Skip to main content
SpringerLink
Log in

A Novel Three-Way Investment Decisions Based on Decision-Theoretic Rough Sets with Hesitant Fuzzy Information

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

As a classic model of three-way decisions, the decision-theoretic rough sets (DTRSs) have been adopted to help make profit-based investment decisions. However, there is epistemic uncertainty in the assessment of investment projects, hence the hesitant fuzzy sets (HFSs) are appropriate tool for characterizing the revenue functions and cost functions. To get a more reasonable result in the three-way investment decisions, we introduce HFSs to DTRSs and explore a new three-way investment decision model. Firstly, we take into account the revenue and cost of DTRSs with hesitant fuzzy elements and propose a hesitant fuzzy decision-theoretic rough sets (HFDTRSs) model. Then, we calculate the revenue functions and cost functions by aggregating hesitant fuzzy elements with the Bayesian decision procedure. Considering the differences in the personalities and attitudes of decision-makers, we propose optimistic strategy and pessimistic strategy to aggregate revenue functions and cost functions. Finally, based on the score of profit maximization, we make three-way investment decisions. A case study of coal investment was used to demonstrate the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  Google Scholar 

  2. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inform. Sci. 177(1), 3–27 (2007)

    Article  MathSciNet  Google Scholar 

  3. Lingras, P., Chen, M., Miao, D.Q.: Rough cluster quality index based on decision theory. IEEE Trans. Knowl. Data Eng. 21(7), 1014–1026 (2008)

    Article  Google Scholar 

  4. Yu, H., Liu, Z. G., Wang, G. Y.: Automatically determining the number of clusters using decision-theoretic rough set. In: International conference on rough sets and knowledge technology. Springer, Berlin, Heidelberg, pp. 504–513 (2011)

  5. Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: a three-way view decision model. Int. J. Comput. Intell. Syst. 4(1), 1–11 (2011)

    Article  MathSciNet  Google Scholar 

  6. Liang, D.C., Liu, D., Pedrycz, W., Hu, P.: Triangular fuzzy decision-theoretic rough sets. Int. J. Approx. Reason. 54(8), 1087–1106 (2013)

    Article  Google Scholar 

  7. Yang, X.P., Yao, J.T.: Modelling multi-agent three-way decisions with decision-theoretic rough sets. Fundam. Inf. 115(2–3), 157–171 (2012)

    Article  MathSciNet  Google Scholar 

  8. Yao, Y. Y.: Decision-theoretic rough set models. In: International conference on rough sets and knowledge technology. Springer, Berlin, Heidelberg, pp. 1–12 (2007)

  9. Yao, Y.Y., Wong, S.K.M.: A decision the oretic framework for approximating concepts. Int. J. Man Mach. Stud. 37(6), 793–809 (1992)

    Article  Google Scholar 

  10. Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundam. Inform. 108(3–4), 267–286 (2011)

    Article  MathSciNet  Google Scholar 

  11. Liu, D., Liang, D.C., Wang, C.C.: A novel three-way decision model based on incomplete information system. Knowl. Based Syst. 91, 32–45 (2016)

    Article  Google Scholar 

  12. Liang, D.C., Liu, D.: Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets. Inform. Sci. 300, 28–48 (2015)

    Article  MathSciNet  Google Scholar 

  13. Liang, D.C., Xu, Z.S., Liu, D.: Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information. Inform. Sci. 396, 127–143 (2017)

    Article  Google Scholar 

  14. Liu, D., Yao, Y.Y., Li, T.R.: Three-way Investment decisions with decision-theoretic rough sets. Int. J. Comput. Intell. Syst. 4(1), 66–74 (2011)

    Article  Google Scholar 

  15. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: 2009 IEEE international conference on fuzzy systems. IEEE, pp. 1378–1382 (2009)

  16. Zadeh, L.A.: Fuzzy sets. Inform. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  17. Chen, N., Xu, Z.S., Xia, M.M.: Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl. Math. Model. 37(4), 2197–2211 (2013)

    Article  MathSciNet  Google Scholar 

  18. Qian, G., Wang, H., Feng, X.Q.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl. Based Syst. 37, 357–365 (2013)

    Article  Google Scholar 

  19. Wei, G.W.: Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl. Based Syst. 31, 176–182 (2012)

    Article  Google Scholar 

  20. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2011)

    Article  Google Scholar 

  21. Feng, X.Q., Tan, Q.Y., Wei, C.P.: Hesitant fuzzy linguistic multi-criteria decision making based on possibility theory. Int. J. Mach. Learn. Cybern. 9(9), 1505–1517 (2018)

    Article  Google Scholar 

  22. Wu, Z.B., Xu, J.P.: Possibility distribution-based approach for MAGDM With hesitant fuzzy linguistic information. IEEE Trans. Cybern. 46(3), 694–705 (2015)

    Article  MathSciNet  Google Scholar 

  23. Xia, M.M., Xu, Z.S., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot. 22(2), 259–279 (2013)

    Article  Google Scholar 

  24. Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)

    Article  MathSciNet  Google Scholar 

  25. Chien, Y.: Pattern classification and scene analysis. IEEE Trans. Autom. Control 19(4), 462–463 (1974)

    Article  Google Scholar 

  26. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inform. Sci. 180(3), 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  27. Liu, D., Liang, D.C.: A novel risk making based on decision-theoretic rough sets under hesitant fuzzy information. IEEE Trans. Fuzzy Syst. 23(2), 237–247 (2015)

    Article  Google Scholar 

Download references

Funding

Funding was provided by National Natural Science Foundation of China (Grant Nos. 11961045, 11661053), Natural Science Foundation of Jiangxi Province (Grant No. 20161BAB201009), Youth Science Foundation of Jiangxi Province (Grant No. 20171BCB23004).

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, People’s Republic of China

    Xiang Li & Xianjiu Huang

Authors
  1. Xiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianjiu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianjiu Huang.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Huang, X. A Novel Three-Way Investment Decisions Based on Decision-Theoretic Rough Sets with Hesitant Fuzzy Information. Int. J. Fuzzy Syst. 22, 2708–2719 (2020). https://doi.org/10.1007/s40815-020-00836-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00836-7

Keywords

Search

Navigation