×

Stochastic multicriteria acceptability analysis. (English) Zbl 1200.90104

Ehrgott, Matthias (ed.) et al., Trends in multiple criteria decision analysis. Berlin: Springer (ISBN 978-1-4419-5903-4/hbk; 978-1-4419-5904-1/ebook). International Series in Operations Research & Management Science 142, 285-315 (2010).
Summary: 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.
For the entire collection see [Zbl 1200.90007].

MSC:

90B50 Management decision making, including multiple objectives
Full Text: DOI

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.
[2] Bana e. Costa, C. A., A multicriteria decision aid methodology to deal with conflicting situations on the weights, European Journal of Operational Research, 26, 22-34 (1986) · Zbl 0589.90048
[3] Bana e. Costa, C. A., A methodology for sensitivity analysis in three-criteria problems: a case study in municipal management, European Journal of Operational Research, 33, 159-173 (1988)
[4] Belton, V.; Stewart, TJ, Multiple Criteria Decision Analysis - An Integrated Approach (2002), Dordrecht: Kluwer Academic Publishers, Dordrecht
[5] Brans, JP; Vincke, Ph, A preference ranking organization method, Management Science, 31, 647-656 (1985) · Zbl 0609.90073 · doi:10.1287/mnsc.31.6.647
[6] Butler, J.; Dia, J.; Dyer, J., Simulation techniques for the sensitivity analysis of multi-criteria decision models, European Journal of Operational Research, 103, 3, 531-545 (1997) · Zbl 0921.90100 · doi:10.1016/S0377-2217(96)00307-4
[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.
[8] Charnetski, JR; Soland, RM, Multiple-attribute decision making with partial information: the comparative hypervolume criterion, Naval Research Logistics Quarterly, 25, 279-288 (1978) · Zbl 0389.90002 · doi:10.1002/nav.3800250208
[9] David, HA, Order Statistics (1970), New York: Wiley and Sons, New York · Zbl 0223.62057
[10] Durbach, I., A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions, European Journal of Operational Research, 170, 3, 923-934 (2006) · Zbl 1091.90511 · doi:10.1016/j.ejor.2004.06.031
[11] Durbach, I., On the estimation of a satisficing model of choice using stochastic multicriteria acceptability analysis, Omega, 37, 3, 497-509 (2009) · doi:10.1016/j.omega.2007.09.001
[12] Durbach, IN, The use of the SMAA acceptability index in descriptive decision analysis, European Journal of Operational Research, 196, 3, 1229-1237 (2009) · Zbl 1176.90284 · doi:10.1016/j.ejor.2008.05.021
[13] Durbach, IN; Stewart, TJ, Using expected values to simplify decision making under uncertainty, Omega, 37, 2, 312-330 (2009) · doi:10.1016/j.omega.2007.02.001
[14] French, S., Uncertainty and imprecision: modelling and analysis, The Journal of the Operational Research Society, 46, 1, 70-79 (1995) · Zbl 0829.90078
[15] García, RG; Aráoz, JA; Palacios, F., Integral analysis method - IAM, European Journal of Operational Research, 193, 3, 891-903 (2009) · Zbl 1157.90522 · doi:10.1016/j.ejor.2007.10.053
[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. · Zbl 0898.90071
[17] Hipel, KW, Fuzzy set techniques in decision making, Resource Management and Optimization, 2, 3, 187-203 (1983)
[18] Hokkanen, J.; Lahdelma, R.; Miettinen, K.; Salminen, P., Determining the implementation order of a general plan by using a multicriteria method, Journal of Multi-Criteria Decision Analysis, 7, 5, 273-284 (1998) · Zbl 0910.90188 · doi:10.1002/(SICI)1099-1360(199809)7:5<273::AID-MCDA198>3.0.CO;2-1
[19] Hokkanen, J.; Lahdelma, R.; Salminen, P., 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) · doi:10.1016/S0038-0121(98)00007-X
[20] Hokkanen, J.; Lahdelma, R.; Salminen, P., Multicriteria decision support in a technology competition for cleaning polluted soil in Helsinki, Journal of Environmental Management, 60, 4, 339-348 (2000) · doi:10.1006/jema.2000.0389
[21] Jia, J.; Fisher, G.; Dyer, J., Attribute weighting methods and decision quality in the presence of response error: a simulation study, Journal of Behavioural Decision Making, 11, 85-105 (1998) · doi:10.1002/(SICI)1099-0771(199806)11:2<85::AID-BDM282>3.0.CO;2-K
[22] A.B. Kahn. Topological sorting of large networks. Communications of the ACM, pages 558-562, 1962. · Zbl 0106.32602
[23] Kahneman, D.; Tversky, A., Prospect theory: an analysis of decisions under risk, Econometrica, 47, 262-291 (1979) · Zbl 0411.90012 · doi:10.2307/1914185
[24] Kangas, A.; Kangas, J.; Lahdelma, R.; Salminen, P., Using SMAA-2 method with dependent uncertainties for strategic forest planning, Forest Policy and Economics, 9, 113-125 (2006) · doi:10.1016/j.forpol.2005.03.012
[25] Kangas, J.; Hokkanen, J.; Kangas, A.; Lahdelma, R.; Salminen, P., Applying stochastic multicriteria acceptability analysis to forest ecosystem management with both cardinal and ordinal criteria, Forest Science, 49, 6, 928-937 (2003)
[26] Keeney, R.; Raiffa, H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs (1976), New York: John Wiley & Sons, New York · Zbl 0396.90001
[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. · Zbl 0910.90188
[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.
[29] Lahdelma, R.; Hokkanen, J.; Salminen, P., SMAA - stochastic multiobjective acceptability analysis, European Journal of Operational Research, 106, 1, 137-143 (1998) · doi:10.1016/S0377-2217(97)00163-X
[30] Lahdelma, R.; Makkonen, S.; Salminen, P., Multivariate Gaussian criteria in SMAA, European Journal of Operational Research, 170, 3, 957-970 (2006) · Zbl 1091.90030 · doi:10.1016/j.ejor.2004.08.022
[31] Lahdelma, R.; Makkonen, S.; Salminen, P., Two ways to handle dependent uncertainties in multi-criteria decision problems, Omega, 37, 1, 79-92 (2009) · doi:10.1016/j.omega.2006.08.005
[32] Lahdelma, R.; Miettinen, K.; Salminen, P., Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA), European Journal of Operational Research, 147, 1, 117-127 (2003) · Zbl 1011.90026 · doi:10.1016/S0377-2217(02)00267-9
[33] Lahdelma, R.; Miettinen, K.; Salminen, P., Reference point approach for multiple decision makers, European Journal of Operational Research, 164, 3, 785-791 (2005) · Zbl 1057.90046 · doi:10.1016/j.ejor.2004.01.030
[34] Lahdelma, R.; Salminen, P., SMAA-2: stochastic multicriteria acceptability analysis for group decision making, Operations Research, 49, 3, 444-454 (2001) · Zbl 1163.90552 · doi:10.1287/opre.49.3.444.11220
[35] Lahdelma, R.; Salminen, P., Pseudo-criteria versus linear utility function in stochastic multi-criteria acceptability analysis, European Journal of Operational Research, 141, 2, 454-469 (2002) · Zbl 1081.90597 · doi:10.1016/S0377-2217(01)00276-4
[36] Lahdelma, R.; Salminen, P., Stochastic multicriteria acceptability analysis using the data envelopment model, European Journal of Operational Research, 170, 1, 241-252 (2006) · Zbl 1079.90556 · doi:10.1016/j.ejor.2004.07.040
[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.
[38] Lahdelma, R.; Salminen, P., Prospect theory and stochastic multicriteria acceptability analysis (SMAA), Omega, 37, 5, 961-971 (2009) · doi:10.1016/j.omega.2008.09.001
[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. · Zbl 1163.90552
[40] Lahdelma, R.; Salminen, P.; Hokkanen, J., Using multicriteria methods in environmental planning and management, Environmental Management, 26, 6, 595-605 (2000) · doi:10.1007/s002670010118
[41] Lahdelma, R.; Salminen, P.; Hokkanen, J., Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria, European Journal of Operational Research, 142, 2, 345-356 (2002) · Zbl 1082.90536 · doi:10.1016/S0377-2217(01)00303-4
[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. · Zbl 1014.90054
[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.
[44] Leskinen, P.; Viitanen, J.; Kangas, A.; Kangas, J., Alternatives to incorporate uncertainty and risk attitude in multicriteria evaluation of forest plans, Forest Science, 52, 3, 304-312 (2006)
[45] Makkonen, S.; Lahdelma, R., Analysis of power pools in the deregulated energy market through simulation, Decision Support Systems, 30, 3, 289-301 (2001) · doi:10.1016/S0167-9236(00)00106-8
[46] Makkonen, S.; Lahdelma, R.; Asell, AM; Jokinen, A., Multicriteria decision support in the liberated energy market, Journal of Multi-Criteria Decision Analysis, 12, 1, 27-42 (2003) · doi:10.1002/mcda.341
[47] Maystre, L-Y; Pictet, J.; Simos, J., Méthodes Multicritères ELECTRE (1994), Lausanne: Presses Polytechniques et Universitaires Romandes, Lausanne
[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. · Zbl 1181.90181
[49] J. S. Milton and J.C. Arnold. Introduction to Probability and Statistics. Probability and Statistics. McGraw-Hill Inc., New York, 3rd edition, 1995.
[50] Paelinck, JHP, Qualitative multiple criteria analysis, environmental protection and multiregional development, Papers of the Regional Science Association, 36, 59-74 (1976) · doi:10.1007/BF01944375
[51] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 341-356 (1982) · Zbl 0501.68053 · doi:10.1007/BF01001956
[52] Pirlot, M., 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) · Zbl 0838.90072 · doi:10.1002/mcda.4020040104
[53] Rietveld, P., Multiple Objective Decision Methods and Regional Planning (1980), Amsterdam: North-Holland, Amsterdam
[54] Rietveld, P.; Ouwersloot, H., Ordinal data in multicriteria decision making, a stochastic dominance approach to siting nuclear power plants, European Journal of Operational Research, 56, 249-262 (1992) · doi:10.1016/0377-2217(92)90226-Y
[55] Roy, B., 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) · Zbl 0377.90003
[56] Roy, B., Multicriteria Methodology for Decision Aiding (1996), Dordrecht: Kluwer Academic Publishers, Dordrecht · Zbl 0893.90108
[57] Salminen, P.; Wallenius, J., Testing prospect theory in a deterministic multiple criteria decision making environment, Decision Sciences, 24, 279-294 (1993) · doi:10.1111/j.1540-5915.1993.tb00475.x
[58] Shafer, G., A Mathematical Theory of Evidence (1976), Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 0359.62002
[59] Stewart, T., Use of piecewise linear value functions in interactive multicriteria decision support, Management Science, 39, 11, 1369-1381 (1993) · Zbl 0800.90607 · doi:10.1287/mnsc.39.11.1369
[60] Stewart, T., Simplified approaches for multicriteria decision making under uncertainty, Journal of Multi-Criteria Decision Analysis, 4, 4, 246-248 (1995) · Zbl 0849.90080 · doi:10.1002/mcda.4020040404
[61] Stewart, T., Robustness of additive value function methods in mcdm, Journal of Multi-Criteria Decision Analysis, 5, 4, 301-309 (1996) · Zbl 0863.90007 · doi:10.1002/(SICI)1099-1360(199612)5:4<301::AID-MCDA120>3.0.CO;2-Q
[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.
[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.
[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.
[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.
[66] Tervonen, T.; Figueira, JR, A survey on stochastic multicriteria acceptability analysis methods, Journal of Multi-Criteria Decision Analysis, 15, 1-2, 1-14 (2008) · Zbl 1205.90268 · doi:10.1002/mcda.407
[67] Tervonen, T.; Figueira, JR; Lahdelma, R.; Almeida Dias, J.; Salminen, P., A stochastic method for robustness analysis in sorting problems, European Journal of Operational Research, 192, 1, 236-242 (2009) · Zbl 1179.90226 · doi:10.1016/j.ejor.2007.09.008
[68] Tervonen, T.; Hakonen, H.; Lahdelma, R., Elevator planning with stochastic multicriteria acceptability analysis, Omega, 36, 3, 352-362 (2008) · doi:10.1016/j.omega.2006.04.017
[69] Tervonen, T.; Lahdelma, R., Implementing stochastic multicriteria acceptability analysis, European Journal of Operational Research, 178, 2, 500-513 (2007) · Zbl 1107.90026 · doi:10.1016/j.ejor.2005.12.037
[70] Tervonen, T.; Linkov, I.; Steevens, J.; Chappell, M.; Figueira, JR; Merad, M., Risk-based classification system of nanomaterials, Journal of Nanoparticle Research, 11, 4, 757-766 (2009) · doi:10.1007/s11051-008-9546-1
[71] Vincke, Ph, Multicriteria Decision-Aid (1992), Chichester: John Wiley & Sons, Chichester · Zbl 0841.90005
[72] von Nitzsch, R.; Weber, M., The effect of attribute ranges on weights in multiattribute utility measurements, Management Science, 39, 8, 937-943 (1993) · Zbl 0800.90071 · doi:10.1287/mnsc.39.8.937
[73] I. Yevseyeva. Solving classification problems with multicriteria decision aiding approaches. PhD thesis, University of Jyväskylä, Finland, 2007. Jyväskylä Studies in Computing 84.
[74] Zadeh, LA, Fuzzy sets, Information and Control, 8, 3, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.