Skip to main content
SpringerLink
Log in

A Unified Framework

  • Chapter
  • First Online:
Linguistic Decision Making

  • 154 Accesses

Abstract

The 2-tuple linguistic representation model is widely used as a basis for linguistic symbolic computational models in linguistic decision making problems. In this chapter we provide a connection between the model of the use of a linguistic hierarchy and the numerical scale model, and then show that the numerical scale model can provide a unified framework [13] to connect different linguistic symbolic computational models. Further, a novel computing with words (CWW) methodology [13] where hesitant fuzzy linguistic term sets (HFLTSs) can be constructed based on unbalanced linguistic term sets (ULTSs) using a numerical scale is proposed. In the proposed CWW methodology, several novel possibility degree formulas for comparing HFLTSs are presented, and novel operators based on a mixed 0–1 linear programming model to aggregate hesitant unbalanced linguistic information are defined.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
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. Abchir, M. A., & Truck, I. (2013). Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets. Kybernetika, 49(1), 164–180.

    Google Scholar 

  2. Cabrerizo, F. J., Alonso, S., & Herrera-Viedma, E. (2009). A consensus model for group decision making problems with unbalanced fuzzy linguistic information. International Journal of Information Technology and Decision Making, 8(1), 109–131.

    Article  Google Scholar 

  3. Cabrerizo, F. J., Pérez, I. J., & Herrera-Viedma, E. (2010). Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowledge-Based Systems, 23(2), 169–181.

    Article  Google Scholar 

  4. Cordón, O., Herrera, F., & Zwir, I. (2002). Linguistic modeling by hierarchical systems of linguistic rules. IEEE Transactions on Fuzzy Systems, 10(1), 2–20.

    Article  Google Scholar 

  5. Delgado, M., Verdegay, J. L., & Vila, M. A. (1993). On aggregation operations of linguistic labels. International Journal of Intelligence Systems, 8(3), 351–370.

    Article  Google Scholar 

  6. Dong, Y. C., & Herrera-Viedma, E. (2015). Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relations. IEEE Transactions on Cybernetics, 45(4), 780–792.

    Article  Google Scholar 

  7. Dong, Y. C., Xu, Y. F., & Yu, S. (2009). Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Transactions on Fuzzy Systems, 17(6), 1366–1378.

    Article  Google Scholar 

  8. Dong, Y. C., Xu, Y. F., & Yu, S. (2009). Linguistic multiperson decision making based on the use of multiple preference relations. Fuzzy Sets and Systems, 160, 603–623.

    Article  Google Scholar 

  9. Dong, Y. C., Xu, Y. F., Li, H. Y., & Feng, B. (2010). The OWA-based consensus operator under linguistic representation models using position indexes. European Journal of Operational Research, 203(2), 455–463.

    Article  Google Scholar 

  10. Dong, Y. C., Zhang, G. Q., Hong, W. C., & Yu, S. (2013). Linguistic computational model based on 2-tuples and intervals. IEEE Transactions on Fuzzy Systems, 21(6), 1006–1018.

    Article  Google Scholar 

  11. Dong, Y. C., Li, C. C., & Herrera, F. (2014). Connecting the numerical scale model to the unbalanced linguistic term sets. In IEEE International Conferences on Fuzzy Systems (FUZZ-IEEE) (pp. 455–462).

    Google Scholar 

  12. Dong, Y. C., Li, C. C., Xu, Y. F., & Gu, X. (2015). Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decision and Negotiation, 24(2), 217–242.

    Article  Google Scholar 

  13. Dong, Y. C., Li, C. C., & Herrera, F. (2016). Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information. Information Sciences, 367–368, 259–278.

    Article  Google Scholar 

  14. Espinilla, M., Liu, J., & Martínez, L. (2011). An extended hierarchical linguistic model for decision-making problems. Computational Intelligence, 27(3), 489–512.

    Article  Google Scholar 

  15. Herrera, F., & Martínez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752.

    Article  Google Scholar 

  16. Herrera, F., & Martínez, L. (2001). A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics, 31(2), 227–234.

    Article  Google Scholar 

  17. Herrera, F., Herrera-Viedma, E., & Martínez, L. (2008). A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy Systems, 16(2), 354–370.

    Article  Google Scholar 

  18. Herrera-Viedma, E., & López-Herrera, A. G. (2007). A model of information retrieval system with unbalanced fuzzy linguistic information. International Journal of Intelligence Systems, 22(11), 1197–1214.

    Article  Google Scholar 

  19. Herrera-Viedma, E., Cabrerizo, F. J., Pérez, I. J., Cobo, M. J., Alonso, S., & Herrera, F. (2011). Applying linguistic OWA operators in consensus models under unbalanced linguistic information. Recent Development on the Ordered Weighted Averaging Operators, 265, 167–186.

    Article  Google Scholar 

  20. Martínez, L., Espinilla, M., Liu, J., Pérez, L. G., & Sánchez, P. J. (2009). An evaluation model with unbalanced linguistic information applied to olive oil sensory evaluation. The Journal of Multiple-Valued Logic and Soft Computing, 15, 229–251.

    Google Scholar 

  21. Meng, D., & Pei, Z. (2013). On weighted unbalanced linguistic aggregation operators in group decision making. Information Sciences, 223, 31–41.

    Article  Google Scholar 

  22. Miller, G. A. (1956). The magical number seven plus or minus two: Some limits on our capacity of processing information. Psychological Review, 63(2), 81–97.

    Article  Google Scholar 

  23. Truck, I., & Malenfant, J. (2010) Towards a unification of some linguistic representation models: A vectorial approach. In The 9th International Flins Conference on Computational Intelligence in Decision and Control, Chengdu (pp. 610–615).

    Google Scholar 

  24. Wang, J. H., & Hao, J. Y. (2006). A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 14(3), 435–445.

    Article  Google Scholar 

  25. Wang, J. H., & Hao, J. Y. (2007). An approach to computing with words based on canonical characteristic values of linguistic labels. IEEE Transactions on Fuzzy Systems, 15(4), 593–604.

    Article  Google Scholar 

  26. Wei, C. P., Zhao, N., & Tang, X. J. (2014). Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Transactions on Fuzzy Systems, 22(3), 575–585.

    Article  Google Scholar 

  27. Wu, D., & Mendel, J. M. (2010). Computing with words for hierarchical decision making applied to evaluating a weapon system. IEEE Transactions on Fuzzy Systems, 18(3), 441–460.

    Article  Google Scholar 

  28. Xu, Z. S. (2004). A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166(1–4), 19–30.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, Sichuan, China

    Yucheng Dong & Jiuping Xu

Authors
  1. Yucheng Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiuping Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dong, Y., Xu, J. (2019). A Unified Framework. In: Linguistic Decision Making. Springer, Singapore. https://doi.org/10.1007/978-981-13-2916-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-2916-6_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-2915-9

  • Online ISBN: 978-981-13-2916-6

  • eBook Packages: Social SciencesSocial Sciences (R0)

Publish with us

Policies and ethics

Search

Navigation