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Operations-Research-Spektrum

, Volume 16, Issue 4, pp 227–241 | Cite as

Visualisierungstechniken in Entscheidungsproblemen bei mehrfacher Zielsetzung

  • Rudolf Vetschera
Entscheidungstheorie

Zusammenfassung

In diesem Beitrag werden Ansätze zur graphischen Darstellung von Elementen von Entscheidungsproblemen bei mehrfacher Zielsetzung vorgestellt. Dabei wird nach den Betrachtungsebenen des Problems zwischen der Darstellung von Entscheidungsvariablen, von Attributwerten sowie von ordinalen und kardinalen Präferenzaussagen unterschieden. Neben der Darstellung der einzelnen Ansätze wird auch auf den damit verbundenen Rechenaufwand sowie mögliche Interpretationsprobleme eingegangen.

Schlüsselwörter

Entscheidungstheorie mehrfache Zielsetzung Graphik Benutzerschnittstelle Übersicht 

Abstract

The paper surveys techniques for visualization in the context of multi-criteria decision problems. Techniques for representing decision variables, attribute values of alternatives, ordinal preference relations and cardinal evaluations are covered. Several techniques are presented for each area, taking into account problems of implementation in interactive systems and cognitive effects that might result from the use of different graphical representations.

Key words

Decision theory multi-criteria decision making graphics user interface survey 

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Literatur

  1. 1.
    Angehrn AA (1991) Triple C: Visual interaction for individual and group decision support. In: Unicom Ltd (Hrsg) Computer supported collective work — the multimedia and networking paradigm. Unicom Seminars Ltd, Uxbridge, pp. 101–109Google Scholar
  2. 2.
    Bamberg G, Coenenberg AG (1992) Betriebswirtschaftliche Entscheidungslehre. 7. Aufl, Vahlen, MünchenGoogle Scholar
  3. 3.
    Belton V, Vickers SP (1993) Demystifying DEA — a visual interactive approach based on multiple criteria analysis. J Oper Res Soc 44:883–896Google Scholar
  4. 4.
    Benayoun R, de Montgolfier J, Tergny J, Laritchev O (1971) Linear programming with multiple objective functions: step method (STEM). Math Program 1:366–375CrossRefGoogle Scholar
  5. 5.
    Benbasat I, Dexter AS, Todd P (1986) An experimental program investigating color enhanced and graphical information presentation: an integration of the findings. Commun ACM 29: 1094–1105CrossRefGoogle Scholar
  6. 6.
    Bruckner LA (1978) On Chernoff faces. In: Wang PCC (Hrsg) Graphical representation of multivariate data. Academic Press, New York, pp 93–121CrossRefGoogle Scholar
  7. 7.
    Chambers JM, Cleveland WS, Kleiner B, Tukey PA (1983) Graphical methods for data analysis. Wadsworth International, Belmont, CAGoogle Scholar
  8. 8.
    Chernoff H (1973) The use of faces to represent points in k-dimensional space graphically. J Am Statist Assoc 68:361–368CrossRefGoogle Scholar
  9. 9.
    Chernoff H, Rizvi MH (1975) Effect on classification error of random permutations of features in representing multivariate data by faces. J Am Statist Assoc 70:548–554Google Scholar
  10. 10.
    Desai A, Walters LC (1991) Graphical presentations of data envelopment analyses: management implications from parallel axes representations. Dec Sci 22:335–353CrossRefGoogle Scholar
  11. 11.
    DeSanctis G (1984) Computer graphics as decision aids: directions for research. Dec Sci 15:463–487CrossRefGoogle Scholar
  12. 12.
    Dickson GW, DeSanctis G, McBride DJ (1986) Understanding the effectiveness of computer graphics for decision support. A cumulative experimental approach. Commun ACM 29:40–47CrossRefGoogle Scholar
  13. 13.
    Dinkelbach W (1992) Operations research. Springer, BerlinCrossRefGoogle Scholar
  14. 14.
    Expert Choice Inc (1990) Expert choice reference manual. PittsburgGoogle Scholar
  15. 15.
    Fandel G (1972) Optimale Entscheidung bei mehrfacher Zielsetzung. Springer, BerlinCrossRefGoogle Scholar
  16. 16.
    Flury B, Riedwyl H (1981) Graphical representation of multivariate data by means of asymmetrical faces. J Am Statist Assoc 76:757–765CrossRefGoogle Scholar
  17. 17.
    Geoffrion AM, Dyer JS, Feinberg A (1972) An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Manag Sci 19:357–368CrossRefGoogle Scholar
  18. 18.
    Hämäläinen RP, Lauri H (1992) HIPRE 3+ user's guide. System Analysis Laboratory, Helsinki University of TechnologyGoogle Scholar
  19. 19.
    Heiler S, Michels P, Abberger K (1992) Abiturzeugnisse und Studienwahl — ein Beispiel zur Anwendung graphischer Verfahren in der Explorativen Datenanalyse. Diskussionsbeitrag 136/s, Universität Konstanz, Fakultät für Wirtschaftswissenschaften und StatistikGoogle Scholar
  20. 20.
    Inselberg A (1985) The plane with parallel coordinates. The Visual Computer 1:69–91CrossRefGoogle Scholar
  21. 21.
    Inselberg A (1986) Multi-dimensional graphics. In: Requicha AAG (Hrsg) EUROGRAPHICS 86. Elsevier, Amsterdam, pp 7–18Google Scholar
  22. 22.
    Jacob RJK (1978) Facial representation of multivariate data. In: Wang PCC (Hrsg) Graphical representation of multivariate data. Academic Press, New York, pp 143–168CrossRefGoogle Scholar
  23. 23.
    Jarvenpaa SL, Dickson GW (1988) Graphics and managerial decision making: research based guidelines. Commun ACM 31: 764–774CrossRefGoogle Scholar
  24. 24.
    Jokinen PA (1994) Visualization of multivariate processes using principal component analysis and nonlinear inverse modelling. Dec Support Syst 11:53–65CrossRefGoogle Scholar
  25. 25.
    Kasanen E, Östermark R, Zeleny M (1991) Gestalt system of holistic graphics: new management support view of MCDM. Comput Oper Res 18:233–239CrossRefGoogle Scholar
  26. 26.
    Kleiner B, Hartigan JA (1981) Representing points in many dimensions by trees and castles. J Am Statist Assoc 76:260–269CrossRefGoogle Scholar
  27. 27.
    Klimberg R (1992) GRADS: A new graphical display system for visualizing multiple criteria solutions. Comp Oper Res 19: 707–711CrossRefGoogle Scholar
  28. 28.
    Korhonen P (1991) Using harmonious houses for visual pairwise comparison of multiple criteria alternatives. Dec Support Syst 7:47–54CrossRefGoogle Scholar
  29. 29.
    Korhonen P (1992) Multiple criteria decision support — the state of research and future directions. Comput Oper Res 19: 549–551CrossRefGoogle Scholar
  30. 30.
    Korhonen P, Laakso J (1986) Solving generalized goal programming problems using a visual interactive approach. Eur J Oper Res 26:355–363CrossRefGoogle Scholar
  31. 31.
    Korhonen P, Moskowitz H, Wallenius J (1992) Multiple criteria decision support — a review. Eur J Oper Res 63:361–375CrossRefGoogle Scholar
  32. 32.
    Kruskal JB (1964) Nonmetric multidimensional scaling: a numerical method. Psychometrica 29:115–129CrossRefGoogle Scholar
  33. 33.
    Laux H (1991) Entscheidungstheorie. 2. Aufl. Springer, BerlinGoogle Scholar
  34. 34.
    Lehert P, de Wasch A (1983) Representation of best buys for a heterogenous population. In: Hansen P (Hrsg) Essays and surveys on multiple criteria decision making. Springer, Berlin, pp 221–228CrossRefGoogle Scholar
  35. 35.
    Lewandowski A, Granat J (1991) Dynamic BIPLOT as an interaction interface for aspiration-based decision support systems. In: Korhonen P, Lewandowski A, Wallenius J (Hrsg) Multiple criteria decision support. Springer, Berlin, pp 229–241Google Scholar
  36. 36.
    Mareschal B, Brans J-P (1988) Geometrical representations for MCDA. Eur J Oper Res 34:69–77CrossRefGoogle Scholar
  37. 37.
    Miller GA (1956) The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Rev 63:81–97CrossRefGoogle Scholar
  38. 38.
    Müller-Merbach H (1991) Entwurf zweidimensionaler Wirtschaftsgraphiken. Technologie und Management 40:24–33Google Scholar
  39. 39.
    Neumann K (1987) Graphen und Netzwerke. In: Gal T (Hrsg) Grundlagen des Operations Research. Springer, Berlin, pp 1–164CrossRefGoogle Scholar
  40. 40.
    Ng W-Y (1991) An interactive descriptive graphical approach to data analysis for trade-off decision in multi-objective programming. Information and Decision Technologies 17:133–149Google Scholar
  41. 41.
    Reeves GR, Franz LS (1985) A simplified interactive multiple objective linear programming procedure. Comput Oper Res 12: 589–610CrossRefGoogle Scholar
  42. 42.
    Rivett PB (1977) Multidimensional scaling for multiobjective policies. Omega 5:367–379CrossRefGoogle Scholar
  43. 43.
    Rivett PB (1980) Indifference mapping for multiple criteria decisions. Omega 8:81–93CrossRefGoogle Scholar
  44. 44.
    Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theory Dec 31:49–73CrossRefGoogle Scholar
  45. 45.
    Schilling DA, McGarity A, ReVelle C (1982) Hidden attributes and the display of information in multiobjective analysis. Manag Sci 28:236–242CrossRefGoogle Scholar
  46. 46.
    Schreüder WA, van Dyk E (1989) A multidimensional scaling model for qualitative pair wise comparisons. In: Lockett G, Islei G (Hrsg) Improving decision making in organisations. Springer, Berlin, pp 68–77CrossRefGoogle Scholar
  47. 47.
    Sobol MG, Klein G (1989) New graphics as computerized displays for human information processing. IEEE Transact Syst Man, Cybern 19:893–898CrossRefGoogle Scholar
  48. 48.
    Sparrow JA (1989) Graphical displays in information systems: some data properties influencing the effectiveness of alternative forms. Behav Inf Technology 8:43–56CrossRefGoogle Scholar
  49. 49.
    Toussaint KJ, Golden BL (1994) Exchange heuristics to improve base/time plots. Comput Oper Res 21:573–586CrossRefGoogle Scholar
  50. 50.
    Vetschera R (1991) Entscheidungsunterstützende Systeme für Gruppen. Physica, HeidelbergCrossRefGoogle Scholar
  51. 51.
    Vetschera R (1992) A preference-preserving projection technique for MCDM. Eur J Oper Res 61:195–203CrossRefGoogle Scholar
  52. 52.
    Vetschera R (1994) MCView: An integrated graphical system to support multi-attribute decisions. Dec Support Syst 11:363–371CrossRefGoogle Scholar
  53. 53.
    Vetschera R (1994) Visualisation of partial preference relations. Paper presented at EURO XIII, GlasgowGoogle Scholar
  54. 54.
    von Winterfeldt D, Edwards W (1986) Decision analysis and behavioral research. Cambridge University Press, CambridgeGoogle Scholar
  55. 55.
    Warfield JN (1973) On arranging elements of a hierarchy in graphic form. IEEE Transact Syst Man, Cybern 3:121–132CrossRefGoogle Scholar
  56. 56.
    Weber M (1983) Entscheidungen bei Mehrfachzielen — Verfahren zur Unterstützung von Individual- und Gruppenentscheidungen. Gabler, WiesbadenGoogle Scholar
  57. 57.
    Wolwach A (1992) Graphical representation of binary relations on discrete sets of alternatives. Unveröffentlichtes Manuskript, TU DresdenGoogle Scholar
  58. 58.
    Zelasny G (1989) Wie aus Zahlen Bilder werden. Gabler, WiesbadenCrossRefGoogle Scholar
  59. 59.
    Zionts S (1992) Some thoughts on research in multiple criteria decision making. Comput Oper Res 19:567–570CrossRefGoogle Scholar
  60. 60.
    Zionts S, Wallenius J (1976) An interactive programming method for solving the multiple criteria problem. Manag Sci 22: 652–663CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Rudolf Vetschera
    • 1
  1. 1.Fakultät für Wirtschaftswissenschaften und StatistikUniversität KonstanzKonstanzGermany

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