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**

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. Modied 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 dierent 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. Shortlie, 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

Transactions on Industrial Engineering (E)

March and April 2021Pages 1001-1013