Recent findings from numerical analysis in multi-criteria decision making
Abstract
Numerical investigations have shown, that different function profiles for the description of variants are possible. This should be taken into account for mapping of characteristic values on a dimensionless interval [1; 0] or [1; ~ 0]. The purpose of the study was to investigate the impact of linear, concave and convex function profiles for mapping on a dimensionless interval (normalisation). Ten different formulas were examined.
The analysis of calculation approaches in the past revealed that only a single transformation formula was used for all criteria. A specific investigation into a functional character of the different initial values has not been done. Hence, the question whether this being a real or fictitious calculation was not answered. The performed analyses are supposed to contribute to the prevention of erroneous decisions.
Keyword : multi-criteria decisions, calculation of dimensionless values, game theory, non-linear decision making problems, optimal variant selection, construction management
How to Cite
Peldschus, F. (2018). Recent findings from numerical analysis in multi-criteria decision making. Technological and Economic Development of Economy, 24(4), 1695-1717. https://doi.org/10.3846/20294913.2017.1356761
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Song, Y.; Wang, X.; Lei, L.; Xue, A. 2014. Combination of interval-valued belief structures based on intuitionistic fuzzy set, Knowledge-Based Systems 67: 61–70. https://doi.org/10.1016/j.knosys.2014.06.008
Stanujkic, D.; Magdalinovic, N.; Jovanovic, R. 2013. A Multi-attribute decision making model based on distance from decision maker’s preferences, Informatica 24(1): 103–118.
Stanujkic, D.; Zavadskas, E. K. 2015. A modified weighted sum method based on the decision-maker’s preferred levels of performances, Studies in Informatics and Control 24(4): 461–470. https://doi.org/10.24846/v24i4y201510
Stopp, F. 1975. Variantenvergleich durch Matrixspiele. Wissenschaftliche Zeitschrift der Hochschule für Bauwesen Leipzig Heft 2.
Turskis, Z.; Zavadskas, E. K. 2010. A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method, Informatica 21(4): 597–610.
Ullah, A. M. M.; Harib, K. H. 2008. An intelligent method for selecting optimal materials and ist application, Advanced Engineering Informatics 22(4): 473–483. https://doi.org/10.1016/j.aei.2008.05.006
Wallace, K.; Burgess, S. 1995. Methods and tools for decision making in engineering design, Journal of Design Studies 16(4): 429–446. https://doi.org/10.1016/0142-694X(95)00019-N
Weitendorf, D. 1976. Beitrag zur Optimierung der räumlichen Struktur eines Gebäudes: Dissertation A. Hochschule für Architektur und Bauwesen Weimar.
Zavadskas, E. K.; Kaklauskas, A.; Bainaitienė, N. 2001. Pastato gyvavimo proceso daugiakriternė analizė. Vilnius: Technika.
Zavadskas, E. K.; Zakarevičius, A.; Turskis, Z.; Antuchevičienė, J. 2006a. Influence of a normalization method on ranking accuracy in multi-criteria decisions, International conference on operational research: simulation and optimisation in business and industry, 17–20 May, 2006 Tallinn, Estonia. Kaunas: Technologija, 147–152.
Zavadskas, E. K.; Zakarevičius, A.; Antuchevičienė, J. 2006b. Evaluation of ranking accuracy in multicriteria decisions, Informatica 17(4): 601–618.
Zavadskas, E. K.; Kaklauskas, A. 2007. Mehrzielselektion für Entscheidungen im Bauwesen. Fraunhofer IRB, Verlag.
Zavadskas, E. K.; Turskis, Z. 2008. A new Logarithmic Normalization Method in Games Theory, Informatica 19(2): 303–314.
Zavadskas, E. K.; Vilutienė, T.; Turskis, Z.; Šaparauskas, J. 2014. Multi-criteria analysis of Projects’ performance in construction, Archives of Civil and Mechanical Engineering 14(1): 114–121. https://doi.org/10.1016/j.acme.2013.07.006
Zavadskas, E. K.; Antucheviciene, J.; Hajiagha, S. H. R.; Hashemi, Sh. S. H. 2015. The Interval-Valued Intuitionistic fuzzy MULTIMOORA method for group decision making in engineering, Mathematical Problems in Engineering Vol. 2015, Article ID 560690. 13 p. https://doi.org/10.1155/2015/560690
Chatterjee, P.; Chakraborty, S. 2012. Materials selection using COPRAS and COPRAS-G methods, International Journal of Materials and Structural Integrity 6(2/3/4): 2012: 111–133.
Chatterjee, P.; Chakraborty, S. 2014. Investigating the effect of normalization norms in flexible manufacturing system selection using multi-criteria decision-making methods, Journal of Engineering Science and Technology Review 7(3):141–150.
Cloquell, V.; Santamarina, C. 2001. A new procedure for the numerical values normalization in multicriteria decision techniques, in MCDA 54th meeting in Durbuy, Belgien. Valencia: Universidad Politécnica de Valencia, 1–10.
Farag, M. M. 2002. Quantitative methods of materials selection, in M. Kutz (Ed.). Handbook of materials selection. New York: Wiley, 3–24. https://doi.org/10.1002/9780470172551.ch1
Hafezalkotob, Arian; Hafezalkotob, Ashkan. 2015. Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications, Materials & Design 87: 949–959. https://doi.org/10.1016/j.matdes.2015.08.087
Hwang, C.-L.; Yoon, K. 1981. Multiple attribute decision making: methods and applications. New York: Springer-Verlag. 259 p. https://doi.org/10.1007/978-3-642-48318-9
Jahan, A.; Edwards, K. L. 2015. A state-of-the-art survey on the influence of normalization techniques in ranking: improving the materials selection process in engineering design, Materials and Design 65: 335–342. https://doi.org/10.1016/j.matdes.2014.09.022
Jüttler, H. 1966. Untersuchungen zu Fragen der Operationsforschung und ihrer Anwendungsmöglichkeiten auf ökonomische Problemstellungen unter besonderer Berücksichtigung der Spieltheorie: Dissertation A. Wirtschaftswissenschaftliche Fakultät der Humbold-Universität Berlin.
Kaftanowicz, M.; Krzemiński, M. 2015. Multiple-criteria analysis of plasterboard systems, Procedia Engineering 111(2015): 364–370. https://doi.org/10.1016/j.proeng.2015.07.102
Körth, H. 1969. Untersuchungen zur nichtlinearen Optimierung ökonomischer Erscheinungen und Prozesse unter besonderer Berücksichtigung der Quotenoptimierung sowie der Lösung ökonomischer mathematischer Modelle bei der Existenz mehrerer Zielfunktionen. Habilitationsschrift, HumboldUniversität Berlin, Sektion Wirtschaftswissenschaften.
Milani, A. S.; Shanian, A.; Madoliat, R.; Nemes, J. A. 2005. The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection, Industrial Applications, Structural and Multidisciplinary Optimization 29(4): 312–318. https://doi.org/10.1007/s00158-004-0473-1
Mir, M. A.; Ghazvinei, P. T.; Sulaiman, N. M. N.; Basri, N. E. A.; Saheri, S.; Mahmood, N. Z.; Jahan, A.; Begum, R. A.; Aghamohammadi, N. 2016. Application of TOPSIS and VIKOR improved versions in a multi criteria decision analysis to develop an optimized municipal solid waste management model, Journal of Environmental Management 166: 109–115. https://doi.org/10.1016/j.jenvman.2015.09.028
Myllyviita, T.; Leskinen, P.; Seppälä, J. 2014. Impact of normalisation, elicitation technique and background information on panel weighting results in life cycle assessment, Life Cycle Sustainability Assessment, The International Journal of Life Cycle Assessment 19(2): 377–386. https://doi.org/10.1007/s11367-013-0645-6
Niekerk van, A.; Plessis du, D.; Boonzaaier, I.; Spocter, M.; Ferreira, S.; Loots, L.; Donaldson, R. 2016. Development of a multi-criteria spatial planning support system forgrowth potential modelling in the Western Cape, South Africa, Land Use Policy 50: 179–193. https://doi.org/10.1016/j.landusepol.2015.09.014
Peldschus, F. 1986. Zur Anwendung der Theorie der Spiele für Aufgaben der Bautechnologie: Dissertation B. Technische Hochschule Leipzig.
Peldschus, F. 2008. Experience of the game theory application in construction management, Technological and Economic Development of Economy 14(4): 531–545. https://doi.org/10.3846/1392-8619.2008.14.531-545
Peldschus, F. 2009. The analysis of the quality of the results obtained with the methods of multicriteria Decisions, Technological and Economic Development of Economy 15(4): 580–592. https://doi.org/10.3846/1392-8619.2009.15.580-592
Peng, A-H.; Xiao, X-M. 2013. Material selection using PROMETHEE combined with analytic network process under hybrid environment, Materials & Design 47: 643–652. https://doi.org/10.1016/j.matdes.2012.12.058
Peschel, M. 1980. Ingenieurtechnische Entscheidungen. Verlag Technik Berlin, 168 Seiten.
Pötzsch, H.; Bansemir, U. 1985. Variantenvergleich als Entscheidungshife bei der Planung der Grundfondsreproduktion, in Bauplanung/Bautechnik Heft 5. Verlag für Bauwesen Berlin, 202–204.
Rao, R. V.; Davim, J. P. 2008. A decision-making framework model for material selection using a combined multiple attribute decision-making method, The International Journal of Advanced Manufacturing Technology 35(7): 751–760. https://doi.org/10.1007/s00170-006-0752-7
Song, Y.; Wang, X.; Lei, L.; Xue, A. 2014. Combination of interval-valued belief structures based on intuitionistic fuzzy set, Knowledge-Based Systems 67: 61–70. https://doi.org/10.1016/j.knosys.2014.06.008
Stanujkic, D.; Magdalinovic, N.; Jovanovic, R. 2013. A Multi-attribute decision making model based on distance from decision maker’s preferences, Informatica 24(1): 103–118.
Stanujkic, D.; Zavadskas, E. K. 2015. A modified weighted sum method based on the decision-maker’s preferred levels of performances, Studies in Informatics and Control 24(4): 461–470. https://doi.org/10.24846/v24i4y201510
Stopp, F. 1975. Variantenvergleich durch Matrixspiele. Wissenschaftliche Zeitschrift der Hochschule für Bauwesen Leipzig Heft 2.
Turskis, Z.; Zavadskas, E. K. 2010. A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method, Informatica 21(4): 597–610.
Ullah, A. M. M.; Harib, K. H. 2008. An intelligent method for selecting optimal materials and ist application, Advanced Engineering Informatics 22(4): 473–483. https://doi.org/10.1016/j.aei.2008.05.006
Wallace, K.; Burgess, S. 1995. Methods and tools for decision making in engineering design, Journal of Design Studies 16(4): 429–446. https://doi.org/10.1016/0142-694X(95)00019-N
Weitendorf, D. 1976. Beitrag zur Optimierung der räumlichen Struktur eines Gebäudes: Dissertation A. Hochschule für Architektur und Bauwesen Weimar.
Zavadskas, E. K.; Kaklauskas, A.; Bainaitienė, N. 2001. Pastato gyvavimo proceso daugiakriternė analizė. Vilnius: Technika.
Zavadskas, E. K.; Zakarevičius, A.; Turskis, Z.; Antuchevičienė, J. 2006a. Influence of a normalization method on ranking accuracy in multi-criteria decisions, International conference on operational research: simulation and optimisation in business and industry, 17–20 May, 2006 Tallinn, Estonia. Kaunas: Technologija, 147–152.
Zavadskas, E. K.; Zakarevičius, A.; Antuchevičienė, J. 2006b. Evaluation of ranking accuracy in multicriteria decisions, Informatica 17(4): 601–618.
Zavadskas, E. K.; Kaklauskas, A. 2007. Mehrzielselektion für Entscheidungen im Bauwesen. Fraunhofer IRB, Verlag.
Zavadskas, E. K.; Turskis, Z. 2008. A new Logarithmic Normalization Method in Games Theory, Informatica 19(2): 303–314.
Zavadskas, E. K.; Vilutienė, T.; Turskis, Z.; Šaparauskas, J. 2014. Multi-criteria analysis of Projects’ performance in construction, Archives of Civil and Mechanical Engineering 14(1): 114–121. https://doi.org/10.1016/j.acme.2013.07.006
Zavadskas, E. K.; Antucheviciene, J.; Hajiagha, S. H. R.; Hashemi, Sh. S. H. 2015. The Interval-Valued Intuitionistic fuzzy MULTIMOORA method for group decision making in engineering, Mathematical Problems in Engineering Vol. 2015, Article ID 560690. 13 p. https://doi.org/10.1155/2015/560690