System Portfolio Selection Under Hesitant Fuzzy Information

  • Zhexuan Zhou
  • Xiangqian Xu
  • Yajie DouEmail author
  • Yuejin Tan
  • Jiang Jiang
Conference paper
Part of the Lecture Notes in Business Information Processing book series (LNBIP, volume 315)


System portfolio selection faces multi-criteria and multi-objective problems, which lead the decision-makers to build a decision model. Otherwise, the system evaluation value is not clear and the multi-objective of the system is difficult to outweigh. To solve the problem, a value-risk ratio model with Hesitant Fuzzy Set (HFS) is used for portfolio selection. To be specific, in this model, the HFS is used to evaluate the value and risk of systems; and the portfolio value and portfolio risk are calculated with HFS operation. Meanwhile, the value-risk rate is applied to address the problem of multi-objective for system portfolio. Finally, one numerical example for system portfolio selection is given to illustrate the applicability of the proposed model.


System portfolio selection Hesitant Fuzzy Set Decision-making Value and risk model 



We are thankful to the Editor and the reviewers for their valuable comments and detailed suggestions to improve the presentation of the paper. Further, we also acknowledge the support in part by the National Natural Science Foundation of China under Grant No. 71690233, No. 71671186 and No. 71401167.


  1. 1.
    Markowitz, H.: Portfolio selection. J. Financ. 7(1), 77–91 (1952)Google Scholar
  2. 2.
    Stummer, C., Heidenberger, K.: Interactive R&D portfolio analysis with project interdependencies and time profiles of multiple objectives. IEEE Trans. Eng. Manag. 50, 175–183 (2003)CrossRefGoogle Scholar
  3. 3.
    Peacock, J., Richardson, R., Carter, D.: Edwards, priority setting in health care using multi-attribute utility theory and programme budgeting and marginal analysis (PBMA). Soc. Sci. Med. 64, 897–910 (2007)CrossRefGoogle Scholar
  4. 4.
    Buede, D., Bresnick, T.: Applications of decision analysis to the military systems acquisition process. Interfaces 22(6), 110–125 (1992)CrossRefGoogle Scholar
  5. 5.
    Zhou, Y., Jiang, J., Yang, Z., Tan, Y.: A hybrid approach for multi-weapon production planning with large-dimensional multi-objective in defence manufacturing. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 228(2), 302–316 (2014)CrossRefGoogle Scholar
  6. 6.
    Dou, Y., Zhang, P., Ge, B., Jiang, J., Chen, Y.: An integrated technology pushing and requirement pulling model for weapon system portfolio selection in defence acquisition and manufacturing. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 229(6), 1781–1789 (2014)Google Scholar
  7. 7.
    Katz, D.R., Sarkani, S., Mazzuchi, T., Conrow, E.H.: The relationship of technology and design maturity to DoD weapon system cost change and schedule change during engineering and manufacturing development. Syst. Eng. 18(1), 1–15 (2015)CrossRefGoogle Scholar
  8. 8.
    Zhou, Z., Dou, Y., Xia, B., et al.: Weapon systems portfolio selection based on fuzzy clustering analysis. In: IEEE International Conference on Control Science and Systems Engineering, pp. 702–705. IEEE (2017)Google Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  10. 10.
    Xia, M., Xu, Z., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision-making. Group Decis. Negot. 22, 259–279 (2013)CrossRefGoogle Scholar
  11. 11.
    Chen, N., Xu, Z.S., Xia, M.M.: Interval-valued hesitant preference relations and their applications to group decision making. Knowl.-Based Syst. 37, 528–540 (2013)CrossRefGoogle Scholar
  12. 12.
    Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)Google Scholar
  13. 13.
    Xia, M., Xu, Z.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)CrossRefGoogle Scholar
  14. 14.
    Farhadinia, B.: A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int. J. Intell. Syst. 28(8), 752–767 (2013)CrossRefGoogle Scholar
  15. 15.
    Farhadinia, B.: A series of score functions for hesitant fuzzy sets. Inf. Sci. 277(2), 102–110 (2014)CrossRefGoogle Scholar
  16. 16.
    Zhao, H., Xu, Z., Wang, H., Liu, S.: Hesitant fuzzy multi-attribute decision-making based on the minimum deviation method. Soft Comput. 21(12), 3439–3459 (2016)CrossRefGoogle Scholar
  17. 17.
    Zhu, B., Xu, Z., Xu, J.: Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans. Cybern. 44(8), 1328–1337 (2017)CrossRefGoogle Scholar
  18. 18.
    Zhang, Z.: A framework of group decision making with hesitant fuzzy preference relations based on multiplicative consistency. Int. J. Fuzzy Syst. 19(4), 1–15 (2016)Google Scholar
  19. 19.
    Xu, Z., Xia, M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181(11), 2128–2138 (2011)CrossRefGoogle Scholar
  20. 20.
    Zhang, X., Xu, Z.: The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl.-Based Syst. 61(2), 48–58 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Zhexuan Zhou
    • 1
  • Xiangqian Xu
    • 1
  • Yajie Dou
    • 1
    Email author
  • Yuejin Tan
    • 1
  • Jiang Jiang
    • 1
  1. 1.College of Systems EngineeringNational University of Defense TechnologyChangshaChina

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