International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

LiangYina and Huan-Jyh Shyurb*

aDepartment of Management Science, Tamkang UniversityaDepartment of Management Science, Tamkang University
bDepartment of Information Management, Tamkang University


 

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ABSTRACT


In this paper, we propose a robust multiple attributes decision-making (MADM) methodIn this paper, we propose a robust multiple attributes decision-making (MADM) methodbased on prospect theory to reflect the decision behavior of a decision maker in face of risk. Insteadof identifying the reference points, the decision makers only need to determine the feasible rangesfor each attribute by their knowledge and experience in the beginning of the decision process. Thepsychological value distances are defined to measure the overall prospect values of eachalternative reference to extreme feasible solutions using the value function and the additiveweighting method. This study further extends the method to a group decision environment. Thepreferences of more than one decision maker are internally aggregated into the decision procedure.Performance of the proposed algorithms is comparatively analyzed and sensitivity analysis isconducted. The results show that it is an appropriate and robust MADM method.


Keywords: Decision support systems; MADM; prospect theory; value function


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REFERENCES


[1] Hwang, C. L. and Yoon, K. 1981. “Multiple Attribute Decision Making Methods andApplications in Lecture Notes in Economics and Mathematical Systems 186”. Springer-Verlag. Berlin. doi: 10.1007/978-3-642-48318-9

[2] Saaty, T. L. 1980. “The Analytic Hierarchy Process”. McGraw-Hill. New York.

[3] Opricovic, S. 1998. “Multicriteria Optimization of Civil Engineering Systems”. Faculty ofCivil Engineering. Belgrade.

[4] Roy, B. 1991. The outranking approach and the foundations of Electre methods. Theory andDecision, 31, 1: 49-73. doi: 10.1007/BF00134132

[5] Gomes, L. F. A. M. and Rangel, L. A. D. 2009. An application of the TODIM method to themulticriteria rental evaluation of residential properties. European Journal of OperationalResearch, 193, 1: 204–211. doi.org/10.1016/j.ejor.2007.10.046

[6] Kahneman, D. and Tversky, A. 1979. Prospect theory: an analysis of decision under risk.Econometrica, 47, 2: 263–292. DOI: 10.2307/1914185

[7] Krohling, R. A. and de Souza, T. T. M. 2012. Combining prospect theory and fuzzy numbersto multi-criteria decision making. Expert Systems with Applications, 39, 13: 11487–11493.doi: 10.1016/j.eswa.2012.04.006

[8] Gomes, L. F. A. M. and Lima, M. M. P. P. 1992. TODIM: Basics and application tomulticriteria ranking of projects with environmental impacts. Foundations of Computing andDecision Sciences, 16, 4: 113–127.

[9] Liu, P., Jin, F., Zhang, X., Su, Y., and Wang, M. 2011. Research on the multi-attributedecision-making under risk with interval probability based on prospect theory and theuncertain linguistic variables. Knowledge-Based Systems, 24, 4: 554-561. doi:10.1016/j.knosys.2011.01.010

[10] Fan, Z.-P., Zhang X., Chen, F.-D., and Liu, Y. 2013. Multiple attribute decision makingconsidering aspiration-levels: A method based on prospect theory. Computers & IndustrialEngineering, 65, 2: 341-350. doi: 10.1016/j.cie.2013.02.013

[11] Wei, C., Ren, Z., and Rodríguez, R. M. 2015. A hesitant fuzzy linguistic TODIM methodbased on a score function. International Journal of Computational Intelligence Systems, 8,4: 701-712. doi: 10.1080/18756891.2015.1046329

[12] Wang, J.-Q., Wu, J.-T., Wang, J., Zhang, H.-Y., and Chen, X.-H. 2016. Multi-criteriadecision-making methods based on the Hausdorff distance of hesitant fuzzy linguisticnumbers. Soft Computing, 20, 4: 1621-1633. doi: 10.1007/s00500-015-1609-5

[13] Cheng, S., Chan, C. W., and Huang, G. H. 2002. Using multiple criteria decision analysisfor supporting decision of solid waste management. Journal of Environmental Science andHealth, Part A, 37, 6: 975-990. doi: 10.1081/ESE-120004517

[14] Zanakis, S. H., Solomon, A., Wishart, N., and Dublish, S. 1998. Multi-attribute decisionmaking: A simulation comparison of select methods. European Journal of OperationalResearch, 107, 3: 507-529. doi: 10.1016/S0377-2217(97)00147-1

[15] Wang, Y. M. and Luo, Y. 2009. On rank reversal in decision analysis. Mathematical andComputer Modelling, 49, 5-6: 1221-1229. doi: 10.1016/j.mcm.2008.06.019

[16] Opricovic, S. and Tzeng, G.-H. 2004. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156, 2: 445-455. doi: 10.1016/S0377-2217(03)00020-1

[17] García-Cascales, M. S. and Lamata, M. T. 2012. On rank reversal and TOPSIS method.Mathematical and Computer Modelling, 56, 5-6: 123-132. doi: 10.1016/j.mcm.2011.12.022

[18] Yue, Z. 2011. An extended TOPSIS for determining weights of decision makers with intervalnumbers. Knowledge-Based Systems, 24, 1: 146-153. doi: 10.1016/j.knosys.2010.07.014

[19] Baky, I. A. and Abo-Sinna, M. A. 2013. TOPSIS for bi-Level MODM problems. Applied Mathematical Modelling, 37, 3: 1004-1015. doi: 10.1016/j.apm.2012.03.002

[20] Kahraman, C., Onar, S. C., and Oztaysi, B. 2015. Fuzzy multicriteria decision-making: A literature review. International Journal of Computational Intelligence Systems, 8, 4: 637-666. doi: 10.1080/18756891.2015.1046325

[21] Tversky, A. and Kahneman, D. 1992. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 4: 297-323. doi:10.1007/BF00122574

[22] Edwards, K. D. 1996. Prospect theory: A literature review. International Review of Financial Analysis, 5, 1:19-38. doi: 10.1016/S1057-5219(96)90004-6

[23] Gurevich, G., Kliger, D., and Levy, O. 2009. Decision-making under uncertainty—A field study of cumulative prospect theory. Journal of Banking & Finance, 33, 7: 1221–1229. doi: 10.1016/j.jbankfin.2008.12.017

[24] Hu, J., Chen, P., and Yang, L. 2014. Dynamic stochastic multi-criteria decision making method based on prospect theory and conjoint analysis. Management Science and Engineering, 8, 3: 65-71. doi: 10.3968/5235

[25] Gomes, L. F. A. M., Machado, M. A. S., and Rangel, L. A. D. 2013. Behavioral multi-criteria decision analysis: The TODIM method with criteria interactions. Annals of Operations Research, 211, 1: 531-548. doi: 10.1007/s10479-013-1345-0

[26] Lourenzutti, R. and Krohling, R.A. 2014. The Hellinger distance in multicriteria decision making: An illustration to the TOPSIS and TODIM methods. Expert Systems with Applications, 41, 9: 4414-4421. doi: 10.1016/j.eswa.2014.01.015

[27] Khamseh, A. A. and Mahmoodi, M. 2014. A new fuzzy TOPSIS-TODIM hybrid method for green supplier selection using fuzzy time function. Advances in Fuzzy Systems, 2014, Article ID 841405. Retrieved from http://dx.doi.org/10.1155/2014/841405.

[28] Shyur, H.-J., Yin, L., Shih, H.-S., and Cheng, C.-B. 2015. A multiple criteria decision making method based on relative value distances. Foundations of Computing and Decision Sciences, 40, 4: 299-315. doi: 10.1515/fcds-2015-0017

[29] Shih, H.-S., Shyur, H.-J., and Lee, E. S. 2007. An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45, 7-8: 801-813. doi: 10.1016/j.mcm. 2006.03.023


ARTICLE INFORMATION


Received: 2017-04-29
Revised: 2017-12-25
Accepted: 2018-01-03
Available Online: 2018-02-01


Cite this article:

Yin, L., Shyur, H.J. 2018. A robust group multiple attributes Decision-Making method based on risk preference of the decision makers. International Journal of Applied Science and Engineering, 15, 33-46. https://doi.org/10.6703/IJASE.201802_15(1).033