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A New Interval Type-2 Fuzzy VIKOR Method for Multi-attribute Decision Making

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Abstract

A new signed area method combined with VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) is proposed for multi-attribute decision-making problems under the environment of interval type-2 fuzzy sets. First, a new signed area function of interval type-2 fuzzy sets is defined and the ranking score method based on the signed area function is proposed, subsequently. Then, we convert the matrix of interval type-2 fuzzy numbers to ranking score values matrix and some theorems of the ranking score method are presented and proved. Furthermore, the decision-making steps combined with VIKOR are given in detail and the comparative analysis with the signed distance method is conducted to show the advantages of our method. Finally, we perform a sensitivity analysis to show the stability of the proposed approach and the effectiveness of our method is illustrated by comparing with other methods.

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References

  1. Chen, T.Y.: An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets. Inf. Sci. 263(3), 1–21 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Hu, J.H., Yang, Yao, Chen, X.H.: A novel TODIM method-based three-way decision model for medical treatment selection. Int. J. Fuzzy Syst. 20(4), 1240–1255 (2018)

    Article  MathSciNet  Google Scholar 

  3. Liu, X.Y., Ju, Y.B., Qu, Q.X.: Hesitant Fuzzy 2-dimension linguistic term set and its application to multiple attribute group decision making. Int. J. Fuzzy Syst. 1–21 (2017). https://doi.org/10.1007/s40815-017-0384-0

  4. Zhou, H., Ma, X.Y., Zhou, L.G., et al.: A novel approach to group decision-making with interval valued intuitionistic fuzzy preference relations via Shapley value. Int. J. Fuzzy Syst 20(4), 1172–1187 (2018)

    Article  MathSciNet  Google Scholar 

  5. Liang, D.C., Xu, Z.S., Liu, D., et al.: Method for three-way decisions using ideal TOPSIS solutions at Pythagorean Fuzzy information. Inf. Sci. 435, 282–295 (2018)

    Article  MathSciNet  Google Scholar 

  6. Cheng, S.H., Chen, S.M., Huang, Z.C.: Autocratic decision making using group recommendations based on ranking interval type-2 fuzzy sets. Inf. Sci. 361, 135–161 (2016)

    Article  Google Scholar 

  7. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199C249 (1975)

    MathSciNet  Google Scholar 

  8. Mendel, J.M., John, R.B.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Article  Google Scholar 

  9. Chen, T.Y.: Likelihoods of interval type-2 trapezoidal fuzzy preference relations and their application to multiple criteria decision analysis. Inf. Sci. 295, 303–322 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhai, D., Mendel, J.M.: Uncertainty measures for general Type-2 fuzzy sets. Inf. Sci. 181(3), 503–518 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ngan, S.C.: A type-2 linguistic set theory and its application to multi-criteria decision making. Comput. Ind. Eng. 64(2), 721–730 (2013)

    Article  Google Scholar 

  12. Zhang, S.H., Zhang, Z.M.: A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl. Math. Modell. 37(7), 4948–4971 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, T.Y.: A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets. Appl. Soft Comput. 13(5), 2735–2748 (2013)

    Article  Google Scholar 

  14. Chen, T.Y., Chang, C.H., Lu, J.F.R.: The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making. Eur. J. Oper. Res. 226(3), 615–625 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Chen, S.M., Lee, L.W.: Fuzzy multiple criteria hierarchical group decisionmaking based on interval type-2 fuzzy sets. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 40(5), 1120–1128 (2010)

    Article  Google Scholar 

  16. Li, C.D., Gao, J.L., Yi, J.L., Zhang, G.Q.: Analysis and design of functionally weighted single-input-rule-modules connected fuzzy inference systems. IEEE Trans. Fuzzy Syst. 26(1), 56–71 (2018)

    Article  Google Scholar 

  17. Li, C.D., Ding, Z.X., Qian, D.W., Lv, Y.S.: Data-driven design of the extended fuzzy neural network having linguistic outputs. J. Intell. Fuzzy Syst. 34(1), 349–360 (2018)

    Article  Google Scholar 

  18. Chen, S.M., Lee, L.W.: Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method. Exp. Syst. Appl. 37(4), 2790–2798 (2010)

    Article  Google Scholar 

  19. Wang, W.Z., Liu, X.W., Qin, Y.: Multi-attribute group decision making models under interval type-2 fuzzy environment. Knowl. Based Syst. 30(10), 121–128 (2012)

    Article  Google Scholar 

  20. Zhang, Z.M., Zhang, S.H.: A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl. Math. Modell. 37(7), 4948–4971 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen, S.M., Yang, M.W., Lee, L.W., Yang, S.W.: Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets. Exp. Syst. Appl. 39, 5295–5308 (2012)

    Article  Google Scholar 

  22. Hu, J.H., Zhang, Y., Chen, X.H., Liu, Y.M.: Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number. Knowl. Based Syst. 43(2), 21–29 (2013)

    Article  Google Scholar 

  23. Chen, S.M., Cheng, Y.W.: Fuzzy decision making systems based on interval type-2 fuzzy sets. Inf. Sci. 242, 1–21 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Qin, J.D., Liu, X.W.: Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment. Inf. Sci. 297(C), 293–315 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Qin, Y., Zhang, Z.Y., Liu, X.W., Li, M., Kou, L.L.: Dynamic risk assessment of metro station with interval type-2 fuzzy set and TOPSIS method. J. Intell. Fuzzy Syst. 29(1), 93–106 (2015)

    Article  Google Scholar 

  26. Sang, X.Z., Liu, X.W.: An interval type-2 fuzzy sets-based TODIM method and its application to green supplier selection. J. Oper. Res. Soc. 67(5), 722–734 (2016)

    Article  Google Scholar 

  27. Chen, T.Y.: An interval type-2 fuzzy LINMAP method with approximate ideal solutions for multiple criteria decision analysis. Inf. Sci. 297(C), 50–79 (2015)

    Article  Google Scholar 

  28. Chen, T.Y.: An integrated approach for assessing criterion importance with interval type-2 fuzzy sets and signed distances. J. Chin. Inst. Ind. Eng. 28(8), 553C572 (2011)

    Google Scholar 

  29. Yu, S.M., Wang, J., Wang, J.Q.: An interval type-2 fuzzy likelihood-based MABAC approach and its application in selecting hotels on a tourism website. Int. J. Fuzzy Syst. 19(1), 47–61 (2017)

    Article  MathSciNet  Google Scholar 

  30. Wu, Q., Wang, F., Zhou, L.G., Chen, H.Y.: Method of multiple attribute group decision making based on 2-dimension interval type-2 fuzzy aggregation operators with multi-granularity linguistic information. Int. J. Fuzzy Syst. 19(6), 1880–1903 (2017)

    Article  MathSciNet  Google Scholar 

  31. Opricovic, S.: Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrad pp. 36–38 (1998)

  32. Wu, Y., Chen, K., Zeng, B.X., Xu, H., Yang, Y.S.: Supplier selection in nuclear power industry with extended VIKOR method under linguistic information. Appl. Soft Comput. 48, 444–457 (2016)

    Article  Google Scholar 

  33. Awasthi, A., Kannan, G.: Green supplier development program selection using NGT and VIKOR under fuzzy environment. Comput. Ind. Eng. 91(C), 100–108 (2016)

    Article  Google Scholar 

  34. Qin, J.D., Liu, X.W., Pedrycz, W.: An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment. Knowl. Based Syst. 86(C), 116–130 (2015)

    Article  Google Scholar 

  35. Soner, S., Celik, E., Akyuz, E.: Application of AHP and VIKOR methods under interval type 2 fuzzy environment in maritime transportation. Ocean Eng. 129, 107–116 (2017)

    Article  Google Scholar 

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Acknowledgements

The authors would like to appreciate the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that helped to improve the quality of this paper. This work was supported by NSFC Foundation under Grant No. 61402260.

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Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China

    Huidong Wang, Xiaohong Pan & Shifan He

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  1. Huidong Wang
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  2. Xiaohong Pan
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  3. Shifan He
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Correspondence to Huidong Wang.

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Wang, H., Pan, X. & He, S. A New Interval Type-2 Fuzzy VIKOR Method for Multi-attribute Decision Making. Int. J. Fuzzy Syst. 21, 145–156 (2019). https://doi.org/10.1007/s40815-018-0527-y

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  • DOI: https://doi.org/10.1007/s40815-018-0527-y

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