Skip to main content

A Review of Hesitant Fuzzy Sets: Quantitative and Qualitative Extensions

  • Chapter
  • First Online:
Fuzzy Logic in Its 50th Year

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 341))

Abstract

Since the concept of fuzzy set was introduced, different extensions and generalizations have been proposed to manage the uncertainty in different problems. This chapter is focused in a recent extension so-called hesitant fuzzy set. Many researchers have paid attention on it and have proposed different extensions both in quantitative and qualitative contexts. Several concepts, basic operations and its extensions are revised in this chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bedregal, B., Reiser, R., Bustince, H., López-Molina, C., Torra, V.: Aggregating functions for typical hesitant fuzzy elements and the action of automorphisms. Inf. Sci. 256(1), 82–97 (2014)

    Article  MATH  Google Scholar 

  3. Beg, I., Rashid, T.: TOPSIS for hesitant fuzzy linguistic term sets. Int. J. Intell. Syst. 28, 1162–1171 (2013)

    Article  Google Scholar 

  4. Chen, N., Xu, Z.S.: Properties of interval-valued hesitant fuzzy sets. J. Intell. Fuzzy Syst. 27(1), 143–158 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Chen, N., Xu, Z.S., Xia, M.M.: Interval-valued hesitant preference relations and their applications to group decision making. Knowl. Based Syst. 37(1), 528–540 (2013)

    Article  MathSciNet  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Chen, Y., Penga, X., Guanb, G., Jiangb, H.: Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 26(5), 2547–2556 (2014)

    MathSciNet  Google Scholar 

  8. Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst. 122(2), 277–291 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Crawford, G., Williams, C.: A note on the analysis of subjective judgment matrices. J. Math. Psychol. 29(4), 387–405 (1985)

    Article  MATH  Google Scholar 

  10. Dong, Y., 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)

    Article  MathSciNet  Google Scholar 

  11. Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory—the case of “intuitionistic fuzzy sets”. Fuzzy Sets Syst. 156(3), 485–491 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Farhadinia, B.: Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf. Sci. 240, 129–144 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(1), 145–174 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hesamian, G., Shams, M.: Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 28(2), 983–990 (2015)

    MathSciNet  Google Scholar 

  15. Huang, H.C., Yang, X.: Pairwise comparison and distance measure of hesitant fuzzy linguistic term sets. Math. Probl. Eng. 1–8, 2014 (2014)

    Google Scholar 

  16. Ju, Y., Yang, S., Liu, X.: Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(6), 2857–2868 (2014)

    MathSciNet  Google Scholar 

  17. Ju, Y., Zhang, W., Yang, S.: Some dual hesitant fuzzy hamacher aggregation operators and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(5), 2481–2495 (2014)

    MathSciNet  Google Scholar 

  18. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall PTR (1995)

    Google Scholar 

  19. 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)

    Article  MathSciNet  Google Scholar 

  20. Li, L.G., Peng, D.H.: Interval-valued hesitant fuzzy hamacher synergetic weighted aggregation operators and their application to shale gas areas selection. Math. Probl. Eng. 1–25, 2014 (2014)

    MathSciNet  Google Scholar 

  21. Li, Y.B., Zhang, J.P.: Approach to multiple attribute decision making with hesitant triangular fuzzy information and their application to customer credit risk assessment. J. Intell. Fuzzy Syst. 26(6), 2853–2860 (2014)

    MathSciNet  MATH  Google Scholar 

  22. Liao, H., 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)

    Article  MathSciNet  Google Scholar 

  23. Liao, H.C., Xu, Z.S.: A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim. Decis. Making 12, 373–392 (2013)

    Article  MathSciNet  Google Scholar 

  24. Lin, R., Zhao, X., Wei, G.: Models for selecting an ERP system with hesitant fuzzy linguistic information. J. Intell. Fuzzy Syst. 26(5), 2155–2165 (2014)

    MathSciNet  MATH  Google Scholar 

  25. Liu, H., Rodríguez, R.M.: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf. Sci. 258, 266–276 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Martínez, L., Liu, J., Yang, J.B., Herrera, F.: A multigranular hierarchical linguistic model for design evaluation based on safety and cost analysis. Int. J. Intell. Syst. 20(12), 1161–1194 (2005)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  28. Meng, F., Chen, X.: An approach to interval-valued hesitant fuzzy multi-attribute decision making with incomplete weight information based on hybrid Shapley operators. Informatica 25(4), 617–642 (2014)

    Article  MathSciNet  Google Scholar 

  29. Pei, Z., Yi, L.: A note on operations of hesitant fuzzy sets. Int. J. Comput. Intell. Syst. 8(2), 226–239 (2015)

    Article  Google Scholar 

  30. Peng, D.H., Wang, T.D., Gao, C.Y., Wang, H.: Continuous hesitant fuzzy aggregation operators and their application to decision making under interval-valued hesitant fuzzy setting. Sci. World J. 1–20, 2014 (2014)

    Google Scholar 

  31. Qian, G., Wang, H., Feng, X.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl. Based Syst. 37(1), 357–365 (2013)

    Article  Google Scholar 

  32. Rodríguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)

    Article  Google Scholar 

  33. Rodríguez, R.M., Martínez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf. Sci. 241(1), 28–42 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. Saaty, L.T.: The Analytic Hierarchy Process. McGraw-Hill (1980)

    Google Scholar 

  36. Saaty, R.W.: The analytic hierarchy process-what it is and how it is used. Math. Model. 9(3–5), 161–176 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sahu, S.K., Sahu, N., Thakur, R.S., Thakur, G.S.: Hesitant fuzzy linguistic term set based document classification. In: Proceedings of the International Conference on Communication Systems and Network Technologies, pp. 586–590, Gwalior, India (2013)

    Google Scholar 

  38. Shi, J., Meng, C., Liu, Y.: Approach to multiple attribute decision making based on the intelligence computing with hesitant triangular fuzzy information and their application. J. Intell. Fuzzy Syst. 27(2), 701–707 (2014)

    MathSciNet  MATH  Google Scholar 

  39. Singh, P.: A new method for solving dual hesitant fuzzy assignment problems with restrictions based on similarity measure. Appl. Soft Comput. 24, 559–571 (2014)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  41. Torra, V.: Artificial intelligence research and development, chapter on the derivation of weights using the geometric mean approach for set-valued matrices. In: Frontiers in Artificial Intelligence and Applications, pp. 193–201 (2014)

    Google Scholar 

  42. Torra, V.: Derivation of priorities and weights for set-valued matrices using the geometric mean approach. Appl. Artif. Intell. 29(5), 500–513 (2015)

    Article  Google Scholar 

  43. Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer, Heidelberg (2007)

    Google Scholar 

  44. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: Proceedings of the 18th IEEE International Conference on Fuzzy Systems, pp. 1378–1382 (2009)

    Google Scholar 

  45. Türksen, I.B.: Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20, 191–210 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wang, C., Li, Q., Zhou, X.: Multiple attribute decision making based on generalized aggregation operators under dual hesitant fuzzy environment. J. Appl. Math. 1–12, 2014 (2014)

    MathSciNet  Google Scholar 

  47. Wang, C., Li, Q., Zhou, X., Yang, T.: Hesitant triangular fuzzy information aggregation operators based on bonferroni means and their application to multiple attribute decision making. Sci. World J. 1–15, 2014 (2014)

    Google Scholar 

  48. 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)

    Article  Google Scholar 

  49. Wang, H., Xu, Z.S.: Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf. Sci. 297, 316–331 (2015)

    Article  MathSciNet  Google Scholar 

  50. Wang, H., Zhao, X., Wei, G.: Dual hesitant fuzzy aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 26(5), 2281–2290 (2014)

    MathSciNet  MATH  Google Scholar 

  51. 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)

    Article  MathSciNet  Google Scholar 

  52. 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)

    Article  MathSciNet  Google Scholar 

  53. Wang, L., Ni, M., Zhu, L.: Correlation measures of dual hesitant fuzzy sets. J. Appl. Math. 1–12, 2013 (2013)

    Google Scholar 

  54. Wei, C., Ren, Z., Rodríguez, R.M.: A hesitant fuzzy linguistic TODIM method based on a score function. Int. J. Comput. Intell. Syst. 8(4), 701–712 (2015)

    Article  Google Scholar 

  55. Wei, C., Zhao, N., Tang, X.: Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans. Fuzzy Syst. 22(3), 575–585 (2014)

    Article  Google Scholar 

  56. Wei, G., Lin, R., Wang, H.: Distance and similarity measures for hesitant interval-valued fuzzy sets. J. Intell. Fuzzy Syst. 27(1), 19–36 (2014)

    MathSciNet  MATH  Google Scholar 

  57. Wei, G., Wang, H., Zhao, X., Lin, R.: Hesitant triangular fuzzy information aggregation in multiple attribute decision making. J. Intell. Fuzzy Syst. 26(3), 1201–1209 (2014)

    MathSciNet  MATH  Google Scholar 

  58. Wei, G., Zhao, X.: Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 24(4), 789–803 (2013)

    MathSciNet  MATH  Google Scholar 

  59. Wei, G., Zhao, X., Lin, R.: Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl. Based Syst. 46, 43–53 (2013)

    Article  Google Scholar 

  60. Wei, G., Zhao, X., Lin, R.: Models for hesitant interval-valued fuzzy multiple attribute decision making based on the correlation coefficient with incomplete weight information. J. Intell. Fuzzy Syst. 26(4), 1631–1644 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  62. Xia, M.M., Xu, Z.S.: Managing hesitant information in GDM problems underfuzzy and multiplicative preference relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 21(06), 865–897 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  63. Yang, S., Ju, Y.: Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making. J. Intell. Fuzzy Syst. 27(4), 1935–1947 (2014)

    MathSciNet  MATH  Google Scholar 

  64. Yavuz, M., Oztaysi, B., Cevik Onar, S., Kahraman, C.: Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model. Expert Syst. Appl. 42(5), 2835–2848 (2015)

    Article  Google Scholar 

  65. Ye, J.: Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Appl. Math. Model. 38(2), 659–666 (2014)

    Article  MathSciNet  Google Scholar 

  66. Yu, D.: Triangular hesitant fuzzy set and its application to teaching quality evaluation. J. Inf. Comput. Sci. 10(7), 1925–1934 (2013)

    Article  Google Scholar 

  67. Yu, D.: Some generalized dual hesitant fuzzy geometric aggregation operators and applications. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 22(3), 367–384 (2014)

    Article  MATH  Google Scholar 

  68. Yu, D., Li, D.F.: Dual hesitant fuzzy multi-criteria decision making and its application to teaching quality assessment. J. Intell. Fuzzy Syst. 27(4), 1679–1688 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  70. Zhang, Y.: Research on the computer network security evaluation based on the DHFHCG operator with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 28(1), 199–204 (2015)

    MathSciNet  Google Scholar 

  71. Zhang, Z., Wu, C.: A decision support model for group decision making with hesitant multiplicative preference relations. Inf. Sci. 282, 136–166 (2014)

    Article  MathSciNet  Google Scholar 

  72. Zhang, Z., 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)

    MathSciNet  MATH  Google Scholar 

  73. Zhang, Z., Wu, C.: On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl. Based Syst. 72, 13–27 (2014)

    Article  Google Scholar 

  74. Zhao, X., Lin, R., Wei, G.: Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Syst. Appl. 41(4, Part 1), 1086–1094

    Google Scholar 

  75. Zhong, G., Xu, L.: Models for multiple attribute decision making method in hesitant triangular fuzzy setting. J. Intell. Fuzzy Syst. 26(5), 2167–2174 (2014)

    MathSciNet  MATH  Google Scholar 

  76. Zhu, B., Xu, Z.S.: Regression methods for hesitant fuzzy preference relations. Technol. Econ. Dev. Econ. 19, S214–S227 (2013)

    Google Scholar 

  77. Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22, 35–45 (2014)

    Article  MathSciNet  Google Scholar 

  78. Zhu, B., Xu, Z.S.: Stochastic preference analysis in numerical preference relations. Eur. J. Oper. Res. 237(2), 628–633 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  79. Zhu, B., Xu, Z.S., Xia, M.M.: Dual hesitant fuzzy sets. J. Appl. Math. 1–13, 2012 (2012)

    MathSciNet  MATH  Google Scholar 

  80. Zhu, J.Q., Fu, F., Yin, K.X., Luo, J.Q., Wei, D.: Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment. J. Intell. Fuzzy Syst. 27(2), 1057–1065 (2014)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is partially funded by the Spanish research projects TIN2011-27076-C03-03, TIN2015-66524-P, the Spanish Ministry of Economy and Finance Postdoctoral Training (FPDI-2013-18193) and ERDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rosa M. Rodríguez .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Rodríguez, R.M., Martínez, L., Herrera, F., Torra, V. (2016). A Review of Hesitant Fuzzy Sets: Quantitative and Qualitative Extensions. In: Kahraman, C., Kaymak, U., Yazici, A. (eds) Fuzzy Logic in Its 50th Year. Studies in Fuzziness and Soft Computing, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-319-31093-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-31093-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31091-6

  • Online ISBN: 978-3-319-31093-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics