Advertisement

International Journal of Fuzzy Systems

, Volume 20, Issue 7, pp 2084–2110 | Cite as

Hesitant Fuzzy Linguistic Term Set and Its Application in Decision Making: A State-of-the-Art Survey

  • Huchang Liao
  • Zeshui XuEmail author
  • Enrique Herrera-Viedma
  • Francisco Herrera
Article

Abstract

The hesitant fuzzy linguistic term set (HFLTS) has gained great success as it can be used to represent several linguistic terms or comparative linguistic expressions together with some context-free grammars. This new approach has enabled the analysis and computing of linguistic expressions with uncertainties and opened the door for the possibility to develop more comprehensive and powerful decision theories and methods based on linguistic knowledge. Lots of new approaches and proposals for decision-making problems have been proposed to overcome the limitations of previous linguistic decision-making approaches. Now and in the future, decision-making methodologies and algorithms with hesitant fuzzy linguistic models would be a quite promising research line representing a high-quality breakthrough in this topic. To facilitate the study on HFLTS theory, this paper makes a state-of-the-art survey on HFLTSs based on the 134 selected papers from Web of Sciences published from January 2012 to October 2017. We justify the motivation, definitions, operations, comparison methods and measures of HFLTSs. We also summarize the different extensions of HFLTSs. The studies on multiple criteria decision making (MCDM) with HFLTSs in terms of aggregation operators and MCDM methods are clearly reviewed. We also conduce some overviews on decision making with hesitant fuzzy linguistic preference relations. The applications, research challenges and future directions are also given.

Keywords

Hesitant fuzzy linguistic term set Multiple criteria decision making Qualitative decision making Hesitant fuzzy linguistic preference relation Linguistic expressions Survey 

Notes

Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71771156, 71501135, 71571123), the China Postdoctoral Science Foundation (2016T90863, 2016M602698), the Scientific Research Foundation for Excellent Young Scholars at Sichuan University (No. 2016SCU04A23), the Scientific Research Foundation for Scholars at Sichuan University (No. YJ201535), the 2016 Key Project of the Key Research Institute of Humanities and Social Sciences in Sichuan Province (CJZ16-01, CJCB2016-02, Xq16B04), the International Visiting Program for Excellent Young Scholars of SCU and the Grant from the FEDER funds (No. TIN2016-75850-R).

References

  1. 1.
    Bai, C.Z., Zhang, R., Qian, L.X., Wu, Y.N.: Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl. Based Syst. 119, 284–291 (2017)CrossRefGoogle Scholar
  2. 2.
    Beg, I., Rashid, T.: Topsis for hesitant fuzzy linguistic term sets. Int. J. Intell. Syst. 28(12), 1162–1171 (2013)Google Scholar
  3. 3.
    Beg, I., Rashid, T.: Hesitant 2-tuple linguistic information in multiple attributes group decision making. J. Intell. Fuzzy Syst. 30(1), 109–116 (2016)zbMATHGoogle Scholar
  4. 4.
    Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Xu, Z.S., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. 24(1), 179–194 (2016)Google Scholar
  5. 5.
    Cabrerizo, F.J., Herrera-Viedma, E., Pedrycz, W.: A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur. J. Oper. Res. 230(3), 624–633 (2013)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Chang, K.H.: A more general reliability allocation method using the hesitant fuzzy linguistic term set and minimal variance owga weights. Appl. Soft Comput. 56, 589–596 (2017)CrossRefGoogle Scholar
  7. 7.
    Chen, S.M., Hong, J.A.: Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf. Sci. 286, 63–74 (2014)Google Scholar
  8. 8.
    Chen, Z.S., Chin, K.S., Li, Y.L., Yang, Y.: Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making. Inf. Sci. 357, 61–87 (2016)MathSciNetGoogle Scholar
  9. 9.
    Chen, Z.S., Chin, K.S., Mu, N.Y., Xiong, S.H., Chang, J.P., Yang, Y.: Generating hflts possibility distribution with an embedded assessing attitude. Inf. Sci. 394, 141–166 (2017)Google Scholar
  10. 10.
    Cui, Y.: An approach to evaluating the performances of the photoelectric devices with hesitant fuzzy linguistic information. Int. J. Knowl. Based Intell. Eng. Syst. 20(4), 245–249 (2016)Google Scholar
  11. 11.
    Da, T., Xu, Y.J.: Evaluation on connectivity of urban waterfront redevelopment under hesitant fuzzy linguistic environment. Ocean Coast. Manag. 132, 101–110 (2016)Google Scholar
  12. 12.
    Dong, J.Y., Yuan, F.F., Wan, S.P.: Extended vikor method for multiple criteria decision-making with linguistic hesitant fuzzy information. Comput. Ind. Eng. 112, 305–319 (2017)Google Scholar
  13. 13.
    Dong, Y.C., Chen, X., Herrera, F.: Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making. Inf. Sci. 297, 95–117 (2015)MathSciNetGoogle Scholar
  14. 14.
    Dong, Y.C., Li, C.C., Herrera, F.: Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information. Inf. Sci. 367, 259–278 (2016)Google Scholar
  15. 15.
    Durand, M., Truck, I.: A new proposal to deal with hesitant linguistic expressions on preference assessments. Inf. Fusion 41, 176–181 (2018)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Faizi, S., Rashid, T., Zafar, S.: An outranking method for multi-criteria group decision making using hesitant intuitionistic fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 32(3), 2153–2164 (2017)zbMATHGoogle Scholar
  18. 18.
    Farhadinia, B.: Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl. Based Syst. 93, 135–144 (2016)Google Scholar
  19. 19.
    Feng, X.Q., Tan, Q.Y., Wei, C.P.: Hesitant fuzzy linguistic multi-criteria decision making based on possibility theory. Int. J. Mach. Learn. Cybern. (2017).  http://dx.doi.org/10.1007/s13042-017-0659-7
  20. 20.
    García-Lapresta, J.L., Pérez-Román, D.: Consensus-based clustering under hesitant qualitative assessments. Fuzzy Sets Syst. 292, 261–273 (2016)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Ghadikolaei, A.S., Madhoushi, M., Divsalar, M.: Extension of the VIKOR method for group decision making with extended hesitant fuzzy linguistic information. Neural Comput. Appl. (2017).  http://dx.doi.org/10.1007/s00521-017-2944-5
  22. 22.
    Gou, X., Xu, Z., Liao, H.: Group decision making with compatibility measures of hesitant fuzzy linguistic preference relations. Soft Comput. (2017).  http://dx.doi.org/10.1007/s00500-017-2871-5
  23. 23.
    Gou, X.J., Liao, H.C., Xu, Z.S., Herrera, F.: Double hierarchy hesitant fuzzy linguistic term set and multimoora method: a case of study to evaluate the implementation status of haze controlling measures. Inf. Fusion 38, 22–34 (2017)Google Scholar
  24. 24.
    Gou, X.J., Xu, Z.S.: Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf. Sci. 372, 407–427 (2016)Google Scholar
  25. 25.
    Gou, X.J., Xu, Z.S., Liao, H.C.: Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making. Inf. Sci. 388, 225–246 (2017)Google Scholar
  26. 26.
    Gou, X.J., Xu, Z.S., Liao, H.C.: Multiple criteria decision making based on bonferroni means with hesitant fuzzy linguistic information. Soft. Comput. 21(21), 6515–6529 (2017)zbMATHGoogle Scholar
  27. 27.
    Gu, G.Y., Wei, F.J., Zhou, S.H.: Risk assessment method for mass unexpected incident in city with hesitant fuzzy linguistic information. J. Intell. Fuzzy Syst. 29(5), 2299–2304 (2015)Google Scholar
  28. 28.
    Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)Google Scholar
  29. 29.
    Hesamian, G., Shams, M.: Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 28(2), 983–990 (2015)MathSciNetGoogle Scholar
  30. 30.
    Huang, H.C., Yang, X.J.: Pairwise comparison and distance measure of hesitant fuzzy linguistic term sets. Math. Probl. Eng. 2014 (2014).  http://dx.doi.org/10.1155/2014/954040 Google Scholar
  31. 31.
    Huo, Z.G., Zhou, Z.G.: Approaches to multiple attribute decision making with hesitant fuzzy uncertain linguistic information. J. Intell. Fuzzy Syst. 28(3), 991–998 (2015)Google Scholar
  32. 32.
    Jin, M., Liao, M.J.: Approaches to multiple attribute decision making based on the hesitant fuzzy uncertain linguistic power aggregation operators and their applications to service quality evaluation in higher education. J. Comput. Theor. Nanosci. 13(10), 7171–7175 (2016)Google Scholar
  33. 33.
    Ju, Y.B., Yang, S.H., Liu, X.Y.: A novel method for multiattribute decision making with dual hesitant fuzzy triangular linguistic information. J. Appli. Math. 2014 (2014).  http://dx.doi.org/10.1155/2014/909823 Google Scholar
  34. 34.
    Khishtandar, S., Zandieh, M., Dorri, B.: A multi criteria decision making framework for sustainability assessment of bioenergy production technologies with hesitant fuzzy linguistic term sets: the case of Iran. Renew. Sustain. Energy Rev. 77, 1130–1145 (2017)Google Scholar
  35. 35.
    Kitchenham, B.: Procedures for performing systematic reviews. Keele UK Keele Univ. 33(2004), 1–26 (2004)Google Scholar
  36. 36.
    Leclercq, J.: Propositions dextension de la notion de dominance en présence de relations dordre sur les pseudo-critères: MELCHIOR. Revue Belge de Recherche Opérationnelle, de Statistique et dInformatique 24(1), 32–46 (1984)zbMATHGoogle Scholar
  37. 37.
    Lee, L.W., Chen, S.M.: Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators. Inf. Sci. 294, 513–529 (2015)MathSciNetzbMATHGoogle Scholar
  38. 38.
    Li, C.C., Dong, Y., Herrera, F., Herrera-Viedma, E., Martínez, L.: Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching. Inf. Fusion 33, 29–40 (2017)Google Scholar
  39. 39.
    Li, Q.X., Zhao, X.F., Wei, G.W.: Model for software quality evaluation with hesitant fuzzy uncertain linguistic information. J. Intell. Fuzzy Syst. 26(6), 2639–2647 (2014)MathSciNetzbMATHGoogle Scholar
  40. 40.
    Li, Z.M., Xu, J.P., Lev, B., Gang, J.: Multi-criteria group individual research output evaluation based on context-free grammar judgments with assessing attitude. Omega 57, 282–293 (2015)Google Scholar
  41. 41.
    Liao, H., Li, Z., Zeng, X.J., Liu, W.: A comparison of distinct consensus measures for group decision making with intuitionistic fuzzy preference relations. Int. J. Comput. Intell. Syst. 10(1), 456–469 (2017)Google Scholar
  42. 42.
    Liao, H., Xu, Z., Zeng, X.J.: Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl. Based Syst. 82, 115–127 (2015)Google Scholar
  43. 43.
    Liao, H.C., Jiang, L.S., Xu, Z.S., Xu, J.P., Herrera, F.: A linear programming method for multiple criteria decision making with probabilistic linguistic information. Inf. Sci. 415–416, 341–355 (2017)Google Scholar
  44. 44.
    Liao, H.C., Wu, X.L., Liang, X.D., Xu, J.P., Herrera, F.: A new hesitant fuzzy linguistic ORESTE method for hybrid multi-criteria decision making. IEEE Trans. Fuzzy Syst. (2017). Technique ReportGoogle Scholar
  45. 45.
    Liao, H.C., Wu, X.L., Liang, X.D., Yang, J.B., Xu, D.L.: Continuous interval-valued linguistic ORESTE method for multi-criteria group decision making in mobile design. Knowl. Based Syst. (2017). Technique ReportGoogle Scholar
  46. 46.
    Liao, H.C., Xu, Z.S.: Satisfaction degree based interactive decision making under hesitant fuzzy environment with incomplete weights. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 22(4), 553–572 (2014)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Liao, H.C., Xu, Z.S.: Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for hfltss and their application in qualitative decision making. Expert Syst. Appl. 42(12), 5328–5336 (2015)Google Scholar
  48. 48.
    Liao, H.C., Xu, Z.S., Xia, M.M.: Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int. J. Inf. Technol. Decis. Mak. 13(1), 47–76 (2014)Google Scholar
  49. 49.
    Liao, H.C., Xu, Z.S., Zeng, X.J.: Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014)MathSciNetzbMATHGoogle Scholar
  50. 50.
    Liao, H.C., Xu, Z.S., Zeng, X.J.: Hesitant fuzzy linguistic vikor method and its application in qualitative multiple criteria decision making. IEEE Trans. Fuzzy Syst. 23(5), 1343–1355 (2015)Google Scholar
  51. 51.
    Liao, H.C., Xu, Z.S., Zeng, X.J., Merigó, J.M.: Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl. Based Syst. 76, 127–138 (2015)Google Scholar
  52. 52.
    Lin, R., Zhao, X.F., Wei, G.W.: Models for selecting an erp system with hesitant fuzzy linguistic information. J. Intell. Fuzzy Syst. 26(5), 2155–2165 (2014)MathSciNetzbMATHGoogle Scholar
  53. 53.
    Liu, D.N.: Model for evaluating the electrical power system safety with hesitant fuzzy linguistic information. J. Intell. Fuzzy Syst. 29(2), 725–730 (2015)MathSciNetGoogle Scholar
  54. 54.
    Liu, H.B., Cai, J.F., Jiang, L.: On improving the additive consistency of the fuzzy preference relations based on comparative linguistic expressions. Int. J. Intell. Syst. 29(6), 544–559 (2014)Google Scholar
  55. 55.
    Liu, H.B., Rodríguez, R.M.: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf. Sci. 258, 220–238 (2014)MathSciNetzbMATHGoogle Scholar
  56. 56.
    Liu, H.C., You, J.X., Li, P., Su, Q.: Failure mode and effect analysis under uncertainty: an integrated multiple criteria decision making approach. IEEE Trans. Reliab. 65(3), 1380–1392 (2016)Google Scholar
  57. 57.
    Liu, W.S., Liao, H.C.: A bibliometric analysis of fuzzy decision research during 1970–2015. Int. J. Fuzzy Syst. 19(1), 1–14 (2017)Google Scholar
  58. 58.
    Liu, X.Y., Ju, Y.B., Yang, S.H.: Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(3), 1187–1201 (2014)MathSciNetzbMATHGoogle Scholar
  59. 59.
    Liu, X.Y., Ju, Y.B., Yang, S.H.: Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making. Soft. Comput. 20(2), 495–510 (2016)zbMATHGoogle Scholar
  60. 60.
    Liu, Y., Fan, Z.P., Zhang, X.: A method for large group decision-making based on evaluation information provided by participators from multiple groups. Inf. Fusion 29, 132–141 (2016)Google Scholar
  61. 61.
    Liu, Y.Z., Fan, Z.P., Gao, G.X.: An extended linmap method for magdm under linguistic hesitant fuzzy environment. J. Intell. Fuzzy Syst. 30(5), 2689–2703 (2016)zbMATHGoogle Scholar
  62. 62.
    Lu, M., Wei, G.W.: Models for multiple attribute decision making with dual hesitant fuzzy uncertain linguistic information. Int. J. Knowl. Based Intell. Eng. Syst. 20(4), 217–227 (2016)Google Scholar
  63. 63.
    Luo, D.C., Yang, M.H., Gao, L.F.: Research on risk assessment of financial markets venture capital project with hesitant fuzzy uncertain linguistic information. J. Comput. Theor. Nanosci. 13(10), 7115–7119 (2016)Google Scholar
  64. 64.
    Massanet, S., Riera, J.V., Torrens, J., Herrera-Viedma, E.: A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf. Sci. 258, 277–290 (2014)MathSciNetzbMATHGoogle Scholar
  65. 65.
    Matarazzo, B.: Multicriterion analysis of preferences by means of pairwise actions and criterion comparisons (MAPPACC). Appl. Math. Comput. 18(2), 119–141 (1986)MathSciNetzbMATHGoogle Scholar
  66. 66.
    Mendel, J.M., Zadeh, L.A., Trillas, E., Yager, R., Lawry, J., Hagras, H., Guadarrama, S.: What computing with words means to me [discussion forum]. IEEE Comput. Intell. Mag. 5(1), 20–26 (2010)Google Scholar
  67. 67.
    Meng, F.Y., Chen, X.H.: A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures. J. Intell. Fuzzy Syst. 28(4), 1519–1531 (2015)MathSciNetzbMATHGoogle Scholar
  68. 68.
    Meng, F.Y., Chen, X.H., Zhang, Q.: Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Inf. Sci. 267, 287–305 (2014)MathSciNetzbMATHGoogle Scholar
  69. 69.
    Meng, F.Y., Wang, C., Chen, X.H.: Linguistic interval hesitant fuzzy sets and their application in decision making. Cognit. Comput. 8(1), 52–68 (2016)Google Scholar
  70. 70.
    Montes, R., Sánchez, A.M., Villar, P., Herrera, F.: A web tool to support decision making in the housing market using hesitant fuzzy linguistic term sets. Appl. Soft Comput. 35, 949–957 (2015)Google Scholar
  71. 71.
    Montes, R., Sanchez, A.M., Villar, P., Herrera, F.: Teranga go!: carpooling collaborative consumption community with multi-criteria hesitant fuzzy linguistic term set opinions to build confidence and trust. Appl. Soft Comput. (2017).  https://doi.org/10.1016/j.asoc.2017.05.039 Google Scholar
  72. 72.
    Montserrat-Adell, J., Agell, N., Sánchez, M., Prats, F., Ruiz, F.J.: Modeling group assessments by means of hesitant fuzzy linguistic term sets. J. Appl. Logic 23, 40–50 (2017)MathSciNetzbMATHGoogle Scholar
  73. 73.
    Montserrat-Adell, J., Agell, N., Sánchez, M., Ruiz, F.J.: Consensus, dissension and precision in group decision making by means of an algebraic extension of hesitant fuzzy linguistic term sets. Inf. Fusion 42, 1–11 (2018)Google Scholar
  74. 74.
    Palomares, I., Martinez, L., Herrera, F.: A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans. Fuzzy Syst. 22(3), 516–530 (2014)Google Scholar
  75. 75.
    Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016)Google Scholar
  76. 76.
    Pedrycz, W., Song, M.: A granulation of linguistic information in ahp decision-making problems. Inf. Fusion 17, 93–101 (2014)Google Scholar
  77. 77.
    Peng, H.G., Wang, J.Q.: Hesitant uncertain linguistic z-numbers and their application in multi-criteria group decision-making problems. Int. J. Fuzzy Syst. 19(5), 1300–1316 (2017)Google Scholar
  78. 78.
    Qi, X.W., Liang, C.Y., Zhang, J.L.: Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment. Int. J. Mach. Learn. Cybernet. 7(6), 1147–1193 (2016)Google Scholar
  79. 79.
    Rashid, T., Faizi, S., Xu, Z.S., Zafar, S.: Electre-based outranking method for multi-criteria decision making using hesitant intuitionistic fuzzy linguistic term sets. Int. J. Fuzzy Syst. (2017).  http://dx.doi.org/10.1007/s40815-017-0297-y
  80. 80.
    Riera, J.V., Massanet, S., Herrera-Viedma, E., Torrens, J.: Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Appl. Soft Comput. 36, 383–391 (2015)Google Scholar
  81. 81.
    Rodríguez, R.M., Bedregal, B., Bustince, H., Dong, Y.C., Farhadinia, B., Kahraman, C., Martínez, L., Torra, V., Xu, Y.J., Xu, Z.S., et al.: A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf. Fusion 29, 89–97 (2016)Google Scholar
  82. 82.
    Rodríguez, R.M., Labella, A., Martínez, L.: An overview on fuzzy modelling of complex linguistic preferences in decision making. Int. J. Comput. Intell. Syst. 9(sup1), 81–94 (2016)Google Scholar
  83. 83.
    Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)Google Scholar
  84. 84.
    RodríGuez, R.M., MartıNez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf. Sci. 241, 28–42 (2013)MathSciNetzbMATHGoogle Scholar
  85. 85.
    Rodríguez, R.M., Martínez, L., Torra, V., Xu, Z.S., Herrera, F.: Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. 29(6), 495–524 (2014)Google Scholar
  86. 86.
    Sellak, H., Ouhbi, B., Frikh, B.: A knowledge-based outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Appl. Soft Comput. (2017).  https://doi.org/10.1016/j.asoc.2017.06.031 Google Scholar
  87. 87.
    Sun, R., Hu, J., Zhou, J., Chen, X.: A hesitant fuzzy linguistic projection-based MABAC method for patients’ prioritization. Int. J. Fuzzy Syst. (2017).  http://dx.doi.org/10.1007/s40815-017-0345-7
  88. 88.
    Tan, Q.Y., Wei, C.P., Liu, Q., Feng, X.Q.: The hesitant fuzzy linguistic TOPSIS method based on novel information measures. Asia-Pacific J. Oper. Res. 33(05), 1650035 (2016)MathSciNetzbMATHGoogle Scholar
  89. 89.
    Tian, Z.P., Wang, J., Wang, J.Q., Zhang, H.Y.: A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cognit. Comput. 8(4), 670–683 (2016)Google Scholar
  90. 90.
    Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)zbMATHGoogle Scholar
  91. 91.
    Tüysüz, F., Şimşek, B.: A hesitant fuzzy linguistic term sets-based AHP approach for analyzing the performance evaluation factors: an application to cargo sector. Complex Intell. Syst. 3, 167–175 (2017)Google Scholar
  92. 92.
    Vansnick, J.C.: On the problem of weights in multiple criteria decision making (the noncompensatory approach). Eur. J. Oper. Res. 24(2), 288–294 (1986)MathSciNetzbMATHGoogle Scholar
  93. 93.
    Wang, H.: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int. J. Comput. Intell. Syst. 8(1), 14–33 (2015)Google Scholar
  94. 94.
    Wang, H., Xu, Z.S.: Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf. Sci. 297, 316–331 (2015)MathSciNetzbMATHGoogle Scholar
  95. 95.
    Wang, H., Xu, Z.S.: Total orders of extended hesitant fuzzy linguistic term sets: definitions, generations and applications. Knowl. Based Syst. 107, 142–154 (2016)Google Scholar
  96. 96.
    Wang, J., Wang, J.Q., Zhang, H.Y.: A likelihood-based todim approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing. Comput. Ind. Eng. 99, 287–299 (2016)Google Scholar
  97. 97.
    Wang, J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: an outranking approach. Knowl. Based Syst. 86, 224–236 (2015)Google Scholar
  98. 98.
    Wang, J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information. Int. J. Fuzzy Syst. 18(1), 81–97 (2016)MathSciNetGoogle Scholar
  99. 99.
    Wang, J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Distance-based multi-criteria group decision-making approaches with multi-hesitant fuzzy linguistic information. Int. J. Inf. Technol. Decis. Mak. 16(4), 1069–1099 (2017)Google Scholar
  100. 100.
    Wang, J.Q., Wang, J., Chen, Q.H., Zhang, H.Y., Chen, X.H.: An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf. Sci. 280, 338–351 (2014)MathSciNetzbMATHGoogle Scholar
  101. 101.
    Wang, J.Q., Wu, J.T., Wang, J., Zhang, H.Y., Chen, X.H.: Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 288, 55–72 (2014)MathSciNetzbMATHGoogle Scholar
  102. 102.
    Wang, J.Q., Wu, J.T., Wang, J., Zhang, H.Y., Chen, X.H.: Multi-criteria decision-making methods based on the hausdorff distance of hesitant fuzzy linguistic numbers. Soft. Comput. 20(4), 1621–1633 (2016)Google Scholar
  103. 103.
    Wang, L., Gong, Z.: Priority of a hesitant fuzzy linguistic preference relation with a normal distribution in meteorological disaster risk assessment. Int. J. Environ. Res. Publ. Health 14(10), 1203 (2017)Google Scholar
  104. 104.
    Wang, Y.H., Li, L.: Models for multiple attribute decision making with hesitant fuzzy linguistic information and their application to enterprise risk evaluation. J. Intell. Fuzzy Syst. 30(3), 1531–1536 (2016)zbMATHGoogle Scholar
  105. 105.
    Webster, J., Watson, R.T.: Analyzing the past to prepare for the future: writing a literature review. MIS Quart. 26(2), xiii–xxiii (2002)Google Scholar
  106. 106.
    Wei, C., Rodríguez, R.M., Martínez, L.: Uncertainty measures of extended hesitant fuzzy linguistic term sets. IEEE Trans. Fuzzy Syst. (2017).  https://doi.org/10.1109/TFUZZ.2017.2724023 CrossRefGoogle Scholar
  107. 107.
    Wei, C.P., Liao, H.C.: A multigranularity linguistic group decision-making method based on hesitant 2-tuple sets. Int. J. Intell. Syst. 31(6), 612–634 (2016)MathSciNetGoogle Scholar
  108. 108.
    Wei, C.P., Ren, Z.L., Rodríguez, R.M.: A hesitant fuzzy linguistic todim method based on a score function. Int. J. Comput. Intell. Syst. 8(4), 701–712 (2015)Google Scholar
  109. 109.
    Wei, C.P., Zhao, N., Tang, X.J.: Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans. Fuzzy Syst. 22(3), 575–585 (2014)Google Scholar
  110. 110.
    Wei, C.P., Zhao, N., Tang, X.J.: A novel linguistic group decision-making model based on extended hesitant fuzzy linguistic term sets. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 23(03), 379–398 (2015)MathSciNetzbMATHGoogle Scholar
  111. 111.
    Wei, G.W.: Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Int. J. Mach. Learn. Cybernet. 7(6), 1093–1114 (2016)Google Scholar
  112. 112.
    Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A.: Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Iran. J. Fuzzy Syst. 13(4), 1–16 (2016)MathSciNetzbMATHGoogle Scholar
  113. 113.
    Wei, G.W., Lin, R., Wang, H.J., Ran, L.G.: Interval-valued dual hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Int. Core J. Eng. 1(6), 12–222 (2015)Google Scholar
  114. 114.
    Wei, G.W., Xu, X.R., Deng, D.X.: Interval-valued dual hesitant fuzzy linguistic geometric aggregation operators in multiple attribute decision making. Int. J. Knowl. Based Intell. Eng. Syst. 20(4), 189–196 (2016)Google Scholar
  115. 115.
    Wu, J.T., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H.: Hesitant fuzzy linguistic multicriteria decision-making method based on generalized prioritized aggregation operator. Sci. World J. 2014 (2014).  http://dx.doi.org/10.1155/2014/645341 Google Scholar
  116. 116.
    Wu, Z., Xu, J.: A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf. Fusion 41, 217–231 (2018)Google Scholar
  117. 117.
    Wu, Z.B., Xu, J.P.: An interactive consensus reaching model for decision making under hesitation linguistic environment. J. Intell. Fuzzy Syst. 31(3), 1635–1644 (2016)zbMATHGoogle Scholar
  118. 118.
    Wu, Z.B., Xu, J.P.: Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65, 28–40 (2016)Google Scholar
  119. 119.
    Wu, Z.B., Xu, J.P.: Possibility distribution-based approach for magdm with hesitant fuzzy linguistic information. IEEE Trans. Cybern. 46(3), 694–705 (2016)Google Scholar
  120. 120.
    Xu, Y.J., Xu, A.W., Merigó, J.M., Wang, H.M.: Hesitant fuzzy linguistic ordered weighted distance operators for group decision making. J. Appl. Math. Comput. 49(1–2), 285–308 (2015)MathSciNetzbMATHGoogle Scholar
  121. 121.
    Xu, Y.J., Xu, A.W., Wang, H.M.: Hesitant fuzzy linguistic linear programming technique for multidimensional analysis of preference for multi-attribute group decision making. Int. J. Mach. Learn. Cybernet. 7(5), 845–855 (2016)Google Scholar
  122. 122.
    Xu, Z., Wang, H.: On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Inf. Fusion 34, 43–48 (2017)Google Scholar
  123. 123.
    Xu, Z.S.: EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 12(06), 791–810 (2004)MathSciNetzbMATHGoogle Scholar
  124. 124.
    Xu, Z.S.: Deviation measures of linguistic preference relations in group decision making. Omega 33(3), 249–254 (2005)MathSciNetGoogle Scholar
  125. 125.
    Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)Google Scholar
  126. 126.
    Xu, Z.S., Wang, H.: Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul. Comput. 1(1), 21–35 (2016)Google Scholar
  127. 127.
    Yager, R.R.: Concepts, theory, and techniques a new methodology for ordinal multiobjective decisions based on fuzzy sets. Decis. Sci. 12(4), 589–600 (1981)Google Scholar
  128. 128.
    Yang, S.H., Ju, Y.B.: Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making. J. Intell. Fuzzy Syst. 27(4), 1935–1947 (2014)MathSciNetzbMATHGoogle Scholar
  129. 129.
    Yang, S.H., Sun, Z., Ju, Y.B., Qiao, C.Y.: A novel multiple attribute satisfaction evaluation approach with hesitant intuitionistic linguistic fuzzy information. Math. Probl. Eng. 2014 (2014).  http://dx.doi.org/10.1155/2014/692782 MathSciNetGoogle Scholar
  130. 130.
    Yang, W., Pang, Y.F., Shi, J.R., Wang, C.J.: Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR. Neural Comput. Appl. (2016).  http://dx.doi.org/10.1007/s00521-016-2526-y
  131. 131.
    Yang, W., Pang, Y.F., Shi, J.R., Yue, H.Y.: Linguistic hesitant intuitionistic fuzzy linear assignment method based on choquet integral. J. Intell. Fuzzy Syst. 32(1), 767–780 (2017)zbMATHGoogle Scholar
  132. 132.
    Yang, W., Shi, J.R., Pang, Y.F.: Generalized linguistic hesitant intuitionistic fuzzy hybrid aggregation operators. Math. Probl. Eng. 2015 (2015).  http://dx.doi.org/10.1155/2015/983628 MathSciNetzbMATHGoogle Scholar
  133. 133.
    Yang, W., Shi, J.R., Zheng, X.Y., Pang, Y.F.: Hesitant interval-valued intuitionistic fuzzy linguistic sets and their applications. J. Intell. Fuzzy Syst. 31(6), 2779–2788 (2016)zbMATHGoogle Scholar
  134. 134.
    Yavuz, M., Oztaysi, B., Onar, S.C., Kahraman, C.: Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model. Expert Syst. Appl. 42(5), 2835–2848 (2015)Google Scholar
  135. 135.
    Yu, S.M., Zhang, H.Y., Wang, J.Q.: Hesitant fuzzy linguistic Maclaurin symmetric mean operators and their applications to multi-criteria decision-making problem. Int. J. Intell. Syst. (2017).  http://dx.doi.org/10.1002/int.21907
  136. 136.
    Yu, S.M., Zhou, H., Chen, X.H., Wang, J.Q.: A multi-criteria decision-making method based on Heronian mean operators under a linguistic hesitant fuzzy environment. Asia-Pacific J. Oper. Res. 32(05), 1550035 (2015)MathSciNetzbMATHGoogle Scholar
  137. 137.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8(3), 199–249 (1975)MathSciNetzbMATHGoogle Scholar
  138. 138.
    Zhai, Y.L., Xu, Z.S., Liao, H.C.: Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information. Appl. Soft Comput. 49, 801–816 (2016)Google Scholar
  139. 139.
    Zhang, B.W., Liang, H.M., Zhang, G.Q.: Reaching a consensus with minimum adjustment in magdm with hesitant fuzzy linguistic term sets. Inf. Fusion 42, 12–23 (2018)Google Scholar
  140. 140.
    Zhang, C., Li, D.Y., Liang, J.Y.: Hesitant fuzzy linguistic rough set over two universes model and its applications. Int. J. Mach. Learn. Cybern. (2016).  http://dx.doi.org/10.1007/s13042-016-0541-z
  141. 141.
    Zhang, F.Y., Luo, L., Liao, H.C., Zhu, T., Shi, Y.K., Shen, W.W.: Inpatient admission assessment in west china hospital based on hesitant fuzzy linguistic VIKOR method. J. Intell. Fuzzy Syst. 30(6), 3143–3154 (2016)Google Scholar
  142. 142.
    Zhang, G.Q., Dong, Y.C., Xu, Y.F.: Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inf. Fusion 17, 46–55 (2014)Google Scholar
  143. 143.
    Zhang, W.K., Ju, Y.B., Liu, X.Y.: Multiple criteria decision analysis based on Shapley fuzzy measures and interval-valued hesitant fuzzy linguistic numbers. Comput. Ind. Eng. 105, 28–38 (2017)Google Scholar
  144. 144.
    Zhang, Y.X., Xu, Z.S., Liao, H.C.: A consensus process for group decision making with probabilistic linguistic preference relations. Inf. Sci. 414, 260–275 (2017)Google Scholar
  145. 145.
    Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 49, 817–833 (2016)Google Scholar
  146. 146.
    Zhang, Z.M., Wu, C.: Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J. Intell. Fuzzy Syst. 26(5), 2185–2202 (2014)MathSciNetzbMATHGoogle Scholar
  147. 147.
    Zhang, Z.M., Wu, C.: On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl. Based Syst. 72, 13–27 (2014)Google Scholar
  148. 148.
    Zhao, N., Xu, Z.S., Ren, Z.L.: Some approaches to constructing distance measures for hesitant fuzzy linguistic term sets with applications in decision making. Int. J. Inf. Technol. Decis. Mak. (2017).  https://doi.org/10.1142/S0219622017500316 CrossRefGoogle Scholar
  149. 149.
    Zhao, X.Q., Yang, L.H., Wang, L.J.: Models for evaluating the resource integration capability of textile enterprise with hesitant fuzzy uncertain linguistic information. J. Intell. Fuzzy Syst. 31(3), 2001–2008 (2016)Google Scholar
  150. 150.
    Zheng, X.M.: Methods for multiple attribute decision making with hesitant fuzzy uncertain linguistic information and their application for evaluating the college english teachers’ professional development competence. J. Intell. Fuzzy Syst. 28(3), 1243–1250 (2015)MathSciNetGoogle Scholar
  151. 151.
    Zhou, H., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. Int. J. Syst. Sci. 47(2), 314–327 (2016)MathSciNetzbMATHGoogle Scholar
  152. 152.
    Zhou, W., Xu, Z.S.: Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites. Eur. J. Oper. Res. 254(2), 610–621 (2016)MathSciNetzbMATHGoogle Scholar
  153. 153.
    Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22(1), 35–45 (2014)Google Scholar
  154. 154.
    Zhu, C.X., Zhu, L., Zhang, X.Z.: Linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision-making. Inf. Sci. 367, 809–826 (2016)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Huchang Liao
    • 1
    • 2
  • Zeshui Xu
    • 1
    Email author
  • Enrique Herrera-Viedma
    • 2
    • 3
  • Francisco Herrera
    • 2
    • 3
  1. 1.Business SchoolSichuan UniversityChengduChina
  2. 2.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  3. 3.Faculty of Computing and Information TechnologyKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations