Advanced Programming Techniques. MIT Press series in logic programming MIT Press, Cambridge, MA, 2. edition.

    Google Scholar 

  • Tüshaus, U. (1983). Aggregation binärer Relationen in der qualitativen Datenanalyse, volume 82 of Mathematical Systems in Economics. Athenäum Hain Hanstein, Königstein/Ts.

    Google Scholar 

  • Van Hentenryck, P. (1989). Constraint Satisfaction in Logic Programming. Logic Programming Series. MIT Press, Cambridge, MA.

    Google Scholar 

  • Van Hentenryck, P. (1999). The OPL Optimization Programming Language. MIT Press, Cambridge, MA.

    Google Scholar 

  • Wakabayashi, Y. (1986). Aggregation of Binary Relations: Algorithmic and Polyhedric Investigations. Dissertation, Universität Augsburg.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Operations Research, University der Bundeswehr Hamburg, Germany

    Ulrich Tüshaus

Authors
  1. Ulrich Tüshaus
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Wirtschafts- und Sozialstatistik, University of Jena, Carl-Zeiss-Straße 3, Jena, 07743, Germany

    Peter Kischka

  2. Fachbereich Mathematik, Technical University of Berlin, Straße des 17. Juni 136, Berlin, 10623, Germany

    Rolf H. Möhring

  3. Institut für Statistik und Operations Research, University of Graz, Universitätsstraße 15, Graz, 8010, Austria

    Ulrike Leopold-Wildburger

  4. Forschungsinstitut für Anwendungsorientierte Wissensverarbeitung, University of Ulm, Helmholtzstraße 16, Ulm, 89081, Germany

    Franz-Josef Radermacher

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© 2001 Springer-Verlag Berlin Heidelberg

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Tüshaus, U. (2001). Modeling Approaches for Median Relations. In: Kischka, P., Möhring, R.H., Leopold-Wildburger, U., Radermacher, FJ. (eds) Models, Methods and Decision Support for Management. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57603-4_5

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  • DOI: https://doi.org/10.1007/978-3-642-57603-4_5

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-642-63306-5

  • Online ISBN: 978-3-642-57603-4

  • eBook Packages: Springer Book Archive

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