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.
Similar content being viewed by others
References
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 131–157
Baracskai Z, Dörfler V (2003) Automated fuzzy-clustering for Doctus expert system. In: International conference on computational cybernetics, Siófok, Hungary
Bede B (2012) Mathematics of fuzzy sets and fuzzy logic. In: Kacprzyk J (ed) Studies in fuzziness and soft computing, vol 295. Springer, Heidelberg
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 90:93–98
Bohanec M (2014) DEXi: program for multi-attribute decision making: user’s manual, version 4.01, IJS Report DP-11739. Jožef Stefan Institute, Ljubljana
Bohanec M (2015a) DEX: an expert system shell for multi-attribute decision making. http://kt.ijs.si/MarkoBohanec/dex.html. Accessed 21 May 2015
Bohanec M (2015b) DEXi: a program for multi-attribute decision making. http://kt.ijs.si/MarkoBohanec/dexi.html. Accessed 21 May 2015
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 92–103
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 63–64
Bohanec M et al (2008) A qualitative multi-attribute model for economic and ecological assessment of genetically modified crops. Ecol Model 215:247–261
Bohanec M, Rajkovič V (1990) DEX: an expert system shell for decision support. Sistemica 1:145–157
Bohanec M, Rajkovič V (1999) Multi-attribute decision modeling: industrial applications of DEX. Informatica 23:487–491
Bohanec M, Rajkovič V, Bratko I, Zupan B, Žnidaršič M (2013) DEX methodology: three decades of qualitative multi-attribute modeling. Informatica 37:49–54
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 239
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
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 404–415
Boose JH, Bradshaw JM, Koszarek JL, Shema DB (1993) Knowledge acquisition techniques for group decision support. Knowl Acquis 5:405–448
Bouyssou D, Marchant T, Pirlot M, Tsoukiàs A, Vincke P (2006) Evaluation and decision models with multiple criteria. Springer, New York
Brans JP, Vincke P (1985) A preference ranking organisation method: the PROMETHEE method for MCDM. Manag Sci 31:647–656
Caflisch RE (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numer 7:1–49
Clemen RT, Reilly T (2001) Making hard decisions with decisiontools. Duxbury/Thomson Learning, Pacific Grove
Corrente S, Greco S, Słowiński R (2012) Multiple criteria hierarchy process in robust ordinal regression. Decis Support Syst 53(3):660–674
Dembczyński K, Greco S, Słowiński R (2009) Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur J Oper Res 198:626–636
Durbach IN, Stewart TJ (2012) Modeling uncertainty in multi-criteria decision analysis. Eur J Oper Res 223:1–14
Feller W (1968) An Introduction to probability theory and its applications, vol 1, 3rd edn. Wiley, New York
Figueira J, Greco S, Ehrogott M (2005) Multiple criteria decision analysis: state of the art surveys. Springer, New York
French S (1986) Decision theory: an introduction to the mathematics of rationality. Halsted Press, New York
Gomes LFAM, Moshkovich HM, Torres A (2010) Marketing decisions in small business: how verbal decision analysis can help. Int J Manag Decis Mak 11:19–36
Greco S, Matarazzo B, Słowiński R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129:1–47
Greco S, Matarazzo B, Słowiński R (2002) Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur J Oper Res 138:247–259
Greco S, Matarazzo B, Słowiński R (2010) Dominance-based rough set approach to decision under uncertainty and time preference. Ann Oper Res 176:41–75
Hadar J, Rusell WR (1969) Rules for ordering uncertain prospects. Am Econ Rev 59:25–34
Hewitt E, Stromberg K (1965) Real and abstract analysis. Springer, Berlin
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 34:4–16
Ishizaka A, Nemery P (2013) Multi-criteria decision analysis: methods and software. Wiley, Chichester
Jacquet-Lagrèze E, Siskos Y (1982) Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur J Oper Res 10:151–164
Jacquet-Lagrèze E, Siskos Y (2001) Preference disaggregation: 20 years of MCDA experience. Eur J Oper Res 130(2):233–245
Kadziński M, Greco S, Słowiński R (2014) Robust ordinal regression for dominance-based rough set approach to multiple criteria sorting. Inf Sci 283:211–228
Kahraman C (2008) Fuzzy multi-criteria decision making. In: Pardalos PM, Du D-Z (eds) Springer optimization and its applications, vol 16. Springer, New York
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 239
Kuzmanovski V, Trajanov A, Leprince F, Džeroski S, Debeljak M (2015) Modeling water outflow from tile-drained agricultural fields. Sci Total Environ 505:390–401
Larichev OI (2001) Ranking multicriteria alternatives: the method ZAPROS III. Eur J Oper Res 131:550–558
Larichev OI, Moshkovich HM (1994) An approach to ordinal classification problems. Int Trans Oper Res 1:375–385
Larichev OI, Moshkovich HM (1995) ZAPROS-LM—a method and system for ordering multiattribute alternatives. Eur J Oper Res 82:503–521
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 York
Lavrač N, Džeroski S (1994) Inductive logic programming: techniques and applications. Ellis Horwood, New York
Leben A, Kunstelj M, Bohanec M, Vintar M (2006) Evaluating public administration e-portals. Inf Polity Dev e-Gov Cent East Eur 11:207–225
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
Mileva-Boshkoska B, Bohanec M (2012) A method for ranking non-linear qualitative decision preferences using copulas. Int J Decis Support Syst Technol 4:42–58
Moshkovich HM, Mechitov AI (2013) Verbal decision analysis: foundations and trends. Adv Decis Sci 2013:9
Nagel SS (1993) Computer-aided decision analysis: theory and applications. Praeger, Westport
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 160:710–725
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 49–60
Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theory Decis 31:44–73
Saaty TL (2008) Decision making with the analytic hierarchy process. Int J Serv Sci 1:83–98
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 York
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, Stanford
Skinner DC (2009) Introduction to decision analysis, 3rd edn. Probabilistic Publishing, Gainesville
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 182–187
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 317
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 Press
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 240
Wang J, Zionts S (2008) Negotiating wisely: considerations based on MCDM/MAUT. Eur J Oper Res 188:191–205
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 171:309–343
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Žnidaršič M, Bohanec M, Bratko I (2003) Categorization of numerical values for DEX hierarchical models. Informatica 27:405–409
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 Stefan
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 75–86
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, London
Žnidaršič M, Bohanec M, Zupan B (2006b) proDEX—a DSS tool for environmental decision-making. Environ Model Softw 21:1514–1516
Žnidaršič M, Bohanec M, Zupan B (2008) Modelling impacts of cropping systems: demands and solutions for DEX methodology. Eur J Oper Res 189:594–608
Acknowledgements
Funding was provided by ARRS, the Slovenian Research Agency, grant number 1000-11-310228.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Trdin, N., Bohanec, M. Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models. Cent Eur J Oper Res 26, 1–41 (2018). https://doi.org/10.1007/s10100-017-0468-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-017-0468-9