A Multistage Risk Decision Making Method for Normal Cloud Model with Three Reference Points

  • Wen Song
  • Jianjun ZhuEmail author
Conference paper
Part of the Lecture Notes in Business Information Processing book series (LNBIP, volume 315)


Decision making problems become more complicated due to the dynamically changing environment. Consequently, decision making methods with reference points are increasing. Reference points provide a good basis for decision makers. This paper proposes a multistage risk decision making method for normal cloud model considering three reference points. Firstly, the setting method of three reference points is proposed considering the dimensions of multistate, development and promotion. The value function is defined based on the characteristics of three reference points. Secondly, the aggregation methods for different prospect values are proposed with the preference coefficients, which are calculated by the synthetic degree of grey incidence. Thirdly, a two-stage weight optimization method is proposed to solve the attribute weights and stage weights based on the idea of minimax reference point optimization. Finally, a numerical example illustrates the feasibility and validity of the proposed method.


Multistage risk decision making Three reference points Normal cloud model Two-stage weight optimization method 



This work was supported by the National Natural Science Foundation of China [71171112, 71502073, 71601002]; Funding of Jiangsu Innovation Program for Graduate Education (“the Fundamental Research Funds for the Central Universities”) [KYZZ16_0147].


  1. 1.
    Pospichal, J., Kvasnicka, V.: Multistage decision-making using simulated annealing applied to a fuzzy automaton. Appl. Soft Comput. 2(2), 140–151 (2003)CrossRefGoogle Scholar
  2. 2.
    Sirbiladze, G., Khutsishvili, I., Ghvaberidze, B.: Multistage decision-making fuzzy methodology for optimal investments based on experts’ evaluations. Eur. J. Oper. Res. 232(1), 169–177 (2014)CrossRefGoogle Scholar
  3. 3.
    Guo, P., Li, Y.: Approaches to multistage one-shot decision making. Eur. J. Oper. Res. 236(2), 612–623 (2014)CrossRefGoogle Scholar
  4. 4.
    Qu, J., Meng, X., You, H.: Multi-stage ranking of emergency technology alternatives for water source pollution accidents using a fuzzy group decision making tool. J. Hazard. Mater. 310, 68–81 (2016)CrossRefGoogle Scholar
  5. 5.
    Zhang, S.W., Guo, H.X., Zhu, K.J., Yu, S.W., Li, J.L.: Multistage assignment optimization for emergency rescue teams in the disaster chain. Knowl. Based Syst. 137, 123–137 (2017)CrossRefGoogle Scholar
  6. 6.
    Yoon, K.: A reconciliation among discrete compromise solutions. J. Oper. Res. Soc. 38(3), 277–286 (1987)CrossRefGoogle Scholar
  7. 7.
    Walczak, D., Rutkowska, A.: Project rankings for participatory budget based on the fuzzy TOPSIS method. Eur. J. Oper. Res. 260(2), 706–714 (2017)CrossRefGoogle Scholar
  8. 8.
    Tavana, M., Caprio, D.D., Santos-Arteaga, F.J.: An extended stochastic VIKOR model with decision maker’s attitude towards risk. Inf. Sci. 432, 301–318 (2018)CrossRefGoogle Scholar
  9. 9.
    Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)CrossRefGoogle Scholar
  10. 10.
    Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5, 297–323 (1992)CrossRefGoogle Scholar
  11. 11.
    Wang, L., Zhang, Z.X., Wang, Y.M.: A prospect theory-based interval dynamic reference point method for emergency DM. Expert Syst. Appl. 42(23), 9379–9388 (2015)CrossRefGoogle Scholar
  12. 12.
    Zhu, J., Ma, Z., Wang, H., Chen, Y.: Risk decision-making method using interval numbers and its application based on the prospect value with multiple reference points. Inf. Sci. 385–386, 415–437 (2017)CrossRefGoogle Scholar
  13. 13.
    Cables, E., Lamata, M.T., Verdegay, J.L.: RIM-reference Ideal method in multicriteria decision making. Inf. Sci. 337–338, 1–10 (2016)CrossRefGoogle Scholar
  14. 14.
    Mandal, P., Kaul, R., Jain, T.: Stocking and pricing decisions under endogenous demand and reference point effects. Eur. J. Oper. Res. 264, 181–199 (2018)CrossRefGoogle Scholar
  15. 15.
    Wang, J.Q., Peng, L., Zhang, H.Y., Chen, X.H.: Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf. Sci. 274, 177–181 (2014)CrossRefGoogle Scholar
  16. 16.
    Li, D., Han, J., Shi, X., Chan, M.C.: Knowledge representation and discovery based on linguistic atoms. Knowl. Based Syst. 10(7), 431–440 (1998)CrossRefGoogle Scholar
  17. 17.
    Yang, X., Zeng, L., Luo, F., Wang, S.: Cloud hierarchical analysis. J. Inf. Comput. Sci. 12, 2468–2477 (2010)Google Scholar
  18. 18.
    Yang, X., Yan, L., Zeng, L.: How to handle uncertainties in AHP: the cloud delphi hierarchical analysis. Inf. Sci. 222(3), 384–404 (2013)CrossRefGoogle Scholar
  19. 19.
    Peng, B., Zhou, J., Peng, D.: Cloud model based approach to group decision making with uncertain pure linguistic information. J. Intell. Fuzzy Syst. 32(3), 1959–1968 (2017)CrossRefGoogle Scholar
  20. 20.
    Wang, D., Liu, D., et al.: A cloud model-based approach for water quality assessment. Environ. Res. 149, 113–121 (2016)CrossRefGoogle Scholar
  21. 21.
    Xu, C.L., Wang, G.Y.: A novel cognitive transformation algorithm based on gaussian cloud model and its application in image segmentation. Algorithms 76(4), 1039–1070 (2017)CrossRefGoogle Scholar
  22. 22.
    Zhang, R.L., Shan, M.Y., Liu, X.H., Zhang, L.H.: A novel fuzzy hybrid quantum artificial immune clustering algorithm based on cloud model. Eng. Appl. AI 35, 1–13 (2014)Google Scholar
  23. 23.
    Li, D., Liu, C., Gan, W.: A new cognitive model: cloud model. Int. J. Intell. Syst. 24(3), 357–375 (2009)CrossRefGoogle Scholar
  24. 24.
    Wang, J., Zhu, J., Liu, X.: An integrated similarity measure method for normal cloud model based on shape and distance. Syst. Eng. Theory Pract. 37(3), 742–751 (2017b). (in Chinese)Google Scholar
  25. 25.
    Liu, S., Lin, Y.: Grey Information: Theory and Practical Applications. Springer, London (2006). Scholar
  26. 26.
    Yang, J.B.: Minimax reference point approach and its application for multiobjective optimisation. Eur. J. Oper. Res. 126(3), 90–105 (2000)CrossRefGoogle Scholar
  27. 27.
    Kim, S.H., Choi, S.H., Kim, J.K.: An interactive procedure for multiple attribute group decision making with incomplete information: range-based approach. Eur. J. Oper. Res. 118(1), 139–152 (1999)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Economics and ManagementNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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