Skip to main content

Stochastic Multicriteria Acceptability Analysis (SMAA)

  • Chapter
  • First Online:
Trends in Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 142))

Abstract

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with uncertain, imprecise or partially missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision. A general approach for applying SMAA in real-life decision problems is to use it repetitively with more and more accurate information until the information is sufficient for making a decision. Between the analyses, information can be added by making more accurate criteria measurements, or assessing the DMs’ preferences more accurately in terms of various preference parameters.

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 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.-P. Ancot and J.H.P Paelinck. Recent experiences with the qualiflex multicriteria method. In J.H.P. Paelinck, editor, Qualitative and Quantitative Mathematical Economics. Martinus Nijhoff Publishers, The Hague, 1982.

    Google Scholar 

  2. C.A. Bana e Costa. A multicriteria decision aid methodology to deal with conflicting situations on the weights. European Journal of Operational Research, 26:22–34, 1986.

    Google Scholar 

  3. C.A. Bana e Costa. A methodology for sensitivity analysis in three-criteria problems: a case study in municipal management. European Journal of Operational Research, 33:159–173, 1988.

    Google Scholar 

  4. V. Belton and T.J. Stewart. Multiple Criteria Decision Analysis – An Integrated Approach. Kluwer Academic Publishers, Dordrecht, 2002.

    Google Scholar 

  5. J.P. Brans and Ph. Vincke. A preference ranking organization method. Management Science, 31:647–656, 1985.

    Article  Google Scholar 

  6. J. Butler, J. Dia, and J. Dyer. Simulation techniques for the sensitivity analysis of multi-criteria decision models. European Journal of Operational Research, 103(3):531–545, 1997.

    Article  Google Scholar 

  7. J.R. Charnetski. The multiple attribute problem with partial information: the expected value and comparative hypervolume methods. PhD thesis, University of Texas at Austin, 1973.

    Google Scholar 

  8. J.R. Charnetski and R.M. Soland. Multiple-attribute decision making with partial information: the comparative hypervolume criterion. Naval Research Logistics Quarterly, 25:279–288, 1978.

    Article  Google Scholar 

  9. H.A. David. Order Statistics. Wiley and Sons, New York, 1970.

    Google Scholar 

  10. I. Durbach. A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions. European Journal of Operational Research, 170(3):923–934, 2006.

    Article  Google Scholar 

  11. I. Durbach. On the estimation of a satisficing model of choice using stochastic multicriteria acceptability analysis. Omega, 37(3):497–509, 2009.

    Article  Google Scholar 

  12. I.N. Durbach. The use of the SMAA acceptability index in descriptive decision analysis. European Journal of Operational Research, 196(3):1229–1237, 2009.

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. S. French. Uncertainty and imprecision: modelling and analysis. The Journal of the Operational Research Society, 46(1):70–79, 1995.

    Google Scholar 

  15. R.G. García, J.A. Aráoz, and F. Palacios. Integral analysis method – IAM. European Journal of Operational Research, 193(3):891–903, 2009.

    Article  Google Scholar 

  16. S. Greco, B. Matarazzo, and R. Słowiński. Rough set approach to multi-attribute choice and ranking problems. ICS Research Report 38/95, Institute of Computer Science, Warsaw University of Technology, 1995.

    Google Scholar 

  17. K.W. Hipel. Fuzzy set techniques in decision making. Resource Management and Optimization, 2(3):187–203, 1983.

    Google Scholar 

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

    Article  Google Scholar 

  19. J. Hokkanen, R. Lahdelma, and P. Salminen. A multiple criteria decision model for analyzing and choosing among different development patterns for the Helsinki cargo harbor. Socio-Economic Planning Sciences, 33:1–23, 1999.

    Article  Google Scholar 

  20. J. Hokkanen, R. Lahdelma, and P. Salminen. Multicriteria decision support in a technology competition for cleaning polluted soil in Helsinki. Journal of Environmental Management, 60(4):339–348, 2000.

    Article  Google Scholar 

  21. J. Jia, G. Fisher, and J. Dyer. Attribute weighting methods and decision quality in the presence of response error: a simulation study. Journal of Behavioural Decision Making, 11:85–105, 1998.

    Article  Google Scholar 

  22. A.B. Kahn. Topological sorting of large networks. Communications of the ACM, pages 558–562, 1962.

    Google Scholar 

  23. D. Kahneman and A. Tversky. Prospect theory: an analysis of decisions under risk. Econometrica, 47:262–291, 1979.

    Article  Google Scholar 

  24. A. Kangas, J. Kangas, R. Lahdelma, and P. Salminen. Using SMAA-2 method with dependent uncertainties for strategic forest planning. Forest Policy and Economics, 9:113–125, 2006.

    Article  Google Scholar 

  25. J. Kangas, J. Hokkanen, A. Kangas, R. Lahdelma, and P. Salminen. Applying stochastic multicriteria acceptability analysis to forest ecosystem management with both cardinal and ordinal criteria. Forest Science, 49(6):928–937, 2003.

    Google Scholar 

  26. R. Keeney and H. Raiffa. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. John Wiley & Sons, New York, 1976.

    Google Scholar 

  27. R. Lahdelma, J. Hokkanen, K. Miettinen, and P. Salminen. Determining the implementation order of a general plan by using a multicriteria method. volume 7, pages 273–284, 1998.

    Google Scholar 

  28. R. Lahdelma, J. Hokkanen, and P. Salminen. Stochastic multi-objective acceptability analysis for development of helsinki cargo harbour. In M. Brännback and M. Kuula, editors, Decision Science and Applications, pages 57–75. Institute for Advanced Management Systems Research, Åbo Academy University Press, Turku.

    Google Scholar 

  29. R. Lahdelma, J. Hokkanen, and P. Salminen. SMAA – stochastic multiobjective acceptability analysis. European Journal of Operational Research, 106(1):137–143, 1998.

    Article  Google Scholar 

  30. R. Lahdelma, S. Makkonen, and P. Salminen. Multivariate Gaussian criteria in SMAA. European Journal of Operational Research, 170(3):957–970, 2006.

    Article  Google Scholar 

  31. R. Lahdelma, S. Makkonen, and P. Salminen. Two ways to handle dependent uncertainties in multi-criteria decision problems. Omega, 37(1):79–92, 2009.

    Article  Google Scholar 

  32. R. Lahdelma, K. Miettinen, and P. Salminen. Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA). European Journal of Operational Research, 147(1):117–127, 2003.

    Article  Google Scholar 

  33. R. Lahdelma, K. Miettinen, and P. Salminen. Reference point approach for multiple decision makers. European Journal of Operational Research, 164(3):785–791, 2005.

    Article  Google Scholar 

  34. R. Lahdelma and P. Salminen. SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Operations Research, 49(3):444–454, 2001.

    Article  Google Scholar 

  35. R. Lahdelma and P. Salminen. Pseudo-criteria versus linear utility function in stochastic multi-criteria acceptability analysis. European Journal of Operational Research, 141(2):454–469, 2002.

    Article  Google Scholar 

  36. R. Lahdelma and P. Salminen. Stochastic multicriteria acceptability analysis using the data envelopment model. European Journal of Operational Research, 170(1):241–252, 2006.

    Article  Google Scholar 

  37. R. Lahdelma and P. Salminen. Ordinal measurements with interval constraints in the EIA process for siting a waste storage area. In Real-Time and Deliberative Decision Making: Application to Emerging Stressors, pages 397–414. NATO Science for Peace and Security Series – C: Environmental Security, Springer, Dordrecht, 2008.

    Google Scholar 

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

    Article  Google Scholar 

  39. R. Lahdelma and P. Salminen. Simple method for ordinal classification in multicriteria decision making. Technical Report 939, TUCS – Turku Center for Computer Science, Turku, Finland, 2009.

    Google Scholar 

  40. R. Lahdelma, P. Salminen, and J. Hokkanen. Using multicriteria methods in environmental planning and management. Environmental Management, 26(6):595–605, 2000.

    Article  Google Scholar 

  41. 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(2):345–356, 2002.

    Article  Google Scholar 

  42. R. Lahdelma, P. Salminen, A. Simonen, and J. Hokkanen. Choosing a reparation method for a landfill using the SMAA-O multicriteria method. In Multiple Criteria Decision Making in the New Millenium, Lecture Notes in Economics and Mathematical Systems, volume 507, pages 380–389. Springer-Verlag, Berlin, 2001.

    Google Scholar 

  43. R. Lahdelma, T. Tervonen, P. Salminen, and J. Figueira. Group preference modelling in SMAA using belief functions. In M.H. Hamza, editor, Proceedings of the 23rd IASTED International Conference on Artificial Intelligence and Applications, pages 361–385, Innsbruck, 2005. ACTA Press.

    Google Scholar 

  44. P. Leskinen, J. Viitanen, A. Kangas, and J. Kangas. Alternatives to incorporate uncertainty and risk attitude in multicriteria evaluation of forest plans. Forest Science, 52(3):304–312, 2006.

    Google Scholar 

  45. S. Makkonen and R. Lahdelma. Analysis of power pools in the deregulated energy market through simulation. Decision Support Systems, 30(3):289–301, 2001.

    Article  Google Scholar 

  46. S. Makkonen, R. Lahdelma, A.M. Asell, and A. Jokinen. Multicriteria decision support in the liberated energy market. Journal of Multi-Criteria Decision Analysis, 12(1):27–42, 2003.

    Article  Google Scholar 

  47. L.-Y. Maystre, J. Pictet, and J. Simos. Méthodes Multicritères ELECTRE. Presses Polytechniques et Universitaires Romandes, Lausanne, 1994.

    Google Scholar 

  48. A. Menou, A. Benallou, R. Lahdelma, and P. Salminen. Decision support for centralizing cargo at a moroccan airport hub using stochastic multicriteria acceptability analysis. In Proceedings of the 67th Meeting of the European Working Group “Multiple Criteria Decision Aiding”. University of Jyväskylä, Reports of the Department of Mathematical Information Technology, Series A. Collections. No A.1, pages 30–41, 2008.

    Google Scholar 

  49. J. S. Milton and J.C. Arnold. Introduction to Probability and Statistics. Probability and Statistics. McGraw-Hill Inc., New York, 3rd edition, 1995.

    Google Scholar 

  50. J.H.P. Paelinck. Qualitative multiple criteria analysis, environmental protection and multiregional development. Papers of the Regional Science Association, 36:59–74, 1976.

    Article  Google Scholar 

  51. Z. Pawlak. Rough sets. International Journal of Computer and Information Sciences, 11: 341–356, 1982.

    Article  Google Scholar 

  52. M. Pirlot. The characterization of ’min’ as a procedure for exploiting valued preference relations and related results. Journal of Multi-Criteria Decision Analysis, 4(1):37–57, 1995.

    Article  Google Scholar 

  53. P. Rietveld. Multiple Objective Decision Methods and Regional Planning. North-Holland, Amsterdam, 1980.

    Google Scholar 

  54. P. Rietveld and H. Ouwersloot. Ordinal data in multicriteria decision making, a stochastic dominance approach to siting nuclear power plants. European Journal of Operational Research, 56:249–262, 1992.

    Article  Google Scholar 

  55. B. Roy. Electre III: Un algorithme de classements fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du CERO, 20(1):3–24, 1978.

    Google Scholar 

  56. B. Roy. Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht, 1996.

    Google Scholar 

  57. P. Salminen and J. Wallenius. Testing prospect theory in a deterministic multiple criteria decision making environment. Decision Sciences, 24:279–294, 1993.

    Article  Google Scholar 

  58. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ, 1976.

    Google Scholar 

  59. T. Stewart. Use of piecewise linear value functions in interactive multicriteria decision support. Management Science, 39(11):1369–1381, 1993.

    Article  Google Scholar 

  60. T. Stewart. Simplified approaches for multicriteria decision making under uncertainty. Journal of Multi-Criteria Decision Analysis, 4(4):246–248, 1995.

    Article  Google Scholar 

  61. T. Stewart. Robustness of additive value function methods in mcdm. Journal of Multi-Criteria Decision Analysis, 5(4):301–309, 1996.

    Article  Google Scholar 

  62. B.N. Taylor and C.E. Kuyatt. Guidelines for evaluating and expressing the uncertainty of NIST measurement results. NIST Technical Note 1297, National Institute of Standards and Technology, Washington, 1994.

    Google Scholar 

  63. T. Tervonen, G.F. Barberis, J.R. Figueira, and M.E. Ródenas. Siting a university kindergarten in Madrid with SMAA-III. Working paper 12/2007 of CEG-IST, Technical University of Lisbon, Portugal, 2007.

    Google Scholar 

  64. T. Tervonen, J. Figueira, R. Lahdelma, and P. Salminen. An inverse approach for ELECTRE III. Research Report 20/2004 of The Institute of Systems Engineering and Computers (INESC-Coimbra), Coimbra, Portugal, 2004.

    Google Scholar 

  65. T. Tervonen, J. Figueira, R. Lahdelma, and P. Salminen. Modelling MCDA group preferences for public human resource management: evaluating the quality of education at the Department of Information Technology, the University of Turku (Finland). Research Report 22/2004 of The Institute of Systems Engineering and Computers (INESC-Coimbra), Coimbra, Portugal, 2004.

    Google Scholar 

  66. T. Tervonen and J.R. Figueira. A survey on stochastic multicriteria acceptability analysis methods. Journal of Multi-Criteria Decision Analysis, 15(1–2):1–14, 2008.

    Article  Google Scholar 

  67. T. Tervonen, J.R. Figueira, R. Lahdelma, J. Almeida Dias, and P. Salminen. A stochastic method for robustness analysis in sorting problems. European Journal of Operational Research, 192(1):236–242, 2009.

    Article  Google Scholar 

  68. T. Tervonen, H. Hakonen, and R. Lahdelma. Elevator planning with stochastic multicriteria acceptability analysis. Omega, 36(3):352–362, 2008.

    Article  Google Scholar 

  69. T. Tervonen and R. Lahdelma. Implementing stochastic multicriteria acceptability analysis. European Journal of Operational Research, 178(2):500–513, 2007.

    Article  Google Scholar 

  70. T. Tervonen, I. Linkov, J. Steevens, M. Chappell, J.R. Figueira, and M. Merad. Risk-based classification system of nanomaterials. Journal of Nanoparticle Research, 11(4):757–766, 2009.

    Article  Google Scholar 

  71. Ph. Vincke. Multicriteria Decision-Aid. John Wiley & Sons, Chichester, 1992.

    Google Scholar 

  72. R. von Nitzsch and M. Weber. The effect of attribute ranges on weights in multiattribute utility measurements. Management Science, 39(8):937–943, 1993.

    Article  Google Scholar 

  73. I. Yevseyeva. Solving classification problems with multicriteria decision aiding approaches. PhD thesis, University of Jyväskylä, Finland, 2007. Jyväskylä Studies in Computing 84.

    Google Scholar 

  74. L.A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pekka Salminen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Lahdelma, R., Salminen, P. (2010). Stochastic Multicriteria Acceptability Analysis (SMAA). In: Ehrgott, M., Figueira, J., Greco, S. (eds) Trends in Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 142. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5904-1_10

Download citation

Publish with us

Policies and ethics