Skip to main content
SpringerLink
Log in

A New Method for Multi-Attribute Decision Making with Intuitionistic Trapezoidal Fuzzy Random Variable

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

Abstract

In consideration of the interaction among attributes and the uncertainty in the decision information, this paper proposes an intuitionistic trapezoidal fuzzy random decision making method based on Mahalanobis-Taguchi Gram-Schmidt and evidence theory. Firstly, by the acquired intuitionistic trapezoidal fuzzy samples in different periods of the decision making process, the unknown parameters of entire intuitionistic trapezoidal fuzzy populations with known distribution pattern are estimated, and then an intuitionistic trapezoidal fuzzy random matrix is obtained. Secondly, an intuitionistic fuzzy decision matrix with expectation and variance is established, and then a new score function is defined to transform a normalized expectation intuitionistic fuzzy number matrix into a score function matrix. Finally, Mahalanobis-Taguchi Gram-Schmidt and improved evidence theory are combined to deal with the score function matrix, and a ranking of alternatives is obtained according to the belief function value. An illustrative example is taken in the present study to make the proposed method comprehensible.

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

Similar content being viewed by others

References

  1. Ngan, S.C.: Evidential reasoning approach for multiple-criteria decision making: a simulation-based formulation. Expert Syst. Appl. 42(9), 4381–4396 (2015)

    Article  Google Scholar 

  2. Sinova, B., Sáa, S.D.L.R.D., Casals, M.R., Gil, M.Á., Salas, A.: The mean square error of a random fuzzy vector based on the support function and the Steiner point. Fuzzy Sets Syst. 292(1), 347–363 (2016)

    Article  MathSciNet  Google Scholar 

  3. Kumar, R.S., Goswami, A.: A continuous review production–inventory system in fuzzy random environment: Minmax distribution free procedure. Comput. Ind. Eng. 79, 65–75 (2015)

    Article  Google Scholar 

  4. Chen, Z.S., Li, Y.L.: Approach for group MULTIMOORA decision making based upon prospect intuitionistic trapezoidal fuzzy number Choquet integral operator. Control Decis. 29(6), 1053–1063 (2014)

    Google Scholar 

  5. Chen, Z.S., Xiong, S.H., Li, Y.L., Qian, G.S.: Approach for intuitionistic trapezoidal fuzzy random prospect decision making based on the combination of parameter estimation and score functions. Syst. Eng. Electron. 37(4), 851–862 (2015)

    MATH  Google Scholar 

  6. Wang, J.Q., Gong, L.: Interval probability fuzzy random multi-criteria decision-making approach based on expectation-hybrid entropy. Control Decis. 24(7), 1065–1069 (2009)

    Google Scholar 

  7. Sinova, B., Casals, M.R., Gil, M.Á., Lubiano, M.A.: The fuzzy characterizing function of the distribution of a random fuzzy number. Appl. Math. Model. 39(14), 4044–4056 (2015)

    Article  MathSciNet  Google Scholar 

  8. Thuan, N.T., Quang, N.V., Nguyen, P.T.: Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces. Fuzzy Sets Syst. 250(5), 52–68 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lou, C.W., Dong, M.C.: A novel random fuzzy neural networks for tackling uncertainties of electric load forecasting. Int. J. Electr. Power Energy Syst. 73, 34–44 (2015)

    Article  Google Scholar 

  10. Xu, J.P., Feng, C.Y.: Two-stage based dynamic earth-rock transportation assignment problem under fuzzy random environment to earth-rock dam construction. J. Civ. Eng. Manag. 21(6), 775–797 (2015)

    Article  Google Scholar 

  11. Wang, C., Qiu, Z.P.: Hybrid uncertain analysis for temperature field prediction with random, fuzzy and interval parameters. Int. J. Therm. Sci. 98, 124–134 (2015)

    Article  Google Scholar 

  12. Sánchez-Lozano, J.M., Serna, J., Dolón-Payán, A.: Evaluating military training aircrafts through the combination of multi-criteria decision making processes with fuzzy logic. A case study in the Spanish Air Force Academy. Aerosp. Sci. Technol. 42, 58–65 (2015)

    Article  Google Scholar 

  13. Wei, M.Y., Li, X., Yu, L.: Time-dependent fuzzy random location-scheduling programming for hazardous materials transportation. Transp. Res. Part C: Emerg. Technol. 57, 146–165 (2015)

    Article  Google Scholar 

  14. Li, M., Guo, P.: A coupled random fuzzy two-stage programming model for crop area optimization—A case study of the middle Heihe River basin, China. Agric. Water Manag. 155, 53–66 (2015)

    Article  Google Scholar 

  15. Kumar, R.S., Goswami, A.: A fuzzy random EPQ model for imperfect quality items with possibility and necessity constraints. Appl. Soft Comput. 34, 838–850 (2015)

    Article  Google Scholar 

  16. Zhang, B., Lu, S.F., Zhang, D., Wen, K.M.: Supply chain coordination based on a buyback contract under fuzzy random variable demand. Fuzzy Sets Syst. 255(16), 1–16 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Düğenci, M.: A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information. Appl. Soft Comput. 41, 120–134 (2016)

    Article  Google Scholar 

  18. Wan, S.P., Wang, F., Lin, L.L., Dong, J.Y.: Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making. Comput. Ind. Eng. 93, 286–301 (2016)

    Article  Google Scholar 

  19. Wan, S.P., Dong, J.Y.: Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl. Soft Comput. 29, 153–168 (2015)

    Article  Google Scholar 

  20. Liu, P.D., Liu, Y.: An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operator. Int. J. Comput. Intell. Syst. 7(2), 291–304 (2014)

    Article  Google Scholar 

  21. Liu, Y.B., Qiao, Z., Wang, G.Y.: Fuzzy random reliability of structures based on fuzzy random variables. Fuzzy Sets Syst. 86(3), 345–355 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Chen, Z.S., Li, Y.L.: An interdependent multi-attribute group decision making method for complex systems based upon fuzzy input with interval-valued intuitionistic trapezoidal fuzzy numbers. Acta Autom. Sin. 40(7), 1442–1471 (2014)

    Google Scholar 

  23. Li, P., Liu, S.F., Zhu, J.J.: Intuitionistic fuzzy stochastic multi-criteria decision-making methods based on prospect theory. Control Decis. 27(11), 1601–1606 (2012)

    MathSciNet  MATH  Google Scholar 

  24. Taguchi, G., Jugulum, R.: The Mahalanobis-Taguchi strategy: A pattern technology system. Wiley, New York (2002)

    Book  Google Scholar 

  25. Chang, Z.P., Cheng, L.S.: Grey fuzzy integral correlation degree decision model based on Mahalanobis-Taguchi Gram-Schmidt and transformation. Control Decis. 29(7), 1257–1261 (2014)

    MATH  Google Scholar 

  26. Lin, G.P., Liang, J.Y., Qian, Y.H.: An information fusion approach by combining multigranulation rough sets and evidence theory. Inf. Sci. 314(1), 184–199 (2015)

    Article  MathSciNet  Google Scholar 

  27. Li, P., Liu, S.F.: Interval-valued intuitionistic fuzzy numbers decision-making method based on grey incidence analysis and D-S evidence theory. Acta Autom. Sin. 37(8), 994–998 (2011)

    Google Scholar 

  28. Joshi, D., Kumar, S.: Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. Eur. J. Oper. Res. 248(1), 183–191 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Xu, Z.S.: A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis. Negot. 19(1), 57–76 (2010)

    Article  Google Scholar 

  30. Yue, Z.L.: TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting. Inf. Sci. 277, 141–153 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the supports by National Natural Science Foundation of China (No. 71271084).

Author information

Authors and Affiliations

  1. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Jiahang Yuan & Cunbin Li

Authors
  1. Jiahang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cunbin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiahang Yuan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, J., Li, C. A New Method for Multi-Attribute Decision Making with Intuitionistic Trapezoidal Fuzzy Random Variable. Int. J. Fuzzy Syst. 19, 15–26 (2017). https://doi.org/10.1007/s40815-016-0184-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0184-y

Keywords

Search

Navigation