A multi-attribute decision-making method based on the third-generation prospect theory and grey correlation degree

Document Type : Article

Authors

School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China

Abstract

Considering the uncertainty of the natural state and the convenience of calculation, based on the third generation prospect theory (3-PT) and grey correlation analysis (GRA), we propose a method to solve the multi-attribute decision-making (MADM) problems where the attributes are described by the linguistic intuitionistic fuzzy numbers (LIFNs). Firstly, we transform the LIFNs into the belief structure that includes identity value and belief degree. Then, the evaluation information represented by belief structure is calculated by using the 3-PT, and the prospect matrix is gotten. The alternatives are ranked by the GRA. Finally, we use the proposed method to calculate an example and compare it with other methods to prove its effectiveness and superiority.

Keywords


References
1. Akram, M. and Shahzadi, S. \Novel intuitionistic
fuzzy soft multiple-attribute decision-making methods",
Neural Computing and Applications, 29, pp.
435{447 (2018).
2. Garg, H. \Hesitant Pythagorean fuzzy sets and their
aggregation operators in multiple attribute decisionmaking",
International Journal for Uncertainty Quanti
cation, 8, pp. 267{289 (2018).
3. Liu, P. and Wang, P. \Some q-rung orthopair fuzzy aggregation
operators and their applications to multipleattribute
decision making", International Journal of
Intelligent Systems, 33, pp. 259{280 (2018).
4. Ren, P., Xu, Z., and Gou, X. \Pythagorean fuzzy
TODIM approach to multi-criteria decision making",
Applied Soft Computing, 42, pp. 246{259 (2016).
5. Wei, G. \Picture fuzzy aggregation operators and their
application to multiple attribute decision making",
Journal of Intelligent & Fuzzy Systems, 33, pp. 713{
724 (2017).
6. Kannan, G., Rajendran, S., Sarkis, J., and Murugesan,
P. \Multi criteria decision making approaches for green
supplier evaluation and selection: A literature review",
Journal of Cleaner Production, 98, pp. 66{83 (2015).
7. Mardani, A., Jusoh, A., Zavadskas, E.K., Cavallaro,
F., and Khalifah, Z. \Sustainable and renewable
energy: an overview of the application of multiple
criteria decision making techniques and approaches",
Sustainability, pp. 13947{13984 (2015).
8. Zadeh, L.A. \Fuzzy collections", Information and
Control, 8, pp. 338{356, (1965).
9. Atanassov, K.T. \Intuitionistic fuzzy sets", Fuzzy sets
and Systems, 20, pp. 87{96 (1986).
10. Chen, Z., Liu, P.H., and Pei, Z. \An approach to
multiple attribute group decision making based on
linguistic intuitionistic fuzzy numbers", International
Journal of Computational Intelligence Systems, 8, pp.
747{760 (2015).
11. Zhang, H., Peng, H., Wang, J., and Wang, J.Q.
\An extended outranking approach for multi-criteria
decision-making problems with linguistic intuitionistic
fuzzy numbers", Applied Soft Computing, 59, pp. 462{
474 (2017).
12. Liu, P.D., Liu, J., and Merigo, M. \Partitioned
Heronian means based on linguistic intuitionistic fuzzy
numbers for dealing with multi-attribute group decision
making",Applied Soft Computing, 62, pp. 395{422
(2018).
13. Ou, Y., Yi, L.Z., Zou, B., and Pei, Z. \The linguistic
intuitionistic fuzzy set TOPSIS method for linguistic
multi-criteria decision makings", International Journal
of Computational Intelligence Systems, 11, pp. 120{
132 (2018).
14. Peng, H.G., Wang, J.Q., and Cheng, P.F. \A linguistic
intuitionistic multi-criteria decision-making method
based on the Frank Heronian mean operator and its
application in evaluating coal mine safety", International
Journal of Machine Learning and Cybernetics,
9, pp. 1053{1068 (2017).
15. Li, Z., Liu, P., and Qin, X. \An extended VIKOR
method for decision making problem with linguistic
intuitionistic fuzzy numbers based on some new operational
laws and entropy", Journal of Intelligent &
Fuzzy Systems, 33, pp. 1919{1931 (2017).
16. Kahneman, D. and Tversky, A. \Prospect Theory: An
analysis of decision under risk", Econometrica, 47, pp.
263{291 (1979).
17. Tversky, A. and Kahneman, D. \Advances in prospect
theory: Cumulative representation of uncertainty",
Journal of Risk and Uncertainty, 5, pp. 297{323
(1992).
18. Tversky, A. and Fox, C.R. \Weighting risk and uncertainty",
Psychological Review, 102, pp. 269{283
(1995).
19. Fox, C.R. and Tversky, A. \A belief-based account of
decision under uncertainty", Management Science, 44,
pp. 879{895 (1998).
20. Zeng, J.M. \An experimental test on cumulative
prospect theory", Journal of Jinan University, 28, pp.
44-47 (2007).
21. Ma, J. and Sun, X.X. \Modi ed value function in
prospect theory based on utility curve", Information
and Control, 40, pp. 501{506 (2011).
1012 P. Liu and X. Liu/Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 1001{1013
22. Wakker, P.P. and Zank, H. \A simple preference
foundation of cumulative prospect theory with power
utility", European Economic Review, 46, pp. 1253{
1271 (2002).
23. Schmidt, U., Starmer, C., and Sugden, R. \Explaining
preference reversal with third-generation prospect theory",
Discussion Papers 2005-19, The Centre for Decision
Research and Experimental Economics, School of
Economics, University of Nottingham (2005).
24. Birnbaum, M.H. \Empirical evaluation of thirdgeneration
prospect theory", Theory and Decision, 84,
pp. 11{27 (2018).
25. Xiang, Y. and Ma, L. \Multi-attribute decision making
under risk based on third-generation prospect theory",
International Conference on Intelligent Science and
Big Data Engineering, Springer, Cham, pp. 433{442
(2015).
26. Wu, Y.N., Xu, C.B., and Zhang, T. \Evaluation of
renewable power sources using a fuzzy MCDM based
on cumulative prospect theory: A case in China",
Energy, 147, pp. 1227{1239 (2018).
27. Jin, L.Q., Fang, X., and Xu, Y. \A method for multiattribute
decision making under uncertainty using evidential
reasoning and prospect theory", International
Journal of Computational Intelligence Systems, 8, pp.
48{62 (2015).
28. Zhang, Z.X., Wang, L., and Wang, Y.M. \An emergency
decision making method for di erent situation
response based on game theory and prospect theory",
Symmetry, 10, pp. 1{22 (2018).
29. Phochanikorn, P. and Tan, C. \An integrated multicriteria
decision-making model based on prospect
theory for green supplier selection under uncertain
environment: A case study of the Thailand palm
oil products industry", Sustainability, 11, pp. 1{30
(2019).
30. Deng, J.L. \Grey system review", World Science, 7,
pp. 1{5 (1983).
31. Liu, P.D. \Study on evaluation methods and application
of enterprise informatization level based on fuzzy
multi-attribute decision making", Doctoral Dissertation
of Beijing Jiaotong University, pp. 92{110 (2009).
32. Liu, W.J., Zhang, J., Jin, M.Z., Liu, S., Chang, X.,
Xie, N., and Wang, Y. \Key indices of the remanufacturing
industry in China using a combined method of
grey correlation analysis and grey clustering", Journal
of Cleaner Production, 168, pp. 1348{1357 (2017).
33. Zhan, H.B., Liu, S.F., and Yu, J.L. \Research on
factors in
uencing consumers' loyalty towards geographical
indication products based on grey correlation
analysis", Grey Systems: Theory and Application, 7,
pp. 397{407 (2017).
34. Xu, Z.S. \Uncertain linguistic aggregation operators
based approach to multiple attribute group decision
making under uncertain linguistic environment", Information
Sciences, 168, pp. 171-184 (2004).
35. Wang, J.Q., Wu, J.T., Zhang, H.Y., and Chen, X.H.
\Interval valued hesitant fuzzy linguistic sets and their
applications in multi-criteria decision-making problems",
Information Sciences, 288, pp. 55{72 (2014).
36. Schmidt, U., Starmer, C., and Sugden, R. \Thirdgeneration
prospect theory", Journal of Risk and
Uncertainty, 36, pp. 203{223 (2008).
37. Shortli e, E.H. and Buchanan, B.G. \A model of inexact
reasoning in medicine", Mathematical Biosciences,
23, pp. 351{379 (1975).
38. Jin, L.Q. \Research on uncertainty multi-attribute
decision making method based on evidential reasoning
with belief degree", Journal of Southwest Jiaotong
University, 20, pp. 34{45 (2016).
39. Liu, P.D. and Qin, X.Y. \Power average operators
of linguistic intuitionistic fuzzy numbers and their
application to multiple-attribute decision making",
Journal of Intelligent & Fuzzy Systems, 32, pp. 1029{
1043 (2017).
40. Szmidt, E. and Kacprzyk, J. \Distances between
intuitionistic fuzzy sets", Fuzzy Sets and Systems, 114,
pp. 505{518 (2000).
41. Guo, K.H. and Li, W.L. \An attitudinal-based method
for constructing intuitionistic fuzzy in hybrid MADM
under uncertainty", Information Sciences, 208, pp.
28{38 (2012).
42. Prelec, D. \The probability weighting function",
Econometrica, 66, pp. 497{527 (1998).
43. Xu, H.L., Zhou, J., and Xu, W. \A decision making
rule for modeling travelers' route choice behavior
based on cumulative prospect theory", Transportation
Research Party, 19, pp. 218{228 (2011).
44. Bleichrodt, H. and Pinto, J.L. \A parameter-free
elicitation of the probability weighting function in
medical decision analysis", Management Science, 46,
pp. 1485{1496 (2000).
45. Li, P., Liu, S.F., and Zhu, J.J. \Intuitionistic
fuzzy stochastic multi-criteria decision-making methods
based on prospect theory", Control and Decision,
27, pp. 1601{1606 (2012).
46. Dang, Y.G., Liu, S.F., Liu, B., and Tao, Y. \Study
on grey correlation decision model of the dynamic
multiple-attribute", Engineering Science, 7, pp. 69{72
(2005).
47. Liu, P., Chen, S.M., and Wang, P. \Multiple-attribute
group decision-making based on q-rung orthopair fuzzy
power maclaurin symmetric mean operators", IEEE
Transactions on Systems, Man, and Cybernetics: Systems,
50, pp. 3741{3756 (2020).
48. Liu, P. and Liu, J. \Some q-rung orthopai fuzzy
Bonferroni mean operators and their application to
multi-attribute group decision making", International
Journal of Intelligent Systems, 33, pp. 315{347 (2018).
P. Liu and X. Liu/Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 1001{1013 1013
Volume 28, Issue 2
Transactions on Industrial Engineering (E)
March and April 2021
Pages 1001-1013
  • Receive Date: 12 February 2019
  • Revise Date: 13 June 2019
  • Accept Date: 21 December 2019