Analysis of Lack of Agreement Between MCDM Methods Related to the Solution of a Problem: Proposing a Methodology for Comparing Methods to a Reference
Abstract
It is a proven fact that at present, there is not a course of action that can evaluate or validate the reliability of the solution reached by a MCDM method, because the ‘true’ solution is not known, and it is impossible to make a comparison to assess the efficiency of a result found. This chapter presents a procedure that can help in this endeavour.
It proposes to use a proxy of the true solution, to test a result of any MCDM method; this proxy solution must be the consequence of a more faithful model to replicate as much as possible real-world conditions, as well as the absence of subjectivity in criteria weighting, and the result achieved by an indisputable mathematical procedure. For this purpose, this book suggests using the SIMUS method that fulfils these conditions. In so doing, a problem is solved by this method and its result used as a benchmark to determine the closeness to this result by other methods. To measure the closeness to the proxy, it is suggested to use the Kendall tau rank correlation coefficient (Kendall, Biometrika 30(1–2): 81–89, 1938).
References1
- Arrow K (1951) Social choice and individual values, 2nd edn. Wiley, New York, p 1963Google Scholar
- Brans J, Vincke P (1985) A preference ranking organisation method: (the PROMETHEE method for multiple criteria decision-making). Manag Sci 31(6):647–656CrossRefGoogle Scholar
- Buchanan J, Hening E, Hening M (1998) Objectivity and subjectivity in the decision-making process. Ann Oper Res 80(1998):333–334CrossRefGoogle Scholar
- Ceballos B, Lamata M, Pelta D (2016) A comparative analysis of multi-criteria decision-making methods. Prog Artif Intell 5(4):315–322CrossRefGoogle Scholar
- Cochrane J, Zeleny M (1973) Multiple criteria decision making. University of South Carolina Press, ColumbiaGoogle Scholar
- Dantzig G (1948) Linear programming and extensions. United States Air Force Linear Programming and Extensions, Princeton University Press, PrincetonGoogle Scholar
- DTLR – Department for Transport Local Government and the Regions (2001) Planning green paper planning: delivering a fundamental change, UKGoogle Scholar
- Fishburn P (1991) Nontransitive preferences in decision theory. J Risk Uncertain 4(2):113–134CrossRefGoogle Scholar
- Hwang C, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New YorkCrossRefGoogle Scholar
- Ishizaka A, Nemery P (2013) Multicriteria decision aid: methods and software. Wiley, ChichesterCrossRefGoogle Scholar
- Jahan A, Edwards K (2015) A state-of-the-art survey on the influence of normalization techniques in ranking: improving the materials selection process in engineering design. Mater Des (1980–2015) 65:335–342CrossRefGoogle Scholar
- Kantorovich L (1939) The best uses of economic resourcesGoogle Scholar
- Keeney R, Raffia H (1993) Decisions with multiples objectives – preferences and values. Cambridge University Press, Cambridge/New YorkCrossRefGoogle Scholar
- Kendall M (1938) A new measure of rank correlation. Biometrika 30(1–2):81–89CrossRefGoogle Scholar
- Lieferink M, Van Till J, Groothuis-Oudshoorn K, Goetghebeur M, Dolan J (2014) Validating a multi-criteria decision analysis (MCDA) framework for health care making – University report. https://ris.utwente.nl/ws/portalfiles/portal/6159219. Accesses 5 May 2018
- Lliso P (2014) Multicriteria decision-making by Simus. http://decisionmaking.esy.es/. Accessed 30 Apr 2018
- MacCrimon K (1968) Decision making among multiple attribute alternatives: A survey and consolidated approach. Rand Memorandum, RM-4823-ARPAGoogle Scholar
- Moshkovich H, Monteiro Gomes L, Mechitov A, Rangel S (2012) Influence of model and scales on the ranking of multiattribute alternatives. Pesquisa Operacional 32(3):523–542CrossRefGoogle Scholar
- Mulliner E, Malys N, Maliene V (2016) Comparative analysis of MCDM methods for the assessment of sustainable housing affordability. Omega 59:146–156CrossRefGoogle Scholar
- Oprocovic S (1980) VIseKriterijumska Optimizacija I Kompromisno Resenje (multicriteria optimization and compromise solution). Science Watch, April 2009Google Scholar
- Pearson K (1895) Notes on regression and inheritance in the case of two parents. Proc R Soc Lond 58:240–224CrossRefGoogle Scholar
- Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31(1):49–73CrossRefGoogle Scholar
- Saaty T (1996) Decision making with dependence and feedback: the analytic network process. RWS Publications, PittsburghGoogle Scholar
- Saaty T (2008) Decision making with the analytic hierarchy process. Int J Serv Sci 1(1):83–98Google Scholar
- Shannon C (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379–423, 623–656CrossRefGoogle Scholar
- Simon H (1957) Models of man. Wiley, New YorkGoogle Scholar
- Stanujkic D (2014) Comparative analysis of some prominent MCDM methods: a case of ranking Serbian banks. Serbian J Manag 8(2):213–241CrossRefGoogle Scholar
- Steuer R, Qi Y, Hirschberger M (2005) Multiple objectives in portfolio selection. J Financ Decis Making 1(1):5–20Google Scholar
- Stewart T (1996) Robustness of additive value function methods in MCDM. https://doi.org/10.1002/(SICI)1099-1360(199612)5:4<301::AID-MCDA120>3.0.CO;2-QGoogle Scholar
- Triantaphyllou E, Mann S (1989) An examination of the effectiveness of multi-dimensional decision-making methods: a decision-making paradox. Int J Decis Support Syst (5):303–312CrossRefGoogle Scholar
- Tversky A, Kahnemann D (1974) Judgment under uncertainty: heuristics and biases science. New Series 185(4157):1124–1131Google Scholar
- Wallenius J, Dyer J, Fishburn P, Steuer R, Zionts S, Deb Wang K (2007) Multiple criteria decision making, multiattribute utility theory: recent accomplishments and what lies ahead- seminar, Helsinki School of EconomicsGoogle Scholar
- *Wang X, Triantaphyllou E (2006) Ranking irregularities when evaluating alternatives by using some multi-criteria decision analysis methods. Handbook of industrial and system engineering. CRC Press/Taylor & Francis Group, Boca RatonGoogle Scholar
- *Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Elsevier – Science Direct. Omega 36(1):45–63CrossRefGoogle Scholar
- Yu P (1973) A class of solutions for group decision problems. Manag Sci 19(8):936–946CrossRefGoogle Scholar
- Zanakis S, Solomon A, Wishart N, Dublish S (1998) Multi-attribute decision making: a simulation comparison of selection methods. Eur J Oper Res 107:507–529CrossRefGoogle Scholar
- Zardari N, Ahmed H, Shirazi K, Yusop Z (2015) Weighting methods and their effects on multi-criteria decision-making model outcomes in water resources management. Springer International Publishing, ChamCrossRefGoogle Scholar
- Zeleny M (1974) A concept of compromise solutions and the method of the displaced ideal. Comput Oper Res 1(4):479–496CrossRefGoogle Scholar