Total area based on orthogonal vectors (TAOV) as a novel method of multi-criteria decision aid
Abstract
Multi criteria decision aid (MCDA) deals with the problem of evaluating a set of finite alternatives regard to a set of finite criteria. A remarkable volume of qualitative and quantitative researches are done on decision making methods and situations, indicating its important role for managers at different organizational levels. These types of problems are applied in many different fields of human life. A challenging feature of these problems is non-existence of an optimal solution due to considering multiple criteria and the proposed methods seeking to find a satisfactory solution called efficient of Pareto-optimal. In consideration of MCDA problem, in this paper a new method is proposed for solving DM problems, consisting three fundamental steps of initialization, orthogonalization, and comparison. Thus, a new MCDA method called total area based on orthogonal vectors (TAOV) is introduced. This method is constructed on orthogonality of decision criteria. Application of TAOV method is illustrated in a decision problem and its performance is evaluated regard to other MCDA methods. Furthermore, its features are explained around the features of a desirable MCDA method. The obtained results indicate that the TAOV method can be considered as an acceptable method of handling multi-criteria decision making problems.
Keyword : decision making, Pareto-optimal, multi-criteria decision aid, orthogonality, principal component analysis, TAOV
How to Cite
Razavi Hajiagha, S. H., Amoozad Mahdiraji, H., & Hashemi, S. S. (2018). Total area based on orthogonal vectors (TAOV) as a novel method of multi-criteria decision aid. Technological and Economic Development of Economy, 24(4), 1679-1694. https://doi.org/10.3846/20294913.2016.1275877
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Keshavarz Ghorabaee, M.; Zavadskas, E. K.; Olfat, L.; Turskis, Z. 2015. Multi-criteria inventory classification using a new method of Evaluation based on Distance from Average Solution (EDAS), Informatica 26(3): 435–451. https://doi.org/10.15388/Informatica.2015.57
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Opricovic, S. 1998. Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering. Belgrade.
Peldschus, F.; Zavadskas, E. K.; Turskis, Z.; Tamosaitiene, J. 2010. Sustainable assessment of construction site by applying game theory, Inzinerine Ekonomika-Engineering Economics 21(3): 223–237.
Rezaei, J. 2015. Best-worst multi-criteria decision-making method, Omega 53: 49–57.
Roubens, M., 1982. Preference relations on actions and criteria in multicriteria decision making, European Journal of Operational Research 10(1): 51–55.
Roy, B. 1968. Classement et choix en présence de points de vue multiples (la méthode ELECTRE), La Revue d’Informatique et de Recherche Opérationelle (RIRO) (8): 57–75.
Roy, B.; Vanderpooten, D. 1996. The European school of MCDA: emergence, basic features and current works, Journal of Multi-Criteria Decision Analysis 5(1): 22–38. https://doi.org/10.1002/(SICI)1099-1360(199603)5:1<22::AID-MCDA93>3.0.CO;2-F
Saaty, T. L. 1980. The analytic hierarchy process. New York: McGraw Hill.
Saaty, T. L.; Ergu, D. 2015. When is a decision-making method trustworthy? Criteria for evaluating multi-criteria decision-making methods, International Journal of Information Technology and Decision Making 14(6): 1171–1188. https://doi.org/10.1142/S021962201550025X
Saaty, T. L.; Vargas, L. G. 2006. Decision making with the analytic network process economic, political, social and technological applications with benefits, opportunities, costs and risks. Springer.
Saaty, T. L. 2005. Theory and applications of the analytic network process: decision making with benefits, opportunities, costs, and risks. Pittsburgh: PA: RWS Publications.
Sivilevicius, H.; Zavadskas, E. K.; Turskis, Z. 2008. Quality attributes and complex assessment methodology of the asphalt mixing plant, Baltic Journal of Road and Bridge Engineering 3(3): 161–166. https://doi.org/10.3846/1822-427X.2008.3.161-166
Srinivasan, V.; Shocker, A. D. 1973. Linear programming techniques for multidimensional analysis of preference, Psychometrica 38: 337–342. https://doi.org/10.1007/BF02291658
Torrance, G. W.; Boyle, M. H.; Horwood, S. P. 1982. Application of multi-attribute utility theory to measure social preferences for health states, Operation research 30(6): 1043–1069. https://doi.org/10.1287/opre.30.6.1043
Turskis, Z.; Zavadskas, E. K.; Peldschus, F. 2009. Multi-criteria optimization system for decision making in construction design and management, Inzinerine Ekonomika-Engineering Economics 61(1): 7–17.
Tzeng, G. H.; Huang, J. J. 2011. Multiple attribute decision making: methods and applications. CRC Press, Taylor & Francis Group, a Chapman & Hall Book.
Wang, X.; Triantaphyllou, E. 2008. Ranking irregularities when evaluating alternatives by using some ELECTRE methods, Omega 36: 45–63. https://doi.org/10.1016/j.omega.2005.12.003
Wang, Z. X.; Wang, Y. Y. 2014. Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method, Expert Systems with Applications 41(6): 2824–2831. https://doi.org/10.1016/j.eswa.2013.10.015
Zavadskas, E. K.; Kaklauskas, A.; Turskis, Z.; Kalibatas, D. 2009. An approach to multi-attribute assessment of indoor environment before and after refurbishment of dwellings, Journal of Environmental Engineering and Landscape Management 17(1): 5–11. https://doi.org/10.3846/1648-6897.2009.17.5-11
Zavadskas, E. K.; Turskis, Z. 2010. A new additive ratio assessment (ARAS) method in multicriteria decision-making, Technological and Economic Development of Economy 16(2): 159–172. https://doi.org/10.3846/tede.2010.10
Zavadskas, E.; Turskis, Z.; Volvaciovas, R.; Kildiene, S. 2013. Multi-criteria assessment model of technologies, Studies in Informatics and Control 22(4): 249–258.
Zavadskas, E. K.; Antucheviciene, J.; Razavi Hajiagha, S. H.; Hashemi, S. S. 2014. Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF), Applied Soft Computing 1013–1021. https://doi.org/10.1016/j.asoc.2014.08.031
Zavadskas, E. K.; Kaklauskas, A.; Sarka, V. 1994. The new method of multicriteria complex proportional assessment of projects, Technological and Economic Development of Economy 1(3): 131–139.
Zavadskas, E. K.; Turskis, Z.; Antucheviciene, J.; Zakarevicius, A. 2012. Optimization of weighted aggregated sum product assessment, Electronics and Electrical Engineering 6(122): 3–6. https://doi.org/10.5755/j01.eee.122.6.1810
Zeleny, M. 1974. A concept of compromise solutions and the method of the displaced ideal, Computers and Operation Research 1(3–4): 479–496. https://doi.org/10.1016/0305-0548(74)90064-1
Zhu, F.; Zhong, P.a.; Xu, B.; Zhang, Y. 2015. A multi-criteria decision-making model dealing with correlation among criteria for reservoir flood control operation, Journal of Hydroinformatics 18(4): 531–543. https://doi.org/10.2166/hydro.2015.055
Antuchevičiene, J.; Zavadskas, E. K.; Zakarevičus, A. 2010. Multiple criteria construction management decisions considering relations between criteria, Technological and Economic Development of Economy 16(1): 109–125. https://doi.org/10.3846/tede.2010.07
Benayoun, R.; Roy, B.; Sussman, N. 1966. Manual de reference du programme electre. Note De Synthese et Formaton, No. 25, Direction Scientifique SEMA, Paris, France.
Bozbura, F. T.; Beskese, A.; Kahraman, C. 2007. Prioritization of human capital measurement indicators using fuzzy AHP, Expert Systems with Applications 32(4): 1100–1112. https://doi.org/10.1016/j.eswa.2006.02.006
Brans, J. P. 1982. L’ingénièrie de la décision; Elaboration d’instruments d’aide à la décision. La méthode PROMETHEE, in R. Nadeau, M. Landry (Eds.). L’aide à la décision: Nature, Instruments et Perspectives d’Avenir. Québec, Canada, Presses de l’Université Laval, 183–213.
Brauers, W. K. M.; Zavadskas, E. K. 2006. The MOORA method and its application to privatization in a transition economy, Control and Cybernetics 35(2): 445–469.
Brauers, W. K. M.; Zavadskas, E. K. 2010. Project management by MULTIMOORA as an instrument for transition economies, Technological and Economic Development of Economy 23(1): 1–25. https://doi.org/10.3846/tede.2010.01
Churchman, C. W.; Ackoff, R. L. 1954. An approximate measure of value, Operations Research 2(2): 172–187. https://doi.org/10.1287/opre.2.2.172
Dinçer, S. E. 2011. The structural analysis of key indicators of Turkish manufacturing industry: ORESTE and MAPPAC applications, European Journal of Scientific Research 60(1): 6–18.
Ginevicius, R. 2011. A new determining method for the criteria weights in multi-criteria evaluation, International Journal of Information Technology & Decision Making 10(6): 1067–1095. https://doi.org/10.1142/S0219622011004713
Givescu, O. 2007. The ORESTE’s method in the multicriteria’s decision process for the management of tourism field, Journal Economia Management 10(1): 37–51.
Hashemi, S. S.; Razavi Hajiagha, S. H.; Zavadskas, E. K.; Amoozad Mahdiraji, H. 2016. Multicriteria group decision making with ELECTRE III methodbased on interval-valued intuitionistic fuzzy information, Applied mathematical modelling 40: 1554–1564. https://doi.org/10.1016/j.apm.2015.08.011
Hwang, C. L.; Yoon, K. 1981. Multiple attributes decision making methods and applications: a state-of-the-art survey. Berlin Heidelberg: Springer. https://doi.org/10.1007/978-3-642-48318-9
Jolliffe, I. T. 2013. Principal component analysis. New York: Springer Science & Business Media.
Keeney, R.; Raiffa, H. 1976. Decisions with multiple objectives: preferences and value trade-offs. New York: John Wiley & Sons, Inc.
Kersuliene, V.; Zavadskas, E. K.; Turskis, Z. 2010. Selection of rational dispute resolution method by applying new Step-Wise Weight Assessment Ratio Analysis (SWARA), Journal of Business Economics and Management 11(2): 243–258. https://doi.org/10.3846/jbem.2010.12
Keshavarz Ghorabaee, M.; Zavadskas, E. K.; Olfat, L.; Turskis, Z. 2015. Multi-criteria inventory classification using a new method of Evaluation based on Distance from Average Solution (EDAS), Informatica 26(3): 435–451. https://doi.org/10.15388/Informatica.2015.57
Köksalan, M.; Wallenius, J.; Zionts, S. 2011. Multiple criteria decision making: from early history to the 21st century. Singapore: World Scientific Publishing Co. https://doi.org/10.1142/8042
Marzouk, M. M. 2011. ELECTRE III model for value engineering applications, Automation in Construction 20(5): 596–600. https://doi.org/10.1016/j.autcon.2010.11.026
Min, H. 1994. International supplier selection: a multi‐attribute utility approach, International Journal of Physical Distribution & Logistics Management 24(5): 24–33. https://doi.org/10.1108/09600039410064008
Neumann, J. V.; Morgenstern, O. 1953. Theory of games and economic behavior. Princeton, NJ.: Princeton University Press.
Opricovic, S. 1998. Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering. Belgrade.
Peldschus, F.; Zavadskas, E. K.; Turskis, Z.; Tamosaitiene, J. 2010. Sustainable assessment of construction site by applying game theory, Inzinerine Ekonomika-Engineering Economics 21(3): 223–237.
Rezaei, J. 2015. Best-worst multi-criteria decision-making method, Omega 53: 49–57.
Roubens, M., 1982. Preference relations on actions and criteria in multicriteria decision making, European Journal of Operational Research 10(1): 51–55.
Roy, B. 1968. Classement et choix en présence de points de vue multiples (la méthode ELECTRE), La Revue d’Informatique et de Recherche Opérationelle (RIRO) (8): 57–75.
Roy, B.; Vanderpooten, D. 1996. The European school of MCDA: emergence, basic features and current works, Journal of Multi-Criteria Decision Analysis 5(1): 22–38. https://doi.org/10.1002/(SICI)1099-1360(199603)5:1<22::AID-MCDA93>3.0.CO;2-F
Saaty, T. L. 1980. The analytic hierarchy process. New York: McGraw Hill.
Saaty, T. L.; Ergu, D. 2015. When is a decision-making method trustworthy? Criteria for evaluating multi-criteria decision-making methods, International Journal of Information Technology and Decision Making 14(6): 1171–1188. https://doi.org/10.1142/S021962201550025X
Saaty, T. L.; Vargas, L. G. 2006. Decision making with the analytic network process economic, political, social and technological applications with benefits, opportunities, costs and risks. Springer.
Saaty, T. L. 2005. Theory and applications of the analytic network process: decision making with benefits, opportunities, costs, and risks. Pittsburgh: PA: RWS Publications.
Sivilevicius, H.; Zavadskas, E. K.; Turskis, Z. 2008. Quality attributes and complex assessment methodology of the asphalt mixing plant, Baltic Journal of Road and Bridge Engineering 3(3): 161–166. https://doi.org/10.3846/1822-427X.2008.3.161-166
Srinivasan, V.; Shocker, A. D. 1973. Linear programming techniques for multidimensional analysis of preference, Psychometrica 38: 337–342. https://doi.org/10.1007/BF02291658
Torrance, G. W.; Boyle, M. H.; Horwood, S. P. 1982. Application of multi-attribute utility theory to measure social preferences for health states, Operation research 30(6): 1043–1069. https://doi.org/10.1287/opre.30.6.1043
Turskis, Z.; Zavadskas, E. K.; Peldschus, F. 2009. Multi-criteria optimization system for decision making in construction design and management, Inzinerine Ekonomika-Engineering Economics 61(1): 7–17.
Tzeng, G. H.; Huang, J. J. 2011. Multiple attribute decision making: methods and applications. CRC Press, Taylor & Francis Group, a Chapman & Hall Book.
Wang, X.; Triantaphyllou, E. 2008. Ranking irregularities when evaluating alternatives by using some ELECTRE methods, Omega 36: 45–63. https://doi.org/10.1016/j.omega.2005.12.003
Wang, Z. X.; Wang, Y. Y. 2014. Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method, Expert Systems with Applications 41(6): 2824–2831. https://doi.org/10.1016/j.eswa.2013.10.015
Zavadskas, E. K.; Kaklauskas, A.; Turskis, Z.; Kalibatas, D. 2009. An approach to multi-attribute assessment of indoor environment before and after refurbishment of dwellings, Journal of Environmental Engineering and Landscape Management 17(1): 5–11. https://doi.org/10.3846/1648-6897.2009.17.5-11
Zavadskas, E. K.; Turskis, Z. 2010. A new additive ratio assessment (ARAS) method in multicriteria decision-making, Technological and Economic Development of Economy 16(2): 159–172. https://doi.org/10.3846/tede.2010.10
Zavadskas, E.; Turskis, Z.; Volvaciovas, R.; Kildiene, S. 2013. Multi-criteria assessment model of technologies, Studies in Informatics and Control 22(4): 249–258.
Zavadskas, E. K.; Antucheviciene, J.; Razavi Hajiagha, S. H.; Hashemi, S. S. 2014. Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF), Applied Soft Computing 1013–1021. https://doi.org/10.1016/j.asoc.2014.08.031
Zavadskas, E. K.; Kaklauskas, A.; Sarka, V. 1994. The new method of multicriteria complex proportional assessment of projects, Technological and Economic Development of Economy 1(3): 131–139.
Zavadskas, E. K.; Turskis, Z.; Antucheviciene, J.; Zakarevicius, A. 2012. Optimization of weighted aggregated sum product assessment, Electronics and Electrical Engineering 6(122): 3–6. https://doi.org/10.5755/j01.eee.122.6.1810
Zeleny, M. 1974. A concept of compromise solutions and the method of the displaced ideal, Computers and Operation Research 1(3–4): 479–496. https://doi.org/10.1016/0305-0548(74)90064-1
Zhu, F.; Zhong, P.a.; Xu, B.; Zhang, Y. 2015. A multi-criteria decision-making model dealing with correlation among criteria for reservoir flood control operation, Journal of Hydroinformatics 18(4): 531–543. https://doi.org/10.2166/hydro.2015.055