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Modeling uncertainty in multi-criteria decision analysis

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  • Durbach, Ian N.
  • Stewart, Theodor J.

Abstract

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.

Suggested Citation

  • Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:1-14
    DOI: 10.1016/j.ejor.2012.04.038
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    References listed on IDEAS

    as
    1. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    2. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    3. Shanteau, James, 1992. "Competence in experts: The role of task characteristics," Organizational Behavior and Human Decision Processes, Elsevier, vol. 53(2), pages 252-266, November.
    4. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    5. Levary, Reuven R. & Wan, Ke, 1999. "An analytic hierarchy process based simulation model for entry mode decision regarding foreign direct investment," Omega, Elsevier, vol. 27(6), pages 661-677, December.
    6. Korhonen, Antti, 2001. "Strategic financial management in a multinational financial conglomerate: A multiple goal stochastic programming approach," European Journal of Operational Research, Elsevier, vol. 128(2), pages 418-434, January.
    7. Yang, J.B. & Wang, Y.M. & Xu, D.L. & Chin, K.S., 2006. "The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties," European Journal of Operational Research, Elsevier, vol. 171(1), pages 309-343, May.
    8. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    9. Wang, Ying-Ming & Luo, Ying & Hua, Zhongsheng, 2008. "On the extent analysis method for fuzzy AHP and its applications," European Journal of Operational Research, Elsevier, vol. 186(2), pages 735-747, April.
    10. Weber, Elke U. & Bottom, William P., 1990. "An empirical evaluation of the transitivity, monotonicity, accounting, and conjoint axioms for perceived risk," Organizational Behavior and Human Decision Processes, Elsevier, vol. 45(2), pages 253-275, April.
    11. Sarin, Rakesh K. & Weber, Martin, 1993. "Risk-value models," European Journal of Operational Research, Elsevier, vol. 70(2), pages 135-149, October.
    12. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834, April.
    13. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 1999. "Rough approximation of a preference relation by dominance relations," European Journal of Operational Research, Elsevier, vol. 117(1), pages 63-83, August.
    14. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
    15. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    16. Yang, Jian-Bo, 2001. "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties," European Journal of Operational Research, Elsevier, vol. 131(1), pages 31-61, May.
    17. Amor, Sarah Ben & Jabeur, Khaled & Martel, Jean-Marc, 2007. "Multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1506-1515, September.
    18. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    19. Jianmin Jia & James S. Dyer, 1996. "A Standard Measure of Risk and Risk-Value Models," Management Science, INFORMS, vol. 42(12), pages 1691-1705, December.
    20. Johnson, Johnnie E. V. & Bruce, Alistair C., 2001. "Calibration of Subjective Probability Judgments in a Naturalistic Setting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 85(2), pages 265-290, July.
    21. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    22. Baruch Fischhoff & Wändi Bruin & Ümit Güvenç & Denise Caruso & Larry Brilliant, 2006. "Analyzing disaster risks and plans: An avian flu example," Journal of Risk and Uncertainty, Springer, vol. 33(1), pages 131-149, September.
    23. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling & Chin, Kwai-Sang, 2006. "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees," European Journal of Operational Research, Elsevier, vol. 175(1), pages 35-66, November.
    24. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    25. Durbach, Ian N. & Stewart, Theodor J., 2011. "An experimental study of the effect of uncertainty representation on decision making," European Journal of Operational Research, Elsevier, vol. 214(2), pages 380-392, October.
    26. Han Bleichrodt & Jose Luis Pinto & Peter P. Wakker, 2001. "Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility," Management Science, INFORMS, vol. 47(11), pages 1498-1514, November.
    27. Martel, Jean-Marc & D'Avignon, Gilles R. & Couillard, Jean, 1986. "A fuzzy outranking relation in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 25(2), pages 258-271, May.
    28. Ballestero, Enrique, 2001. "Stochastic goal programming: A mean-variance approach," European Journal of Operational Research, Elsevier, vol. 131(3), pages 476-481, June.
    29. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    30. Chang, Da-Yong, 1996. "Applications of the extent analysis method on fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 649-655, December.
    31. Xu, Dong-Ling & Yang, Jian-Bo & Wang, Ying-Ming, 2006. "The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1914-1943, November.
    32. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    33. Zaras, Kazimierz, 2001. "Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems," European Journal of Operational Research, Elsevier, vol. 130(2), pages 305-314, April.
    34. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    35. Stewart, Theodor J. & Losa, Fabio B., 2003. "Towards reconciling outranking and value measurement practice," European Journal of Operational Research, Elsevier, vol. 145(3), pages 645-659, March.
    36. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    37. Leung, L. C. & Cao, D., 2000. "On consistency and ranking of alternatives in fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 124(1), pages 102-113, July.
    38. Abdellaoui, Mohammed & Barrios, Carolina & Wakker, Peter P., 2007. "Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory," Journal of Econometrics, Elsevier, vol. 138(1), pages 356-378, May.
    39. Durbach, Ian N. & Stewart, Theodor J., 2012. "A comparison of simplified value function approaches for treating uncertainty in multi-criteria decision analysis," Omega, Elsevier, vol. 40(4), pages 456-464.
    40. Robert J. Lempert & David G. Groves & Steven W. Popper & Steve C. Bankes, 2006. "A General, Analytic Method for Generating Robust Strategies and Narrative Scenarios," Management Science, INFORMS, vol. 52(4), pages 514-528, April.
    41. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    42. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    43. Durbach, Ian N. & Stewart, Theodor J., 2009. "Using expected values to simplify decision making under uncertainty," Omega, Elsevier, vol. 37(2), pages 312-330, April.
    44. Zaras, Kazimierz, 2004. "Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems," European Journal of Operational Research, Elsevier, vol. 159(1), pages 196-206, November.
    45. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    46. Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April.
    47. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    48. Islei, Gerd & Lockett, Geoff & Naudé, Peter, 1999. "Judgemental modelling as an aid to scenario planning and analysis," Omega, Elsevier, vol. 27(1), pages 61-73, February.
    49. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    50. Mingers, John & Rosenhead, Jonathan, 2004. "Problem structuring methods in action," European Journal of Operational Research, Elsevier, vol. 152(3), pages 530-554, February.
    51. Azondekon, Sebastien H. & Martel, Jean-Marc, 1999. ""Value" of additional information in multicriterion analysis under uncertainty," European Journal of Operational Research, Elsevier, vol. 117(1), pages 45-62, August.
    52. C. C. Huang & D. Kira & I. Vertinsky, 1978. "Stochastic Dominance Rules for Multi-attribute Utility Functions," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 611-615.
    53. Craig W. Kirkwood, 1992. "Estimating the Impact of Uncertainty on a Deterministic Multiattribute Evaluation," Management Science, INFORMS, vol. 38(6), pages 819-826, June.
    54. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    55. Carl S. Spetzler & Carl-Axel S. Staël Von Holstein, 1975. "Exceptional Paper--Probability Encoding in Decision Analysis," Management Science, INFORMS, vol. 22(3), pages 340-358, November.
    56. Fan, Zhi-Ping & Liu, Yang & Feng, Bo, 2010. "A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations," European Journal of Operational Research, Elsevier, vol. 207(2), pages 906-915, December.
    57. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
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