Skip to main content
SpringerLink
Log in

Dealing with Uncertainties in MCDA

  • Chapter
Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 233))

Abstract

This chapter presents various approaches to incorporating formal modelling of risks and uncertainties into multi-criteria decision analysis, in a theoretically valid but also operationally meaningful manner. We consider both internal uncertainties (in the formulation and modelling of the decision problem), and external uncertainties arising from exogenous factors, but with greater attention paid to the latter. After a broad discussion on the meaning of uncertainty, we first review approaches to sensitivity analysis, which is particularly, although not exclusively, relevant to internal uncertainties. We discuss the role, but also some limitations, of representing uncertainties in formal probabilistic structures, linked also to concepts of expected (multi-attribute) utility theory. Such probability/utility approaches may be used in explicitly identifying a most preferred solution, or simply to eliminate certain courses of action when stochastically dominated (in various senses) by others. In some contexts it may be useful to view minimization of various risk measures as additional criteria in more standard MCDA models, and we comment on advantages and disadvantages of such approaches. Finally we discuss the integration of MCDA with scenario planning, in order to deal with deeper uncertainties (not easily if at all representable by probability models), particularly in a strategic planning context. The emphasis throughout is on the practice of MCDA rather than on esoteric theoretical results.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 449.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For a detailed description, see Global Business Network, paper accessed on 4 Jan 2011 from http://www.generonconsulting.com/publications/papers/pdfs/MontFleur.pdf.

References

  1. Abdellaoui, M.: Parameter-free elicitation of utility and probability weighting functions. Manag. Sci. 46(11), 1497–1512 (2000)

    Article  Google Scholar 

  2. Abdellaoui, M., Barrios, C., Wakker, P.: Reconciling introspective utility with revealed preference: experimental arguments based on prospect theory. J. Econ. 138(1), 356–378 (2007)

    Article  Google Scholar 

  3. Abdellaoui, M., Bleichrodt, H., Paraschiv, C.: Loss aversion under prospect theory: a parameter-free measurement. Manag. Sci. 53(10), 1659–1674 (2007)

    Article  Google Scholar 

  4. Angilella, S., Greco, S., Matarazzo, B.: Non-additive robust ordinal regression: a multiple criteria decision model based on the choquet integral. Eur. J. Oper. Res. 201(1), 277–288 (2010)

    Article  Google Scholar 

  5. Azondékon, S.H., Martel, J.M.: “Value” of additional information in multicriterion analysis under uncertainty. Eur. J. Oper. Res. 117, 45–62 (1999)

    Article  Google Scholar 

  6. Ballestero, E.: Stochastic goal programming: a mean-variance approach. Eur. J. Oper. Res. 131, 476–481 (2001)

    Article  Google Scholar 

  7. Banuelas, R., Antony, J.: Application of stochastic analytic hierarchy process within a domestic appliance manufacturer. Eur. J. Oper. Res. Soc. 58(1), 29 (2007)

    Article  Google Scholar 

  8. Bawa, V.S.: Optimal rules for ordering uncertain prospects. J. Financ. Econ. 2, 95–121 (1975)

    Article  Google Scholar 

  9. Bazerman, M.H.: Judgment in Managerial Decision Making, 5th edn. Wiley, New York (2002)

    Google Scholar 

  10. Bell, D.E.: One-switch utility functions and a measure of risk. Manag. Sci. 34, 1416–1424 (1988)

    Article  Google Scholar 

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

    Book  Google Scholar 

  12. Ben, A.S., Jabeur, K., Martel, J.: Multiple criteria aggregation procedure for mixed evaluations. Eur. J. Oper. Res. 181(3), 1506–1515 (2007)

    Article  Google Scholar 

  13. Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling. OMEGA: Int. J. Manag. Sci. 28, 37–50 (2000)

    Article  Google Scholar 

  14. Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, 2nd edn. Springer, New York (2011)

    Book  Google Scholar 

  15. Bleichrodt, H., Miyamoto, J.: A characterization of quality-adjusted life-years under cumulative prospect theory. Math. Oper. Res. 28(1), 181–193 (2003)

    Article  Google Scholar 

  16. Bleichrodt, H., Pinto, J.: A parameter-free elicitation of the probability weighting function in medical decision analysis. Manag. Sci. 46(11), 1485–1496 (2000)

    Article  Google Scholar 

  17. Bleichrodt, H., Pinto, J., Wakker, P.: Making descriptive use of prospect theory to improve the prescriptive use of expected utility. Manag. Sci. 47(11), 1498–1514 (2001)

    Article  Google Scholar 

  18. Bordley, R.F., Hazen, G.: Nonlinear utility models arising from unmodelled small world intercorrelations. Manag. Sci. 38, 1010–1017 (1992)

    Article  Google Scholar 

  19. Bordley, R., Kirkwood, C.: Multiattribute preference analysis with performance targets. Oper. Res. 52(6), 823 (2004)

    Article  Google Scholar 

  20. Boujelben, M., Smet, Y., Frikha, A., Chabchoub, H.: Building a binary outranking relation in uncertain, imprecise and multi-experts contexts: the application of evidence theory. Int. J. Approx. Reason. 50(8), 1259–1278 (2009)

    Article  Google Scholar 

  21. Castagnoli, E., Calzi, M.: Expected utility without utility. Theory Decis. 41(3), 281–301 (1996)

    Article  Google Scholar 

  22. Chang, N.B., Wang, S.: A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems. Eur. J. Oper. Res. 99, 303–321 (1997)

    Article  Google Scholar 

  23. Chang, N.B., Wen, C., Chen, Y.: A fuzzy multi-objective programming approach for optimal management of the reservoir watershed. Eur. J. Oper. Res. 99, 289–302 (1997)

    Article  Google Scholar 

  24. D’Avignon, G.R., Vincke, P.: An outranking method under uncertainty. Eur. J. Oper. Res. 36, 311–321 (1988)

    Article  Google Scholar 

  25. Dembo, R., Rosen, D.: The practice of portfolio replication. a practical overview of forward and inverse problems. Ann. Oper. Res. 85, 267–284 (1999)

    Google Scholar 

  26. Dendrou, B., Dendrou, S., Houstis, E.: Multiobjective decision analysis for engineering systems. Comput. Oper. Res. 7, 301–312 (1980)

    Article  Google Scholar 

  27. Dentcheva, D., Ruszczynski, A.: Optimization with stochastic dominance constraints. SIAM J. Optim. 14(2), 548–566 (2003)

    Article  Google Scholar 

  28. Dimitras, A., Slowinski, R., Susmaga, R., Zopounidis, C.: Business failure prediction using rough sets. Eur. J. Oper. Res. 114, 263–280 (1999)

    Article  Google Scholar 

  29. Durbach, I.: A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions. Eur. J. Oper. Res. 170, 923–934 (2006)

    Article  Google Scholar 

  30. Durbach, I., Davis, S.: Decision support for selecting a shortlist of electricity-saving options: a modified SMAA approach. ORiON 28(2), 99–116 (2012)

    Article  Google Scholar 

  31. Durbach, I., Stewart, T.: Using expected values to simplify decision making under uncertainty. Omega 37(2), 312–330 (2009)

    Article  Google Scholar 

  32. Durbach, I.N., Stewart, T.J.: Modelling uncertainty in multi-criteria decision analysis. Eur. J. Oper. Res. 223, 1–14 (2012)

    Article  Google Scholar 

  33. Fan, Z., Liu, Y., Feng, B.: A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations. Eur. J. Oper. Res. 207(2), 906–915 (2010)

    Article  Google Scholar 

  34. Fishburn, P.C.: Foundations of risk measurement. I. Risk as probable loss. Manag. Sci. 30, 396–406 (1984)

    Google Scholar 

  35. French, S.: Uncertainty and imprecision: modelling and analysis. J. Oper. Res. Soc. 46, 70–79 (1995)

    Article  Google Scholar 

  36. French, S., Maule, J., Papamichail, N.: Decision Behaviour, Analysis and Support. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  37. Friend, J.: The strategic choice approach. In: Rosenhead, J., Mingers, J. (eds.) Rational Analysis for a Problematic World Revisited, 2nd edn. pp. 115–149. Wiley, Chichester (2001)

    Google Scholar 

  38. Gal, T., Stewart, T.J., Hanne, T. (eds.): Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications. Kluwer Academic Publishers, Boston (1999)

    Google Scholar 

  39. Goicoechea, A., Hansen, D.R., Duckstein, L.: Multiobjective Decision Analysis with Engineering and Business Applications. Wiley, New York (1982)

    Google Scholar 

  40. Goodwin, P., Wright, G.: Decision Analysis for Management Judgement, 4th edn. Wiley, Chichester (2009)

    Google Scholar 

  41. Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations. Eur. J. Oper. Res. 117, 63–83 (1999)

    Article  Google Scholar 

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

    Google Scholar 

  43. Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1–47 (2001)

    Article  Google Scholar 

  44. Greco, S., Matarazzo, B., Slowinski, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur. J. Oper. Res. 138, 247–259 (2002)

    Article  Google Scholar 

  45. Greco, S., Mousseau, V., Słowiński, R.: Multiple criteria sorting with a set of additive value functions. Eur. J. Oper. Res. 207(3), 1455–1470 (2010)

    Article  Google Scholar 

  46. Greco, S., Słowiński, R., Figueira, J., Mousseau, V.: Robust ordinal regression. In: Greco, S., Ehrgott, M., Figuera, J. (eds.) Trends in Multiple Criteria Decision Analysis, Chap 9. Springer, New York (2010)

    Google Scholar 

  47. Greco, S., Kadziński, M., Mousseau, V., Słowiński, R.: ELECTRE-GKMS: robust ordinal regression for outranking methods. Eur. J. Oper. Res. 214(1), 118–135 (2011)

    Article  Google Scholar 

  48. Hadar, J., Russell, W.R.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59, 25–34 (1969)

    Google Scholar 

  49. Harries, C.: Correspondence to what? Coherence to what? What is good scenario-based decision making. Technol. Forecast. Soc. Chang. 70, 797–817 (2003)

    Article  Google Scholar 

  50. Hokkanen, J., Lahdelma, R., Miettinen, K., Salminen, P.: Determining the implementation order of a general plan by using a multicriteria method. J. Multi-Criteria Decis. Anal. 7(5), 273–284 (1998)

    Article  Google Scholar 

  51. Hughes, N.: A historical overview of strategic scenario planning. Technical Report. UKERC and EON.UK/EPSRC Project on Transition Pathways to a Low Carbon Economy (2009)

    Google Scholar 

  52. Insua, D., French, S.: A framework for sensitivity analysis in discrete multi-objective decision-making. Eur. J. Oper. Res. 54(2), 176–190 (1991)

    Article  Google Scholar 

  53. Jacquet-Lagrèze, E., Siskos, Y.: Preference disaggregation: 20 years of MCDA experience. Eur. J. Oper. Res. 130, 233–245 (2001)

    Article  Google Scholar 

  54. Jia, J., Dyer, J.S.: A standard measure of risk and risk-value models. Manag. Sci. 42, 1691–1705 (1996)

    Article  Google Scholar 

  55. Jiménez, A., Mateos, A., Ríos-Insua, S.: Missing consequences in multiattribute utility theory. Omega Int. J. Manag. Sci. 37, 395–410 (2009)

    Article  Google Scholar 

  56. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)

    Article  Google Scholar 

  57. Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives. Wiley, New York (1976)

    Google Scholar 

  58. Keown, A.J., Taylor III, B.W.: A chance-constrained integer goal programming model for capital budgeting in the production area. J. Oper. Res. Soc. 31, 579–589 (1980)

    Article  Google Scholar 

  59. Kirkwood, C.: Estimating the impact of uncertainty on deterministic multiattribute evaluation. Manag. Sci. 38(6), 819–826 (1992)

    Article  Google Scholar 

  60. Klein, G., Moskowitz, H., Ravindran, A.: Interactive multiobjective optimization under uncertainty. Manag. Sci. 36, 58–75 (1990)

    Article  Google Scholar 

  61. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs, NJ (1988)

    Google Scholar 

  62. Korhonen, A.: Strategic financial management in a multinational financial conglomerate: a multiple goal stochastic programming approach. Eur. J. Oper. Res. 128, 418–434 (2001)

    Article  Google Scholar 

  63. Krokhmal, P., Zabarankin, M., Uryasev, S.: Modeling and optimization of risk. Surv. Oper. Res. Manag. Sci. 16(2), 49–66 (2011)

    Google Scholar 

  64. Lahdelma, R., Salminen, P.: SMAA-2: stochastic multi-criteria acceptability analysis for group decision making. Oper. Res. 49(3), 444–454 (2001)

    Article  Google Scholar 

  65. Lahdelma, R., Salminen, P.: Prospect theory and stochastic multicriteria acceptability analysis (SMAA). Omega 37(5), 961–971 (2009)

    Article  Google Scholar 

  66. Lahdelma, R., Hokkanen, J., Salminen, P.: SMAA – Stochastic multiobjective acceptability analysis. Eur. J. Oper. Res. 106, 137–143 (1998)

    Article  Google Scholar 

  67. Lahdelma, R., Miettinen, K., Salminen, P.: Reference point approach for multiple decision makers. Eur. J. Oper. Res. 164(3), 785–791 (2005)

    Article  Google Scholar 

  68. Levary, R.R., Wan, K.: A simulation approach for handling uncertainty in the analytic hierarchy process. Eur. J. Oper. Res. 106, 116–122 (1998)

    Article  Google Scholar 

  69. Levary, R.R., Wan, K.: An analytic hierarchy process based simulation model for entry mode decision regarding foreign direct investment. Omega 27(6), 661–677 (1999)

    Article  Google Scholar 

  70. Linares, P.: Multiple criteria decision making and risk analysis as risk management tools for power systems planning. IEEE Trans. Power Syst. 17, 895–900 (2002)

    Article  Google Scholar 

  71. Liu, Y., Fan, Z., Zhang, Y.: A method for stochastic multiple criteria decision making based on dominance degrees. Inform. Sci. 181(19), 4139–4153 (2011)

    Article  Google Scholar 

  72. Mareschal, B.: Stochastic multicriteria decision making and uncertainty. Eur. J. Oper. Res. 26, 58–64 (1986)

    Article  Google Scholar 

  73. Martel, J.M., Zaras, K.: Stochastic dominance in multicriterion analysis under risk. Theory Decis. 39, 31–49 (1995)

    Article  Google Scholar 

  74. Martel, J., d’Avignon, G., Couillard, G.: A fuzzy outranking relation in multicriteria decision making. Eur. J. Oper. Res. 25, 258–271 (1986)

    Article  Google Scholar 

  75. Mateos, A., Ríos-Insua, S., Jiménez, A.: Dominance, potential optimality and alternative ranking in imprecise multi-attribute decision making. J. Oper. Res. Soc. 58(3), 326–336 (2006)

    Article  Google Scholar 

  76. Millet, I., Wedley, W.C.: Modelling risk and uncertainty with the analytic hierarchy process. J. Multi-Criteria Decis. Anal. 11, 97–107 (2002)

    Article  Google Scholar 

  77. Miranda, V., Proença, L.M.: Why risk analysis outperforms probabilistic choice as the effective decision support paradigm for power system planning. IEEE Trans. Power Syst. 13, 643–648 (1998)

    Article  Google Scholar 

  78. Miyamoto, J.M., Wakker, P.: Multiattribute utility theory without expected utility foundations. Oper. Res. 44, 313–326 (1996)

    Article  Google Scholar 

  79. Montibeller, G., Gummer, H., Tumidei, D.: Combining scenario planning and multi-criteria decision analysis in practice. J. Multi-Criteria Decis. Anal. 14, 5–20 (2006)

    Article  Google Scholar 

  80. Nowak, M.: Preference and veto thresholds in multicriteria analysis based on stochastic dominance. Eur. J. Oper. Res. 158(2), 339–350 (2004)

    Article  Google Scholar 

  81. Parnell, G.S., Jackson, J.A., Burk, R.C., Lehmkuhld, L.J., Engelbrecht, Jr. J.A.: R&D concept decision analysis: using alternate futures for sensitivity analysis. J. Multi-Criteria Decis. Anal. 8, 119–127 (1999)

    Article  Google Scholar 

  82. Pomerol, J.C.: Scenario development and practical decision making under uncertainty. Decis. Support Syst. 31, 197–204 (2001)

    Article  Google Scholar 

  83. Rios Insua, D.: Sensitivity Analysis in Multi-Objective Decision Making. Lecture Notes in Economics and Mathematical Systems, vol. 347. Springer, Berlin (1990)

    Google Scholar 

  84. Roman, D., Darby-Dowman, K., Mitra, G.: Portfolio construction based on stochastic dominance and target return distributions. Math. Program. 108(2), 541–569 (2006)

    Article  Google Scholar 

  85. Rosqvist, T.: Simulation and multi-attribute utility modelling of life cycle profit. J. Multi-Criteria Decis. Anal. 10, 205–218 (2001)

    Article  Google Scholar 

  86. Saltelli, A., Tarantola, A.S., Chan, K.: A role for sensitivity analysis in presenting the results from MCDA studies to decision makers. J. Multi-Criteria Decis. Anal. 8, 139–145 (1999)

    Article  Google Scholar 

  87. Sarin, R.K., Weber, M.: Risk-value models. Eur. J. Oper. Res. 70, 135–149 (1993)

    Article  Google Scholar 

  88. Shafer, G.:A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    Google Scholar 

  89. Stewart, T.J.: Simplified approaches for multi-criteria decision making under uncertainty. J. Multi-Criteria Decis. Anal. 4, 246–258 (1995)

    Article  Google Scholar 

  90. Stewart, T.J.: Robustness of additive value function methods in MCDM. J. Multi-Criteria Decis. Anal. 5, 301–309 (1996)

    Article  Google Scholar 

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

    Google Scholar 

  92. Stewart, T.J.: Concepts of interactive programming. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, Chap. 10. Kluwer Academic Publishers, Boston (1999)

    Google Scholar 

  93. Stewart, T.J., French, S., Rios, J.: Integrating multicriteria decision analysis and scenario planning – review and extension. Omega Int. J. Manag. Sci. 41, 679–688 (2013). doi:10.1016/j.omega.2012.09.003

    Article  Google Scholar 

  94. Teghem, Jr. J., Dufrane, D., Thauvoye, M.: STRANGE: an interactive method for multi-objective linear programming under uncertainty. Eur. J. Oper. Res. 26, 65–82 (1986)

    Article  Google Scholar 

  95. Urli, B., Nadeau, R.: PROMISE/scenarios: an interactive method for multiobjective stochastic linear programming under partial uncertainty. Eur. J. Oper. Res. 155, 361–372 (2004)

    Article  Google Scholar 

  96. Van der Heijden, K.: Scenarios: The Art of Strategic Conversation. Wiley, Chichester (1996)

    Google Scholar 

  97. von Winterfeldt, D., Edwards, W.: Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  98. Wakker, P., Deneffe, D.: Eliciting von Neumann-Morgenstern utilities when probabilities are distorted or unknown. Manag. Sci. 42(8), 1131–1150 (1996)

    Article  Google Scholar 

  99. Walker, W.E., Harremoes, P., Rotmans, J., van der Sluijs, J.P., van Asselt, M.B.A., Janssen, P., Krayer von Krausswalker, M.P.: Defining uncertainty: a conceptual basis for uncertainty management in model based decision support. Integr. Asess. 4(1), 5–17 (2003)

    Google Scholar 

  100. Watkins, Jr. D.W., McKinney, D.C., Lasdon, L.S., Nielsen, S.S., Martin, Q.W.: A scenario-based stochastic programming model for water supplies from the highland lakes. Int. Trans. Oper. Res. 7, 211–230 (2000)

    Article  Google Scholar 

  101. Whitmore, G.A.: Third order stochastic dominance. Am. Econ. Rev. 60, 457–459 (1970)

    Google Scholar 

  102. Xu, D.: An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis. Ann. Oper. Res. 195(1), 163–187 (2012)

    Article  Google Scholar 

  103. Yang, J.B.: Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. Eur. J. Oper. Res. 131, 31–61 (2001)

    Article  Google Scholar 

  104. Yeh, C., Deng, H., Pan, H.: Multi-criteria analysis for dredger dispatching under uncertainty. J. Oper. Res. Soc. 50, 35–43 (1999)

    Article  Google Scholar 

  105. Yilmaz, M.R.: An information-expectation framework for decisions under uncertainty. J. Multi-Criteria Decis. Anal. 1, 65–80 (1992)

    Article  Google Scholar 

  106. Zank, H.: Cumulative prospect theory for parametric and multiattribute utilities. Math. Oper. Res. 26(1), 67–81 (2001)

    Article  Google Scholar 

  107. Zaras, K.: Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems. Eur. J. Oper. Res. 159(1), 196–206 (2004)

    Article  Google Scholar 

  108. Zhang, Y., Fan, Z., Liu,Y.: A method based on stochastic dominance degrees for stochastic multiple criteria decision making. Comput. Ind. Eng. 58(4), 544–552 (2010)

    Article  Google Scholar 

  109. Zimmermann, H.: An application-oriented view of modeling uncertainty. Eur. J. Oper. Res. 122, 190–198 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistical Sciences, University of Cape Town, Rondebosch, 7701, South Africa

    Theodor J. Stewart & Ian Durbach

  2. Research Center, African Institute for Mathematical Sciences, 6–8 Melrose Road, Muizenberg, 7945, South Africa

    Ian Durbach

Authors
  1. Theodor J. Stewart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ian Durbach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Theodor J. Stewart .

Editor information

Editors and Affiliations

  1. Department of Economics and Business; Portsmouth Business School, Operations & Systems Management, University of Catania; University of Portsmouth, Catania; Portsmouth, Italy

    Salvatore Greco

  2. Department of Management Science, Lancaster University, Lancaster, United Kingdom

    Matthias Ehrgott

  3. Universidade de Lisboa, CEG-IST, Instituto Superior Técnico, Lisboa, Portugal

    José Rui Figueira

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this chapter

Cite this chapter

Stewart, T.J., Durbach, I. (2016). Dealing with Uncertainties in MCDA. In: Greco, S., Ehrgott, M., Figueira, J. (eds) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 233. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3094-4_12

Download citation

Publish with us

Policies and ethics

Search

Navigation