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Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models

  • Nejc Trdin
  • Marko Bohanec
Original Paper

Abstract

DEX is a qualitative multi-criteria decision analysis method. The method supports decision makers in making complex decisions based on multiple, possibly conflicting, attributes. The attributes in DEX have qualitative value scales and are structured hierarchically. The hierarchical topology allows for decomposition of the decision problem into simpler sub-problems. In DEX, alternatives are described with qualitative values, taken from the scales of corresponding input attributes in the hierarchy. The evaluation of alternatives is performed in a bottom-up way, utilizing aggregation functions, which are defined for every aggregated attribute in the form of decision rules. DEX has been used in numerous practical applications—from everyday decision problems to solving decision problems in the financial and ecological domains. Based on experience, we identified the need for three major methodological extensions to DEX: introducing numeric attributes, the probabilistic and fuzzy aggregation of values and relational models. These extensions were proposed by users of the existing method and by the new demands of complex decision problems, which require advanced decision making approaches. In this paper, we introduce these three extensions by describing the extensions formally, justifying their contributions to the decision making process and illustrating them on a didactic example, which is followed throughout the paper.

Keywords

Multiple criteria analysis Qualitative decision models DEX method Relational models Probability and fuzzy distributions 

Notes

Acknowledgements

Funding was provided by ARRS, the Slovenian Research Agency, grant number 1000-11-310228.

References

  1. Bana e Costa C, Vansnick J-C (1999) The MACBETH approach: basic ideas, software, and an application. In: Meskens N, Roubens M (eds) Advances in decision analysis, vol 4. Kluwer Academic Publishers, Netherlands, pp 131–157CrossRefGoogle Scholar
  2. Baracskai Z, Dörfler V (2003) Automated fuzzy-clustering for Doctus expert system. In: International conference on computational cybernetics, Siófok, HungaryGoogle Scholar
  3. Bede B (2012) Mathematics of fuzzy sets and fuzzy logic. In: Kacprzyk J (ed) Studies in fuzziness and soft computing, vol 295. Springer, HeidelbergGoogle Scholar
  4. Bergez J-E (2013) Using a genetic algorithm to fefine worst-best and best-worst options of a DEXi-type model: application to the MASC model of cropping-system sustainability. Comput Electron Agric 90:93–98CrossRefGoogle Scholar
  5. Bohanec M (2014) DEXi: program for multi-attribute decision making: user’s manual, version 4.01, IJS Report DP-11739. Jožef Stefan Institute, LjubljanaGoogle Scholar
  6. Bohanec M (2015a) DEX: an expert system shell for multi-attribute decision making. http://kt.ijs.si/MarkoBohanec/dex.html. Accessed 21 May 2015
  7. Bohanec M (2015b) DEXi: a program for multi-attribute decision making. http://kt.ijs.si/MarkoBohanec/dexi.html. Accessed 21 May 2015
  8. Bohanec M, Aprile G, Constante M, Foti M, Trdin N (2014) A hierarchical multi-attribute model for bank reputational risk assessment. In: Phillips-Wren G, Carlsson S, Respício A (eds) 17th conference for IFIP WG8.3 DSS, Paris, France. IOS Press, pp 92–103Google Scholar
  9. Bohanec M et al (2009) The co-extra decision support system: a model-based integration of project results. In: Co-extra international conference. France, Paris, pp 63–64Google Scholar
  10. Bohanec M et al (2008) A qualitative multi-attribute model for economic and ecological assessment of genetically modified crops. Ecol Model 215:247–261CrossRefGoogle Scholar
  11. Bohanec M, Rajkovič V (1990) DEX: an expert system shell for decision support. Sistemica 1:145–157Google Scholar
  12. Bohanec M, Rajkovič V (1999) Multi-attribute decision modeling: industrial applications of DEX. Informatica 23:487–491Google Scholar
  13. Bohanec M, Rajkovič V, Bratko I, Zupan B, Žnidaršič M (2013) DEX methodology: three decades of qualitative multi-attribute modeling. Informatica 37:49–54Google Scholar
  14. Bohanec M, Trdin N (2014) Qualitative multi-attribute decision method DEX: theory and practice. In: 20th conference of the international federation of operational research societies, Barcelona Spain. p 239Google Scholar
  15. Bohanec M, Trdin N, Kontić B (2016) A qualitative multi-criteria modelling approach to the assessment of electric energy production technologies in Slovenia. Cent Eur J Oper Res. doi: 10.1007/s10100-016-0457-4 Google Scholar
  16. Bohanec M, Žnidaršič M (2008) Supporting decisions about the introduction of genetically modified crops. In: Zaraté P, Belaud JP, Camilleri G, Ravat F (eds) Collaborative decision making: perspectives and challenges. Frontiers in artificial intelligence and applications, vol 176. IOS Press, Amsterdam, pp 404–415Google Scholar
  17. Boose JH, Bradshaw JM, Koszarek JL, Shema DB (1993) Knowledge acquisition techniques for group decision support. Knowl Acquis 5:405–448CrossRefGoogle Scholar
  18. Bouyssou D, Marchant T, Pirlot M, Tsoukiàs A, Vincke P (2006) Evaluation and decision models with multiple criteria. Springer, New YorkGoogle Scholar
  19. Brans JP, Vincke P (1985) A preference ranking organisation method: the PROMETHEE method for MCDM. Manag Sci 31:647–656CrossRefGoogle Scholar
  20. Caflisch RE (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numer 7:1–49CrossRefGoogle Scholar
  21. Clemen RT, Reilly T (2001) Making hard decisions with decisiontools. Duxbury/Thomson Learning, Pacific GroveGoogle Scholar
  22. Corrente S, Greco S, Słowiński R (2012) Multiple criteria hierarchy process in robust ordinal regression. Decis Support Syst 53(3):660–674CrossRefGoogle Scholar
  23. Dembczyński K, Greco S, Słowiński R (2009) Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur J Oper Res 198:626–636CrossRefGoogle Scholar
  24. Durbach IN, Stewart TJ (2012) Modeling uncertainty in multi-criteria decision analysis. Eur J Oper Res 223:1–14CrossRefGoogle Scholar
  25. Feller W (1968) An Introduction to probability theory and its applications, vol 1, 3rd edn. Wiley, New YorkGoogle Scholar
  26. Figueira J, Greco S, Ehrogott M (2005) Multiple criteria decision analysis: state of the art surveys. Springer, New YorkCrossRefGoogle Scholar
  27. French S (1986) Decision theory: an introduction to the mathematics of rationality. Halsted Press, New YorkGoogle Scholar
  28. Gomes LFAM, Moshkovich HM, Torres A (2010) Marketing decisions in small business: how verbal decision analysis can help. Int J Manag Decis Mak 11:19–36Google Scholar
  29. Greco S, Matarazzo B, Słowiński R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129:1–47CrossRefGoogle Scholar
  30. Greco S, Matarazzo B, Słowiński R (2002) Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur J Oper Res 138:247–259CrossRefGoogle Scholar
  31. Greco S, Matarazzo B, Słowiński R (2010) Dominance-based rough set approach to decision under uncertainty and time preference. Ann Oper Res 176:41–75CrossRefGoogle Scholar
  32. Hadar J, Rusell WR (1969) Rules for ordering uncertain prospects. Am Econ Rev 59:25–34Google Scholar
  33. Hewitt E, Stromberg K (1965) Real and abstract analysis. Springer, BerlinCrossRefGoogle Scholar
  34. Holt J et al (2013) Eliciting and combining decision criteria using a limited palette of utility functions and uncertainty distributions: illustrated by application to pest risk analysis. Risk Anal 34:4–16CrossRefGoogle Scholar
  35. Ishizaka A, Nemery P (2013) Multi-criteria decision analysis: methods and software. Wiley, ChichesterCrossRefGoogle Scholar
  36. Jacquet-Lagrèze E, Siskos Y (1982) Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur J Oper Res 10:151–164CrossRefGoogle Scholar
  37. Jacquet-Lagrèze E, Siskos Y (2001) Preference disaggregation: 20 years of MCDA experience. Eur J Oper Res 130(2):233–245CrossRefGoogle Scholar
  38. Kadziński M, Greco S, Słowiński R (2014) Robust ordinal regression for dominance-based rough set approach to multiple criteria sorting. Inf Sci 283:211–228CrossRefGoogle Scholar
  39. Kahraman C (2008) Fuzzy multi-criteria decision making. In: Pardalos PM, Du D-Z (eds) Springer optimization and its applications, vol 16. Springer, New YorkGoogle Scholar
  40. Kontić B, Bohanec M, Trdin N, Kontić D, Zagorc-Kontić S, Matko M (2014) Comparative evaluation of various energy options using qualitative multi-attribute models. In: 20th conference of the international federation of operational research societies, Barcelona, Spain, p 239Google Scholar
  41. Kuzmanovski V, Trajanov A, Leprince F, Džeroski S, Debeljak M (2015) Modeling water outflow from tile-drained agricultural fields. Sci Total Environ 505:390–401CrossRefGoogle Scholar
  42. Larichev OI (2001) Ranking multicriteria alternatives: the method ZAPROS III. Eur J Oper Res 131:550–558CrossRefGoogle Scholar
  43. Larichev OI, Moshkovich HM (1994) An approach to ordinal classification problems. Int Trans Oper Res 1:375–385CrossRefGoogle Scholar
  44. Larichev OI, Moshkovich HM (1995) ZAPROS-LM—a method and system for ordering multiattribute alternatives. Eur J Oper Res 82:503–521CrossRefGoogle Scholar
  45. Larichev OI, Moshkovich HM (1997) Verbal decision analysis for unstructured problems. In: Herings JJ, Jackson MO, Kaneko M, Peters H, Peleg B, Puppe C, Roth AE, Schmeidler D, Thomson W, Vohra R, Wakker PP, Tijs SH (eds) Theory and decision library C, vol 17. Springer, US, New YorkGoogle Scholar
  46. Lavrač N, Džeroski S (1994) Inductive logic programming: techniques and applications. Ellis Horwood, New YorkGoogle Scholar
  47. Leben A, Kunstelj M, Bohanec M, Vintar M (2006) Evaluating public administration e-portals. Inf Polity Dev e-Gov Cent East Eur 11:207–225Google Scholar
  48. Mihelčić M, Bohanec M (2016) Approximating incompletely defined utility functions of qualitative multi-criteria modeling method DEX. Cent Eur J Oper Res. doi: 10.1007/s10100-016-0451-x Google Scholar
  49. Mileva-Boshkoska B, Bohanec M (2012) A method for ranking non-linear qualitative decision preferences using copulas. Int J Decis Support Syst Technol 4:42–58CrossRefGoogle Scholar
  50. Moshkovich HM, Mechitov AI (2013) Verbal decision analysis: foundations and trends. Adv Decis Sci 2013:9Google Scholar
  51. Nagel SS (1993) Computer-aided decision analysis: theory and applications. Praeger, WestportGoogle Scholar
  52. Omero M, D’Ambrosio L, Pesenti R, Ukovich W (2005) Multiple-attribute decision support system based on fuzzy logic for performance assessment. Eur J Oper Res 160:710–725CrossRefGoogle Scholar
  53. Rajkovič V, Bohanec M, Efstathiou J (1987) Ranking multiple options with DECMAK. In: Hagwood J, Humphreys P (eds) Effective decision support systems. Gower Technical Press, Aldershot, pp 49–60Google Scholar
  54. Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theory Decis 31:44–73CrossRefGoogle Scholar
  55. Saaty TL (2008) Decision making with the analytic hierarchy process. Int J Serv Sci 1:83–98Google Scholar
  56. Saaty TL, Vargas LG (2012) Models, methods, concepts & applications of the analytic hierarchy process. In: Price CC, Zhu J, Hillier FS (eds) International series in operations research & management science, vol 175. Springer, US, New YorkGoogle Scholar
  57. Shachter RD, Peot MA (1992) Decision making using probabilistic inference methods. In: Dubois D, Wellman MP, D’Ambrosio B, Smets P (eds) Eighth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers Inc, StanfordGoogle Scholar
  58. Skinner DC (2009) Introduction to decision analysis, 3rd edn. Probabilistic Publishing, GainesvilleGoogle Scholar
  59. Trdin N, Bohanec M (2012) Extending the multi-criteria decision making method DEX. In: Petelin D, Tavčar A, Kaluža B (eds) 4th Jožef Stefan international postgraduate school students conference. Ljubljana, Slovenia, pp 182–187Google Scholar
  60. Trdin N, Bohanec M (2013) Relational multi-attribute models in DEX methodology. In: Ruiz F (ed) 22nd international conference on multiple criteria decision making. Málaga, Spain, p 317Google Scholar
  61. Trdin N, Bohanec M (2014a) New generation platform for multi-criteria decision making with method DEX. In: Phillips-Wren G, Carlsson S, Burstein F, Respício A, Brézillon P (eds) 17th conference for IFIP WG8.3 DSS, Paris, France. DSS 2.0—Supporting decision making with new technologies. IOS PressGoogle Scholar
  62. Trdin N, Bohanec M (2014b) Numerical relational multi-attribute models in qualitative multi-attribute method DEX. In: 20th conference of the international federation of operational research societies, Barcelona, Spain, p 240Google Scholar
  63. Wang J, Zionts S (2008) Negotiating wisely: considerations based on MCDM/MAUT. Eur J Oper Res 188:191–205CrossRefGoogle Scholar
  64. Yang JB, Wang YM, Xu DL, Chin KS (2006) The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties. Eur J Oper Res 171:309–343CrossRefGoogle Scholar
  65. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefGoogle Scholar
  66. Žnidaršič M, Bohanec M, Bratko I (2003) Categorization of numerical values for DEX hierarchical models. Informatica 27:405–409Google Scholar
  67. Žnidaršič M, Bohanec M, Lavrač N, Cestnik B (2009) Project self-evaluation methodology: the healthreats project case study. In: Bohanec M et al (eds) Information Society—IS 2009. Ljubljana, Slovenia, Institut Jožef StefanGoogle Scholar
  68. Žnidaršič M, Bohanec M, Trdin N (2012) Qualitative assessment of data-mining workflows. In: Respício A, Burstein F (eds) Fusing decision support systems into the fabric of the context. Frontiers in artificial intelligence and applications. IOS Press, Amsterdam, pp 75–86Google Scholar
  69. Žnidaršič M, Bohanec M, Zupan B (2006a) Higher-order uncertainty approach to revision of probabilistic qualitative multi-attribute decision models. In: Adam F, Brézillon P, Carlsson S, Humphreys P (eds) IFIP WG8.3 international conference on creativity and innovation in decision making and decision support. Ludic Publishing, LondonGoogle Scholar
  70. Žnidaršič M, Bohanec M, Zupan B (2006b) proDEX—a DSS tool for environmental decision-making. Environ Model Softw 21:1514–1516CrossRefGoogle Scholar
  71. Žnidaršič M, Bohanec M, Zupan B (2008) Modelling impacts of cropping systems: demands and solutions for DEX methodology. Eur J Oper Res 189:594–608CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.“Jožef Stefan” InstituteLjubljanaSlovenia
  2. 2.Jožef Stefan International Postgraduate SchoolLjubljanaSlovenia

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