Skip to main content

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 78))

Abstract

Many MCDA models are based on essentially deterministic evaluations of the consequences of each action in terms of each criterion, possibly subjecting final results and recommendations to a degree of sensitivity analysis. In many situations, such an approach may be justified when the primary source of complexity in decision making relates to the multicriteria nature of the problem rather than to the stochastic nature of individual consequences. Nevertheless, situations do arise, especially in strategic planning problems, when risks and uncertainties are as critical as the issue of conflicting management goals. In such situations, more formal modelling of these uncertainties become necessary. In this paper, we start by reviewing the meaning and origin of risk and uncertainty. We recognize both internal uncertainties (related to decision maker values and judgements) and external uncertainties (related to imperfect knowledge concerning consequences of action), but for this paper focus on the latter. Four broad approaches to dealing with external uncertainties are discussed. These are multiattribute utility theory and some extensions; stochastic dominance concepts, primarily in the context of pairwise comparisons of alternatives; the use of surrogate risk measures as additional decision criteria; and the integration of MCDA and scenario planning. To a large extent, the concepts carry through to all schools of MCDA. A number of potential areas for research are identified, while some suggestions for practice are included in the final section.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. H. Azondékon and J.-M. Martel. “Value” of additional information in multicriterion analysis under uncertainty. European Journal of Operational Research, 117:45–62, 1999.

    Google Scholar 

  2. E. Ballestero. Stochastic goal programming: A mean-variance approach. European Journal of Operational Research, 131:476–481, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  3. V. S. Bawa. Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2:95–121, 1975.

    Article  Google Scholar 

  4. M. H. Bazerman. Judgment in Managerial Decision Making. John Wiley & Sons, New York, fifth edition, 2002.

    Google Scholar 

  5. D. E. Bell. One-switch utility functions and a measure of risk. Management Science, 34:1416–1424, 1988.

    MATH  MathSciNet  Google Scholar 

  6. V. Belton and T. J. Stewart. Multiple Criteria Decision Analysis: An Integrated Approach. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  7. M. Beynon, B. Curry, and P. Morgan. The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling. OMEGA: International Journal of Management Science, 28:37–50, 2000.

    Article  Google Scholar 

  8. N.-B. Chang and S. Wang. A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems. European Journal of Operational Research, 99:303–321, 1997.

    MathSciNet  Google Scholar 

  9. N.-B. Chang, C. Wen, and Y. Chen. A fuzzy multi-objective programming approach for optimal management of the reservoir watershed. European Journal of Operational Research, 99:289–302, 1997.

    Google Scholar 

  10. W. D. Cook and M. A. Kress. Multiple criteria decision model with ordinal preference data. European Journal of Operational Research, 54:191–198, 1991.

    Article  Google Scholar 

  11. G. R. D’Avignon and P. Vincke. An outranking method under uncertainty. European Journal of Operational Research, 36:311–321, 1988.

    Google Scholar 

  12. A. Dimitras, R. Slowinski, R. Susmaga, and C. Zopounidis. Business failure prediction using rough sets. European Journal of Operational Research, 114:263–280, 1999.

    Article  Google Scholar 

  13. P. C. Fishburn. Foundations of risk measurement. I. Risk as probable loss. Management Science, 30:396–406, 1984.

    MATH  MathSciNet  Google Scholar 

  14. S. French. Uncertainty and imprecision: modelling and analysis. Journal of the Operational Research Society, 46:70–79, 1995.

    MATH  Google Scholar 

  15. J. Friend. The strategic choice approach. In J. Rosenhead and J. Mingers, editors, Rational Analysis for a Problematic World Revisited, pages 115–149. John Wiley & Sons, Chichester, second edition, 2001.

    Google Scholar 

  16. A. Goicoechea, D. R. Hansen, and L. Duckstein. Multiobjective Decision Analysis with Engineering and Business Applications. John Wiley & Sons, New York, 1982

    Google Scholar 

  17. P. Goodwin and G. Wright. Decision Analysis for Management Judgement. John Wiley & Sons, Chichester, second edition, 1997.

    Google Scholar 

  18. P. Goodwin and G. Wright. Enhancing strategy evaluation in scenario planning: a role for decision analysis. Journal of Management Studies, 38:1–16, 2001.

    Article  Google Scholar 

  19. S. Greco, B. Matarazzo, and R. Slowinski. Rough approximation of a preference relation by dominance relations. European Journal of Operational Research, 117:63–83, 1999.

    Article  Google Scholar 

  20. S. Greco, B. Matarazzo, and R. Slowinski. The use of rough sets and fuzzy sets in MCDM. In T. Gal, T. J. Stewart, and T. Hanne, editors, Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, chapter 14. Kluwer Academic Publishers, Boston, 1999.

    Google Scholar 

  21. S. Greco, B. Matarazzo, and R. Slowinski. Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129:1–47, 2001.

    Article  MathSciNet  Google Scholar 

  22. S. Greco, B. Matarazzo, and R. Slowinski. Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European Journal of Operational Research, 138:247–259, 2002.

    Article  MathSciNet  Google Scholar 

  23. J. Hadar and W. R. Russell. Rules for ordering uncertain prospects. The American Economic Review, 59:25–34, 1969.

    Google Scholar 

  24. C. Harries. Correspondence to what? Coherence to what? What is good scenario-based decision making. Technological Forecasting & Social Change, 70:797–817, 2003.

    Google Scholar 

  25. J. Jia and J. S. Dyer. A standard measure of risk and risk-value models. Management Science, 42:1691–1705, 1996.

    Google Scholar 

  26. D. Kahneman and A. Tversky. Prospect theory: An analysis of decision under risk. Econometrica, 47:263–291, 1979.

    Google Scholar 

  27. R. L. Keeney and H. Raiffa. Decisions with Multiple Objectives. John Wiley & Sons, New York, 1976.

    Google Scholar 

  28. A. J. Keown and B. W. Taylor III. A chance-constrained integer goal programming model for capital budgeting in the production area. Journal of the Operational Research Society, 31:579–589, 1980.

    Google Scholar 

  29. G. Klein, H. Moskowitz, and A. Ravindran. Interactive multiobjective optimization under uncertainty. Management Science, 36:58–75, 1990.

    MathSciNet  Google Scholar 

  30. G. J. Klir and T. A. Folger. Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs, New Jersey, 1988.

    Google Scholar 

  31. A. Korhonen. Strategic financial management in a multinational financial conglomerate: A multiple goal stochastic programming approach. European Journal of Operational Research, 128:418–434, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  32. R. Lahdelma and P. Salminen. Pseudo-criteria versus linear utility function in stochastic multi-criteria acceptability analysis. European Journal of Operational Research, 141:454–469, 2002.

    Article  MathSciNet  Google Scholar 

  33. R. Lahdelma, P. Salminen, and J. Hokkanen. Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria. European Journal of Operational Research, 142:345–356, 2002.

    Article  Google Scholar 

  34. R. R. Levary and K. Wan. A simulation approach for handling uncertainty in the analytic hierarchy process. European Journal of Operational Research, 106:116–122, 1998.

    Article  Google Scholar 

  35. B. Mareschal. Stochastic multicriteria decision making and uncertainty. European Journal of Operational Research, 26:58–64, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  36. J.-M. Martel and K. Zaras. Stochastic dominance in multicriterion analysis under risk. Theory and Decision, 39:31–49, 1995.

    Article  Google Scholar 

  37. I. Millet and W. C. Wedley. Modelling risk and uncertainty with the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis, 11:97–107, 2002.

    Article  Google Scholar 

  38. J. M. Miyamoto and P. Wakker. Multiattribute utility theory without expected utility foundations. Operations Research, 44:313–326, 1996.

    MathSciNet  Google Scholar 

  39. G. S. Parnell, J. A. Jackson, R. C. Burk, L. J. Lehmkuhld, and J. A. Engelbrecht Jr. R&D concept decision analysis: using alternate futures for sensitivity analysis. Journal of Multi-Criteria Decision Analysis, 8:119–127, 1999.

    Article  Google Scholar 

  40. J.-C. Pomerol. Scenario development and practical decision making under uncertainty. Decision Support Systems, 31:197–204, 2001.

    Article  Google Scholar 

  41. D. Rios Insua. Sensitivity Analysis in Multi-Objective Decision Making, volume 347 of Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, 1990.

    Google Scholar 

  42. T. Rosqvist. Simulation and multi-attribute utility modelling of life cycle profit. Journal of Multi-Criteria Decision Analysis, 10:205–218, 2001.

    Article  MATH  Google Scholar 

  43. A. Ruszczyński and A. Shapiro, editors. Stochastic Programming. Handbooks in Operations Research and Management Science, Volume 10. Elsevier, Amsterdam, 2003.

    Google Scholar 

  44. A. Saltelli, A. S. Tarantola, and K. Chan. A role for sensitivity analysis in presenting the results from MCDA studies to decision makers. Journal of Multi-Criteria Decision Analysis, 8:139–145, 1999.

    Article  Google Scholar 

  45. R. K. Sarin and M. Weber. Risk-value models. European Journal of Operational Research, 70:135–149, 1993.

    Article  Google Scholar 

  46. T. J. Stewart. Simplified approaches for multi-criteria decision making under uncertainty. Journal of Multi-Criteria Decision Analysis, 4:246–258, 1995.

    MATH  Google Scholar 

  47. T. J. Stewart. Robustness of additive value function methods in MCDM. Journal of Multi-Criteria Decision Analysis, 5:301–309, 1996.

    Article  MATH  Google Scholar 

  48. T.J. Stewart. Measurements of risk in fisheries management. ORiON, 14:1–15, 1998.

    Google Scholar 

  49. T. J. Stewart. Evaluation and refinement of aspiration-based methods in MCDM. European Journal of Operational Research, 113:643–652, 1999.

    Article  MATH  Google Scholar 

  50. J. Teghem Jr., D. Dufrane, and M. Thauvoye. STRANGE: An interactive method for multi-objective linear programming under uncertainty. European Journal of Operational Research, 26:65–82, 1986.

    Article  MathSciNet  Google Scholar 

  51. B. Urli and R. Nadeau. PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty. European Journal of Operational Research, 155:361–372, 2004.

    Article  MathSciNet  Google Scholar 

  52. K. Van der Heijden. Scenarios: The Art of Strategic Conversation. John Wiley & Sons, Chichester, 1996.

    Google Scholar 

  53. D. von Winterfeldt and W. Edwards. Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge, 1986.

    Google Scholar 

  54. D. W. Watkins Jr., D. C. McKinney, L. S. Lasdon, S. S. Nielsen, and Q. W. Martin. A scenario-based stochastic programming model for water supplies from the highland lakes. International Transactions in Operational Research, 7:211–230, 2000.

    Article  Google Scholar 

  55. G. A. Whitmore. Third order stochastic dominance. The American Economic Review, 60:457–459, 1970.

    Google Scholar 

  56. J.-B. Yang. Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. European Journal of Operational Research, 131:31–61, 2001.

    MATH  MathSciNet  Google Scholar 

  57. C. Yeh, H. Deng, and H. Pan. Multi-criteria analysis for dredger dispatching under uncertainty. Journal of the Operational Research Society, 50:35–43, 1999.

    Google Scholar 

  58. M. R. Yilmaz. An information-expectation framework for decisions under uncertainty. Journal of Multi-Criteria Decision Analysis, 1:65–80, 1992.

    Google Scholar 

  59. H. Zimmermann. An application-oriented view of modeling uncertainty. European Journal of Operational Research, 122:190–198, 2000.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science + Business Media, Inc.

About this chapter

Cite this chapter

Stewart, T.J. (2005). Dealing with Uncertainties in MCDA. In: Multiple Criteria Decision Analysis: State of the Art Surveys. International Series in Operations Research & Management Science, vol 78. Springer, New York, NY. https://doi.org/10.1007/0-387-23081-5_11

Download citation

Publish with us

Policies and ethics