Linguistic Z-number weighted averaging operators and their application to portfolio selection problem


Autoři: Amir Hosein Mahmoodi aff001;  Seyed Jafar Sadjadi aff002;  Soheil Sadi-Nezhad aff003;  Roya Soltani aff001;  Farzad Movahedi Sobhani aff001
Působiště autorů: Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran aff001;  Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran aff002;  Department of Statistic and Actuarial Science, University of Waterloo, Ontario, Canada aff003
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0227307

Souhrn

Z-numbers can generate a more flexible structure to model the real information because of capturing expert’s reliability. Moreover, various semantics can flexibly be reflected by linguistic terms under various circumstances. Thus, this study aims to model the portfolio selection problems based on aggregation operators under linguistic Z-number environment. Therefore, a multi-stage methodology is proposed and linguistic Z-numbers are applied to describe the assessment information. Moreover, the weighted averaging (WA) aggregation operator, the ordered weighted averaging (OWA) aggregation operator and the hybrid weighted averaging (HWA) aggregation operator are developed to fuse the input arguments under the linguistic Z-number environment. Then, using the max-score rule and the score-accuracy trade-off rule, three qualitative portfolio models are presented to allocate the optimal assets. These models are suitable for general investors and risky investors. Finally, to illustrate the validity of the proposed qualitative approach, a real case including 20 corporations of Tehran stock exchange market in Iran is provided and the obtained results are analyzed. The results show that combining linguistic Z-numbers with portfolio selection processes can increase the tendencies and capabilities of investors in the capital market and it helps them manage their portfolios efficiently.

Klíčová slova:

Arithmetic – Computational linguistics – Decision making – Entropy – Finance – Financial markets – Optimization – Research validity


Zdroje

1. Zadeh L.A. Fuzzy sets, Information and Control. 1965; 8: 338–353.

2. Turksen I. B. Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems. 1986; 20: 191–210.

3. Dubois D., Prade H Fundamentals of fuzzy sets, Springer, Berlin, 2000.

4. Yager R.R. On the theory of bags, International Journal of General Systems. 1986; 13: 23–37.

5. Atanassov K.T. Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 1986; 20: 87–96.

6. Torra V. Hesitant fuzzy sets, International Journal of Intelligent Systems. 2010; 25: 529–539.

7. Chen N., Xu Z.S., Xia M.M. Interval-valued hesitant preference relations and their applications to group decision making, Knowledge-Based Systems. 2013; 37: 528–540.

8. Cuong B.C. Picture fuzzy sets, Journal of Computer Science and Cybernetics. 2014; 30(4): 409–420.

9. Wang R., Li Y. Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making, Symmetry. 2018; 10(7): doi: 10.3390/sym10070295

10. Chen Z.S., Chin K.S., Li Y.L., Yang Y. Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making, Information Sciences. 2016; 357: 61–87.

11. Chen Z.S., Yang Y., Wang X.J., Chin K.S., Tsui K.L. Fostering linguistic decision-making under uncertainty: A proportional interval type-2 hesitant fuzzy TOPSIS approach based on Hamacher aggregation operators and andness optimization models, Information Sciences. 2019; 500: 229–258.

12. Zadeh L. A. A Note on Z-numbers, Information Sciences. 2011; 181: 2923–2932.

13. Kang B., Wei D., Li Y., Deng Y. A method of converting Z-number to classical fuzzy number, Journal of Information and Computational Science. 2012; 9: 703–709.

14. Azadeh A., Kokabi R. Z-number DEA: A new possibilistic DEA in the context of Z-numbers, Advanced Engineering Informatics. 2016; 30: 604–617.

15. Aliev R. A., Alizadeh A. V., Huseynov O. H. The arithmetic of discrete Z-numbers, Information Sciences. 2015; 290: 134–155.

16. Aliev R. A., Huseynov O. H., Zeinalova L. M. The arithmetic of continuous Z-numbers, Information Sciences. 2016; 373: 441–460.

17. Bhanu M.S., Velammal G. Operations on Zadeh’s Z-number. IOSR Journal of Mathematics. 2015; 11: 88–94.

18. Bakar A. S. A., Gegov A. Multi-layer decision methodology for ranking Z-numbers, International Journal of Computational Intelligence Systems. 2015; 8: 395–406.

19. Aliev R. A., Huseynov O. H., Serdaroglu R. Ranking of Z-numbers and its application in decision making, International Journal of Information Technology and Decision Making. 2016; 15, https://doi.org/10.1142/S0219622016500310.

20. Ezadi S., Allahviranloo T. New multi-layer method for Z-number ranking using hyperbolic tangent function and convex combination, Intelligent Automation and Soft Computing. 2017; https://doi.org/10.1080/10798587.2017.1367146.

21. Jiang W., Xie C., Luo Y., Tang Y. Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers, Journal of Intelligent and Fuzzy Systems. 2017; 32: 1931–1943.

22. Qiu D., Xing Y., Dong R. On ranking of continuous Z-numbers with generalized centroids and optimization problems based on Z-numbers, International Journal of Intelligent System. 2018; 33: 4–13.

23. Yager R.R. On Z-valuations using Zadeh’s Z-numbers, International Journal of Intelligent Systems. 2012; 27: 259–278.

24. Aliev R. A., Pedrycz W., Huseynov O.H. Functions defined on a set of Z-numbers, Information Sciences. 2018; 423: 353–375.

25. Wang J., Cao Y., Zhang H. Multi-criteria decision-making method based on distance measure and Choquet integral for linguistic Z-numbers, Cognitive Computation. 2017; 9: 827–842.

26. Peng H., Wang J. Hesitant uncertain linguistic Z-numbers and their application in multi-criteria group decision-making problems, International Journal of Fuzzy Systems. 2017; 19: 1300–1316.

27. Yang Y., Wang J. SMAA-based model for decision aiding using regret theory in discrete Z-number context, Applied Soft Computing. 2018; 65: 590–602.

28. Shen K., Wang J. Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application, IEEE Transactions on Fuzzy Systems. 2018: doi: 10.1109/TFUZZ.2018.2816581

29. Kang B., Deng Y., Sadiq R. Total utility of Z-number, Applied Intelligence. 2018; 48: 703–729.

30. Sadi-Nezhad S., Sotoudeh-Anvari A. A new data envelopment analysis under uncertain environment with respect to fuzziness and an estimation of reliability, OPSEARCH. 2016; 53: 103–115.

31. Yaakob A. M., Gegov A. Interactive TOPSIS based group decision making methodology using Z-numbers, International Journal of Computational Intelligence Systems. 2016; 9: 311–324.

32. Martínez L., Ruan D., Herrera F., Herrera-Viedma E., Wang P.P. Linguistic decision making: tools and applications, Information Sciences. 2009; 179: 2297–2298.

33. Rodríguez R.M., Martínez L., Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets, Information Sciences. 2013; 241: 28–42.

34. Yang W.E., Wang J.Q. Multi-criteria semantic dominance: a linguistic decision aiding technique based on incomplete preference information, European Journal of Operational Research. 2013; 231: 171–181.

35. Rodríguez R.M., Martínez L., Herrera F. Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems. 2012; 20: 109–119.

36. Wang X.F., Wang J.Q., Yang W.E. Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators, Journal of Intelligent and Fuzzy Systems. 2014; 26: 115–125.

37. Wang X.F., Wang J.Q. and Yang W.E. Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators, Journal of Intelligent & Fuzzy Systems. 2014; 26: 115–125.

38. Wang J.Q., Wu J.T., Wang J., Zhang H., Chen X. Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems, Information Sciences. 2014; 288: 55–72.

39. Liu P.D., Teng F. Some Muirhead Mean operators for Probabilistic Linguistic Term Sets and Their Applications to Multiple Attribute Decision-Making, Applied Soft Computing. 2018; 68: 396–431.

40. Bonferroni C. Sulle medie multiple di potenze, Bolletino Matematica Italiana. 1950; 5: 267–270.

41. Yager R.R. Prioritized aggregation operators, International Journal of Approximate Reasoning. 2008; 48: 263–274.

42. Zhu B., Xu Z.S., Xia M.M. Hesitant fuzzy geometric Bonferroni means, Information Sciences. 2010; 205: 72–85.

43. Xia M., Xu Z. Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning. 2011; 52: 395–407.

44. Yager R. R. On prioritized multiple-criteria aggregation, IEEE Trans. Syst. Man Cybernet. Part B: Cybernet. 2012; 42: 1297–1305.

45. Wei G., Zhao X., Lin R., Wang H. Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making, Applied Mathematical Modelling. 2013; 37: 5277–5285.

46. Liu P.D., Jin F. The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making, Scientia Iranica. 2012; 19: 1947–1959.

47. Liu P., Chen S., Liu J. Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators, Information Sciences. 2017; 411: 98–121.

48. Liu P.D., Teng F. Multiple attribute group decision making methods based on some normal neutrosophic number Heronian Mean operators, Journal of Intelligent & Fuzzy Systems. 2017; 32(3): 2375–2391.

49. Markowitz H., Portfolio selection, The Journal of Finance. 1952; 7: 77–91.

50. Zadeh L.A. The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences. 1975; 8: 199–249.

51. Delgado M., Verdegay J.L., Vila M.A. Linguistic decision making models, International Journal of Intelligent Systems. 1992; 7: 479–492.

52. Xu Z.S. Group decision making based on multiple types of linguistic preference relations, Information Sciences. 2008; 178: 452–467.

53. Xu Z.S. A note on linguistic hybrid arithmetic averaging operator in multiple attribute decision-making with linguistic information, Group Decision and Negotiation. 2006; 15: 593–604.

54. Xu Z. and Yager R.R. Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems. 2006; 35(4): 417–433.

55. Xu Z.S. and Da D.L. An overview of operators for aggregating information, International Journal of Intelligent Systems. 2003; 18: 953–969.

56. Yager R. R. On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man, and Cybernetics. 1988; 18: 183–190.

57. Xu Z. Intuitionistic fuzzy aggregation operators, IEEE Transaction on Fuzzy Systems. 2007; 15(6): 1179–1187.

58. Liao H.C., Xu Z.S. Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment, Journal of Intelligent & Fuzzy Systems. 2013; 26: 1601–1617.

59. Hong D.H., Choi C.H. Multi-criteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets Systems. 2000; 114: 103–113.

60. Shannon C.E. The mathematical theory of communication, Bell System Technical Journal, 1948; 27: 379–423.

61. Tehran stock exchange market. Database available from: https://www.tse.ir/.

62. Phillis Y.A., Andriantiatsaholiniaina L.A. Sustainability: an ill-defined concept and its assessment using fuzzy logic, Ecological Economics. 2001; 37 (3): 435–456.

63. Xu Z. An Overview of Methods for Determining OWA Weights, International Journal of Intelligent Systems, 2005; 20: 843–865.

64. Spernza M. G. A heuristic algorithm for a portfolio optimization model applied to the Milan Stock Market, Computers and Operations Research. 1996; 23: 433–441.

65. Mansini R., Speranza M.G. Heuristic algorithms for the portfolio selection problem with minimum transaction lots, European Journal of Operational Research. 1999; 114: 219–233.

66. Zhou W., Xu Z. Portfolio selection and risk investment under the hesitant fuzzy environment, Knowledge-Based Systems. 2018; 144: 21–31.

67. Herrera F., Herrera-Viedma E., Martinez L. A fusion approach for managing multi granularity linguistic term sets in decision making, Fuzzy Sets and Systems. 2000; 114: 43–58.

68. Wang R., Shuai B., Chen Z.S., Chin K.S., Zhu J.H. Revisiting the role of hesitant multiplicative preference relations in group decision making with novel consistency improving and consensus reaching processes, International Journal of Computational Intelligence Systems. 2019; 12(2): 1029–1046.

69. Chen Z.S., Martínez L., Chang J.P., Wang X.J., Xionge S.H., Chin K.S. Sustainable building material selection: A QFD- and ELECTRE III-embedded hybrid MCGDM approach with consensus building, Engineering Applications of Artificial Intelligence. 2019; 85: 783–807.

70. Chen Z.S., Chin K.S., Tsui K.L. Constructing the geometric Bonferroni mean from the generalized Bonferroni mean with several extensions to linguistic 2-tuples for decision-making, Applied Soft Computing. 2019; 78: 595–613.

71. Chen Z.S., Yu C., Chin K.S., Martínez L. An enhanced ordered weighted averaging operators generation algorithm with applications for multi-criteria decision making, Applied Mathematical Modelling. 2019; 71: 467–490.

72. Kim J.H., Ahn B.S. Extended VIKOR method using incomplete criteria weights, Expert Systems with Applications. 2019; 126: 124–132.

73. Zhang C., Wang C., Zhang Z., Tian D. A novel technique for multiple attribute group decision making in interval-valued hesitant fuzzy environments with incomplete weight information, Journal of Ambient Intelligence and Humanized Computing. 2019; 10(6): 2417–2433.


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2020 Číslo 1