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Extended ELECTRE I Method with Multi-hesitant Fuzzy Information

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Abstract

Multi-hesitant fuzzy sets (MHFSs) are hesitant fuzzy sets (HFSs) with membership function, permitting the same evaluation value to be repeated several times. MHFSs can depict uncertain information more effectively than HFSs. This study defined three outranking relations of multi-hesitant fuzzy numbers (MHFNs), namely strong dominant, weak dominant and indifferent relationships, based on the elimination and choice translating reality (ELECTRE) I method. Thereafter, we discussed the corresponding properties of the three outranking relations. We also presented an extended ELECTRE I method, in which the criteria are correlated to select the optimal alternatives, by combination of outranking relations and Choquet integral. Eventually, an application example of MHFNs was presented, and a comparative analysis was performed based on the same example.

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References

  1. Benayoun, R., Roy, B., Sussman, B.: ELECTRE: Une méthode pour guider le choix en présence de points de vue multiples. Rev. franaise Informat. recherche Opérationnelle 3, 31–56 (1969)

    Google Scholar 

  2. Roy, B.: The outranking approach and the foundations of ELECTRE methods. Theor. Decis. 31(1), 49–73 (1991)

    Article  MathSciNet  Google Scholar 

  3. Rohaninejad, M., Kheirkhah, A., Fattahi, P., Vahedi-Nouri, B.: A hybrid multi-objective genetic algorithm based on the ELECTRE method for a capacitated flexible job shop scheduling problem. Int. J. Adv. Manuf. Technol. 77, 51–66 (2015)

    Article  Google Scholar 

  4. Wang, X., Triantaphyllou, E.: Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega 36(1), 45–63 (2008)

    Article  Google Scholar 

  5. Ermatita, S., Hartati, S., Wardoyo, R., Harjoko, A.: Electre methods in solving group decision support system bioinformatics on gene mutation detection simulation. Int. J. Comput. Sci. Inf. Technol. 3(1), 40–52 (2011)

    Google Scholar 

  6. Hashemi, S.S., Hajiagha, S.H.R., Zavadskas, E.K., Mahdiraji, H.A.: Multicriteria group decision making with ELECTRE III method based on interval-valued intuitionistic fuzzy information. Appl. Math. Model. 40(2), 1554–1564 (2016)

    Article  MathSciNet  Google Scholar 

  7. Fahmi, A., Kahraman, C., Bilen, Ü.: ELECTRE I method using hesitant linguistic term sets: an application to supplier selection. Int. J. Comput. Intell. Syst. 9(1), 153–167 (2016)

    Article  Google Scholar 

  8. Peng, H.G., Shen, K.W., He, S.S., Zhang, H.Y., Wang, J.Q.: Investment risk evaluation for new energy resources: an integrated decision support model based on regret theory and ELECTRE III. Energy Convers. Manag. 183, 332–348 (2019)

    Article  Google Scholar 

  9. Hatami-Marbini, A., Tavana, M.: An extension of the Electre I method for group decision-making under a fuzzy environment. Omega 39(4), 373–386 (2011)

    Article  MATH  Google Scholar 

  10. Chen, N., Xu, Z.S., Xia, M.M.: The ELECTRE I multi-criteria decision-making mtheod based on hesitant fuzzy sets. Int. J. Inf. Technol. Decis. Mak. 14(3), 621–657 (2015)

    Article  Google Scholar 

  11. Chen, N., Xu, Z.S.: Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf. Sci. 292, 175–197 (2015)

    Article  Google Scholar 

  12. Peng, J.J., Wang, J.Q., Wu, X.H.: An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput. Appl. 28(Suppl 1), S1011–S1022 (2017)

    Article  Google Scholar 

  13. Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. 69(3), 279–298 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liang, R.X., Wang, J.Q., Li, L.: Multi-criteria group decision making method based on interdependent inputs of single valued trapezoidal neutrosophic information. Neural Comput. Appl. 30, 241–260 (2018)

    Article  Google Scholar 

  15. Peng, H.G., Wang, X.K., Wang, T.L., Wang, J.Q.: Multi-criteria game model based on the pairwise comparisons of strategies with Z-numbers. Appl. Soft Comput. 74, 451–465 (2019)

    Article  Google Scholar 

  16. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yager, R.R.: Induced aggregation operators. Fuzzy Sets Syst. 137(1), 59–69 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Meyer, P., Roubens, M.: On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support. Fuzzy Sets Syst. 157(7), 927–938 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yu, D.J., Wu, Y.Y., Zhou, W.: Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment. J. Comput. Inf. Syst. 7(12), 4506–4513 (2011)

    Google Scholar 

  20. Deepa, J., Sanjay, K.: 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 

  21. Wang, L., Zhang, H.Y., Wang, J.Q.: Frank Choquet Bonferroni mean operators of bipolar neutrosophic sets and their application to multi-criteria decision-making problems. Int. J. Fuzzy Syst. 20(1), 13–28 (2018)

    Article  MathSciNet  Google Scholar 

  22. Peng, J.J., Wang, J.Q., Hu, J.H., Tian, C.: Multi-criteria decision-making approach based on single-valued neutrosophic hesitant fuzzy geometric weighted Choquet integral heronian mean operator. J. Intell. Fuzzy Syst. 35(5), 1–14 (2018)

    Google Scholar 

  23. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

    MATH  Google Scholar 

  24. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, pp. 1378–1382 (2009)

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Wei, G.W.: Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl. Based Syst. 31(7), 176–182 (2012)

    Article  Google Scholar 

  28. Zhao, H., Xu, Z., Cui, F.: Generalized hesitant fuzzy harmonic mean operators and their applications in group decision making. Int. J. Fuzzy Syst. 18(4), 685–696 (2016)

    Article  MathSciNet  Google Scholar 

  29. Zhang, Z.M., Wang, C., Tian, D.Z., Li, K.: Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Comput. Ind. Eng. 67(1), 116–138 (2014)

    Article  Google Scholar 

  30. Qin, J., Liu, X., Pedrycz, W.: Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making. Appl. Soft Comput. 41, 428–452 (2015)

    Article  Google Scholar 

  31. Zhang, Z.M.: Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf. Sci. 234(10), 150–181 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yu, D.J.: Some hesitant fuzzy information aggregation operators based on Einstein operational laws. Int. J. Intell. Syst. 29(4), 320–340 (2014)

    Article  Google Scholar 

  33. Qian, G., Wang, H., Feng, X.Q.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl. Based Syst. 37(4), 357–365 (2013)

    Article  Google Scholar 

  34. Xu, Z.S., Xia, M.M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181(11), 2128–2138 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhang, Z.M.: Hesitant fuzzy multi-criteria group decision making with unknown weight information. Int. J. Fuzzy Syst. 19(3), 615–636 (2017)

    Article  MathSciNet  Google Scholar 

  36. Farhadinia, B.: Distance and similarity measures for higher order hesitant fuzzy sets. Knowl. Based Syst. 55, 43–48 (2014)

    Article  MATH  Google Scholar 

  37. Wei, C., Yan, F., Rodríguez, R.M.: Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making. J. Intell. Fuzzy Syst. 31(1), 673–685 (2016)

    Article  MATH  Google Scholar 

  38. Zhang, N., Wei, G.W.: Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl. Math. Model. 37(7), 4938–4947 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  39. Liang, R.X., Wang, J.Q., Zhang, H.Y.: Projection-based PROMETHEE methods based on hesitant fuzzy linguistic term sets. Int. J. Fuzzy Syst. 20(7), 2161–2174 (2018)

    Article  Google Scholar 

  40. Sun, R.X., Hu, J.H., Zhou, J.D., Chen, X.H.: A hesitant fuzzy linguistic projection-based MABAC method for patients’ prioritization. Int. J. Fuzzy Syst. 20(7), 2144–2160 (2018)

    Article  Google Scholar 

  41. Zhang, X.L., Xu, Z.S.: The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl. Based Syst. 61(2), 48–58 (2014)

    Article  MathSciNet  Google Scholar 

  42. Lin, Y., Wang, Y.M., Chen, S.Q.: Hesitant fuzzy multiattribute matching decision making based on regret theory with uncertain weights. Int. J. Fuzzy Syst. 19(4), 955–966 (2017)

    Article  MathSciNet  Google Scholar 

  43. Hu, J.H., Yang, Y., Zhang, X.L., Chen, X.H.: Similarity and entropy measures for hesitant fuzzy sets. Int. Trans. Oper. Res. 25(3), 857–886 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  44. Liao, H.C., Xu, Z.S., Zeng, X.J.: Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl. Based Syst. 82(C), 115–127 (2015)

    Article  Google Scholar 

  45. Li, D.Q., Zeng, W.Y., Li, J.H.: New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Eng. Appl. Artif. Intell. 40, 11–16 (2015)

    Article  Google Scholar 

  46. Farhadinia, B.: Weighted hesitant fuzzy information measures in decision making. J. Intell. Fuzzy Syst. 33(6), 1–10 (2017)

    MathSciNet  Google Scholar 

  47. Khalid, A., Beg, I.: Incomplete hesitant fuzzy preference relations in group decision making. Int. J. Fuzzy Syst. 19(3), 637–645 (2017)

    Article  MathSciNet  Google Scholar 

  48. Zhang, Z.M.: A framework of group decision making with hesitant fuzzy preference relations based on multiplicative consistency. Int. J. Fuzzy Syst. 19(4), 982–996 (2017)

    Article  MathSciNet  Google Scholar 

  49. Peng, J.J., Wang, J.Q., Wang, J., Yang, L.J., Chen, X.H.: An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Inf. Sci. 307(C), 113–126 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  50. Ji, P., Zhang, H.Y., Wang, J.Q.: A projection-based outranking method with multi-hesitant fuzzy linguistic term sets for hotel location selection. Cogn. Comput. 10(5), 737–751 (2018)

    Article  Google Scholar 

  51. Tian, Z.P., Wang, J.Q., Zhang, H.Y., Wang, T.L.: Signed distance-based consensus in multi-criteria group decision-making with multi-granular hesitant unbalanced linguistic information. Comput. Ind. Eng. 124, 125–138 (2018)

    Article  Google Scholar 

  52. Wang, Z., Klir, G.J.: Fuzzy measure theory. Plenum press, New York (1992)

    Book  MATH  Google Scholar 

  53. Wang, J., Wang, J.Q., Tian, Z.-P., Zhao, D.Y.: A multi-hesitant fuzzy linguistic multi-criteria decision-making approach for logistics outsourcing with incomplete weight information. Int. Trans. Oper. Res. 25(3), 831–856 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  54. Wan, S.P., Wang, F., Lin, L.L., Dong, J.Y.: An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection. Knowl. Based Syst. 82, 80–94 (2015)

    Article  Google Scholar 

  55. Cabrerizo, F.J., Chiclana, F., Al-Hmouz, R., Morfeq, A., Balamash, A.S., Herrera-Viedma, E.: Fuzzy decision making and consensus: challenges. J. Intell. Fuzzy Syst. 29(3), 1109–1118 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  56. Xu, Y., Cabrerizo, F.J., Herrera-Viedma, E.: A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Appl. Soft Comput. 58, 265–284 (2017)

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the editors and anonymous referees for their valuable and constructive comments and suggestions that immensely facilitated the improvement of this paper. This study was supported by the National Natural Science Foundation of China (Nos. 71701065 and 71871228), and China Postdoctoral Science Foundation (No. 2017M610511).

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Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Juan-juan Peng, Jian-qiang Wang & Xiao-hui Wu

  2. School of Information, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Juan-juan Peng

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  1. Juan-juan Peng
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Correspondence to Jian-qiang Wang.

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Peng, Jj., Wang, Jq. & Wu, Xh. Extended ELECTRE I Method with Multi-hesitant Fuzzy Information. Int. J. Fuzzy Syst. 21, 2192–2203 (2019). https://doi.org/10.1007/s40815-019-00716-9

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