Skip to main content
Log in

Entropy Measures for Hesitant Fuzzy Linguistic Term Sets Using the Concept of Interval-Transformed Hesitant Fuzzy Elements

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

Abstract

This article first aims to critically review the existing literature on entropy measures for hesitant fuzzy linguistic term set (HFLTS) and then exploits a bridge between HFLTSs and interval-valued fuzzy sets. The intension of introducing the concept of interval-transformed HFLTS is to derive another class of entropy measures for HFLTSs satisfying different axioms. The comparison results and the experimental evidence show that the proposed entropy measures for HFLTSs are more confident in distinguishing different HFLTSs rather than the most existing entropy measures. Finally, the practical application of proposed entropy measures is illustrated in solving a problem of multiple criteria decision making.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78, 305–316 (1996)

    Article  MathSciNet  Google Scholar 

  2. Bustince, H., Galar, M., Bedregal, B., Kolesarova, A., Mesiar, R.: A new approach to interval-valued choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans. Fuzzy Syst. 21, 1150–1162 (2013)

    Article  Google Scholar 

  3. Chen, S.M., Hong, J.A.: Multi-criteria 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 

  4. Chiclana, F., Garcia, J.M.T., Moral, M.J.D., Herrera-Viedma, E.: A statistical comparative study of different similarity measures of consensus in group decision making. Inf. Sci. 221, 110–123 (2013)

    Article  MathSciNet  Google Scholar 

  5. Deligiorgis, S., Tzimopoulos, C., Evangelides, C.: Dam location selection in the basin of Nestos river using multicriteria analysis. Environ. Process. 2, 101–111 (2015)

    Article  Google Scholar 

  6. Dengfeng, L., Chuntian, C.: New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit. Lett. 23, 221–225 (2002)

    Article  Google Scholar 

  7. Dong, Y., Zhang, H., Herrera-Viedma, E.: Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decis. Support Syst. 84, 1–15 (2016)

    Article  Google Scholar 

  8. Farhadinia, B.: Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int. J. Intell. Syst. 29, 184–205 (2014)

    Article  Google Scholar 

  9. Farhadinia, B.: Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl. Based Syst. 93, 135–144 (2016)

    Article  Google Scholar 

  10. Farhadinia, B., Xu, Z.S.: Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cogn. Comput. (2017). doi:10.1007/s12559-016-9436-2

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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. 388–389, 225–246 (2017)

    Article  Google Scholar 

  13. Herrera, F., Alonso, S., Chiclana, F., Herrera-Viedma, E.: Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim. Decis. Making 8, 337–364 (2009)

    Article  Google Scholar 

  14. Kaufmann, A.: Introduction to the Theory of Fuzzy Sets: Fundamental Theoretical Elements, vol. 1. Academic Press, New York (1975)

    MATH  Google Scholar 

  15. Liang, X., Wei, C., Cheng, X.: Entropy measures for extended hesitant fuzzy linguistic term sets and their applications, knowledge and systems sciences, pp. 151–164 (2016)

    Google Scholar 

  16. 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, 1343–1355 (2015)

    Article  Google Scholar 

  17. Liao, H.C., Xu, Z.S., Zeng, X.J., Merigo, J.M.: Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl. Based Syst. 76, 127–138 (2015)

    Article  Google Scholar 

  18. 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)

    Article  MathSciNet  Google Scholar 

  19. 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, 5328–5336 (2015)

    Article  Google Scholar 

  20. Luca, A.D., Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy theory. Inf. Control 20, 301–312 (1972)

    Article  Google Scholar 

  21. Rodríguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)

    Article  Google Scholar 

  22. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118, 467–477 (2001)

    Article  MathSciNet  Google Scholar 

  23. Tao, Z., Liu, X., Chen, H., Liu, J.: Entropy measures for linguistic information and its application to decision making. J. Intell. Fuzzy Syst. 29(2), 747–759 (2015)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  25. Wang, W.J., Chiu, C.H.: Entropy and information energy for fuzzy sets. Fuzzy Sets Syst. 108, 333–339 (1999)

    Article  MathSciNet  Google Scholar 

  26. Wang, C.H., Wang, L.P., Chen, W.H., Hu, Y.C.: Using fuzzy grey correlation TOPSIS evaluation for service quality of online bookstore. In: 2007 IEEE International Conference on Grey Systems and Intelligent Services. doi:10.1109/GSIS.2007.4443424

  27. Wang, J., Wang, J., Zhang, H.: A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing. Comput. Ind. Eng. 99, 287–299 (2016)

    Article  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. 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 

  30. Xie, X., Zhu, Q., Chang, Z.: Performance evaluation of automobile ASPs using TOPSIS. In: 2013 Fourth International Conference on Digital Manufacturing and Automation. doi:10.1109/ICDMA.2013.214

  31. Xu, Z.S.: Linguistic Decision Making: Theory and Methods. Science Press, Beijing (2012)

    Book  Google Scholar 

  32. Yager, R.R.: On the measure of fuzziness and negation, Part 1: membership in the unit interval. Int. J. Gen. Syst. 5, 221–229 (1979)

    Article  Google Scholar 

  33. Ye, J.: Multiple attribute group decision-making methods with completely unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. Group Decis. Negot. 22, 173–188 (2013)

    Article  Google Scholar 

  34. Zeng, W.Y., Li, H.X.: Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst. 157, 1477–1484 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge the support of FEDER funds under Grants TIN2013-40658-P and TIN2016-75850-R.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Enrique Herrera-Viedma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Farhadinia, B., Herrera-Viedma, E. Entropy Measures for Hesitant Fuzzy Linguistic Term Sets Using the Concept of Interval-Transformed Hesitant Fuzzy Elements. Int. J. Fuzzy Syst. 20, 2122–2134 (2018). https://doi.org/10.1007/s40815-017-0379-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0379-x

Keywords

Navigation