Skip to main content

Advertisement

SpringerLink
Log in

A Stochastic Perspective on a Group Decision-Making Method Based on Two-Dimension 2-Tuple Linguistic Information

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

Abstract

The two-dimension 2-tuple linguistic (TD2L) label, based on the traditional 2-tuple linguistic representation model, adds another 2-tuple linguistic term to express the reliability degree of the assessments. However, the reliability degree is a subjective evaluation on reliability of the given assessments and variables due to the limitations in cognitions and the complexity of decision objects. All assessments without total reliability degree are viewed as uncertain ones. Based on this idea, this paper proposes a new TD2L representation model from a stochastic perspective. The assessment expressed by TD2L is a variable that fluctuates around the given linguistic term, and the fluctuation range is decided by the reliability of the assessment. Therefore, the assessments are regarded as stochastic variables, where the expectancy and deviation of the stochastic variable are corresponding to the first dimension and the second dimension information of TD2Ls, respectively. Consequently, two new aggregation functions for aggregating TD2L labels based on the algorithms among stochastic variables are proposed. In addition, the comparison and similarity measure between TD2L labels are developed, which considers the relative importance of the two dimensions of TD2L labels. Finally, the proposed method is applied to an investment decision of medium sized enterprise and alternatives ranking is provided with the probability of superiority. A comparison analysis conducted from three aspects illustrates the effectiveness of the proposed method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8, 199–249 (1975)

    MathSciNet  MATH  Google Scholar 

  2. Cid-López, A., Hornos, M.J., Carrasco, R.A., Herrera-Viedma, E., Chiclana, F.: Linguistic multi-criteria decision-making model with output variable expressive richness. Expert Syst. Appl. 83, 350–362 (2017)

    Google Scholar 

  3. Gong, Z.W., Forrest, J., Yang, Y.J.: The optimal group consensus models for 2-tuple linguistic preference relations. Knowl. Based Syst. 37, 427–437 (2013)

    Google Scholar 

  4. Li, C.C., Rodríguez, R.M., Martínez, L., Dong, Y.C., Herrera, F.: Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions. Knowl. Based Syst. 145, 156–165 (2018)

    Google Scholar 

  5. Xu, Z.S.: A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 166, 19–30 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Xu, Z.S.: An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis. Negot. 18, 119–145 (2009)

    Google Scholar 

  7. Zeng, S., Qiyas, M., Arif, M., Mahmood, T.: Extended version of linguistic picture fuzzy TOPSIS method and its applications in enterprise resource planning systems. Math. Probl. Eng. 2019, 1–8 (2019)

    Google Scholar 

  8. Khan, A.A., Qiyas, M., Abdullah, S., Luo, J., Bano, M.: Analysis of robot selection based on 2-tuple picture fuzzy linguistic aggregation operators. Mathematics 7, 1000 (2019)

    Google Scholar 

  9. Qiyas, M., Abdullah, S., Ashraf, S., Khan, S., Khan, A.: Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems. Math. Found. Comput. 2, 183 (2019)

    Google Scholar 

  10. Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8, 746–752 (2000)

    Google Scholar 

  11. Abchir, M.A., Truck, I.: Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets. Kybernetika 49, 164–180 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Truck, I.: Comparison and links between two 2-tuple linguistic models for decision making. Knowl. Based Syst. 87, 61–68 (2015)

    Google Scholar 

  13. Truck, I., Akdag, H.: Manipulation of qualitative degrees to handle uncertainty: formal models and applications. Knowl. Inf. Syst. 9, 385–411 (2006)

    Google Scholar 

  14. Dong, Y.C., Wu, Y.Z., Zhang, H.J., Zhang, G.Q.: Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions. Knowl. Based Syst. 82, 139–151 (2015)

    Google Scholar 

  15. Herrera, F., Martinez, L.: A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans Syst Man Cybern B 31, 227–234 (2001)

    Google Scholar 

  16. Wang, J.H., Hao, J.Y.: A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 14, 435–445 (2006)

    Google Scholar 

  17. Wang, J.H., Hao, J.Y.: An approach to computing with words based on canonical characteristic values of linguistic labels. IEEE Trans. Fuzzy Syst. 15, 593–604 (2007)

    Google Scholar 

  18. Dong, Y.C., Xu, Y.F., Yu, S.: Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Trans. Fuzzy Syst. 17, 1366–1378 (2009)

    Google Scholar 

  19. Dong, Y.C., Zhang, G.Q., Hong, W.C., Yu, S.: Linguistic computational model based on 2-tuples and intervals. IEEE Trans. Fuzzy Syst. 21, 1006–1018 (2013)

    Google Scholar 

  20. Dong, Y.C., Li, C.C., Xu, Y.F., Gu, X.: Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decis. Negot. 24, 217–242 (2015)

    Google Scholar 

  21. Martínez, L., Herrera, F.: An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf. Sci. 207, 1–18 (2012)

    MathSciNet  Google Scholar 

  22. Liu, W.Q., Dong, Y.C., Chiclana, F., Cabrerizo, F.J., Herrera-Viedma, E.: Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optim. Decis. Mak. 16, 429–447 (2017)

    MathSciNet  MATH  Google Scholar 

  23. Zhu, W.D., Zhou, G.Z., Yang, S.L.: An approach to group decision making based on 2-dimension linguistic assessment information. Syst. Eng. 27, 113–118 (2009)

    Google Scholar 

  24. Verma, R., Merigó, J.M.: Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators. Soft Comput. 1–24 (2020).

  25. Sun, Y., Zhang Q., Li, Z., Ren, Y., Zhang, Y., Yuan, Z.: Multi-attribute group decision making method based on 2-dimension 2-tuple linguistic information. In: 2020 IEEE International Conference on Artificial Intelligence and Information Systems (ICAIIS), IEEE, 2020, pp. 44–48.

  26. Liu, Y., Wang, X.-K., Wang, J.-Q., Li, L., Cheng, P.-F.: Cloud model-based PROMETHEE method under 2D uncertain linguistic environment, J. Intell. Fuzzy Syst. 1–19 (2020).

  27. Liu, P.D.: An approach to group decision making based on 2-dimension uncertain linguistic information. Technol. Econ. Dev. Econ. 18, 424–437 (2012)

    Google Scholar 

  28. Yu, X.H., Xu, Z.S., Liu, S.S., Chen, Q.: Multicriteria decision making with 2-dimension linguistic aggregation techniques. Int. J. Intell. Syst. 27, 539–562 (2012)

    Google Scholar 

  29. Liu, P.D., Yu, X.C.: 2-Dimension uncertain linguistic power generalized weighted aggregation operator and its application in multiple attribute group decision making. Knowl. Based Syst. 57, 69–80 (2014)

    Google Scholar 

  30. Zhu, H., Zhao, J.B., Xu, Y.: 2-Dimension linguistic computational model with 2-tuples for multi-attribute group decision making. Knowl. Based Syst. 103, 132–142 (2016)

    Google Scholar 

  31. Wu, Y.N., Sun, X.K., Lu, Z.M., Zhou, J.L., Xu, C.B.: Optimal site selection of straw biomass power plant under 2-dimension uncertain linguistic environment. J. Clean Prod. 212, 1179–1192 (2019)

    Google Scholar 

  32. Wu, Y.N., Xu, C.B., Li, L.W., Wang, Y., Chen, K.F., Xu, R.H.: A risk assessment framework of PPP waste-to-energy incineration projects in China under 2-dimension linguistic environment. J. Clean Prod. 183, 602–617 (2018)

    Google Scholar 

  33. Wang, Z.L., Rodríguez, R.M., Wang, Y.-M., Martínez, L.: A two-stage minimum adjustment consensus model for large scale decision making based on reliability modeled by two-dimension 2-tuple linguistic information. Comput. Ind. Eng. (2020). https://doi.org/10.1016/j.cie.2020.106973

    Article  Google Scholar 

  34. Zhao, J., Zhu, H., Li, H.: 2-Dimension linguistic PROMETHEE methods for multiple attribute decision making. Expert Syst. Appl. 127, 97–108 (2019)

    Google Scholar 

  35. Liu, H.-C., Hu, Y.-P., Wang, J.-J., Sun, M.: Failure mode and effects analysis using two-dimensional uncertain linguistic variables and alternative queuing method. IEEE Trans. Reliab. 68, 554–565 (2018)

    Google Scholar 

  36. Ding, X.-F., Liu, H.-C.: A 2-dimension uncertain linguistic DEMATEL method for identifying critical success factors in emergency management. Appl. Soft Comput. 71, 386–395 (2018)

    Google Scholar 

  37. Liu, P.D., Qi, X.F.: Some generalized dependent aggregation operators with 2-dimension linguistic information and their application to group decision making. J. Intell. Fuzzy Syst. 27, 1761–1773 (2014)

    MathSciNet  MATH  Google Scholar 

  38. J. Zhao, H. Zhu, H. Li, 2-dimension linguistic PROMETHEE methods for multiple attribute decision making. Expert Syst. Appl. (2019).

  39. Van den Honert, R.: Stochastic group preference modelling in the multiplicative AHP: a model of group consensus. Eur. J. Oper. Res. 110, 99–111 (1998)

    MATH  Google Scholar 

  40. Ramanathan, R.: Stochastic decision making using multiplicative AHP. Eur. J. Oper. Res. 97, 543–549 (1997)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  42. Ross, S.M.: Introduction to Probability Models. Academic Press, New York (2014)

    MATH  Google Scholar 

  43. Bertsimas, D., Freund, R.M.: Data, Models, and Decisions: The Fundamentals of Management Science. South-Western College Press, Cambridge (2002)

    Google Scholar 

  44. Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22, 79–86 (1951)

    MathSciNet  MATH  Google Scholar 

  45. Lin, J.H.: Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 37, 145–151 (1991)

    MathSciNet  MATH  Google Scholar 

  46. Fenton, N., Wang, W.: Risk and confidence analysis for fuzzy multicriteria decision making. Knowl. Based Syst. 19, 430–437 (2006)

    Google Scholar 

  47. Fu, C., Yang, J.B., Yang, S.L.: A group evidential reasoning approach based on expert reliability. Eur. J. Oper. Res. 246, 886–893 (2015)

    MathSciNet  MATH  Google Scholar 

  48. Guha, D., Chakraborty, D.: Fuzzy multi attribute group decision making method to achieve consensus under the consideration of degrees of confidence of experts’ opinions. Comput. Ind. Eng. 60, 493–504 (2011)

    Google Scholar 

  49. Liu, W.Q., Zhang, H.J., Chen, X., Yu, S.: Managing consensus and self-confidence in multiplicative preference relations in group decision making. Knowl. Based Syst. 162, 62–73 (2018)

    Google Scholar 

  50. Ureña, R., Chiclana, F., Fujita, H., Herrera-Viedma, E.: Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations. Knowl. Based Syst. 89, 86–96 (2015)

    Google Scholar 

  51. Liu, P.D., Teng, F.: An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic variable. Complexity 21, 20–30 (2016)

    MathSciNet  Google Scholar 

Download references

Funding

The work is supported by the National Nature Science Foundation of China (Grant No. 61773123) and by the Spanish National Research Project PGC2018-099402-B-I00.

Author information

Authors and Affiliations

  1. Decision Sciences Institute, Fuzhou University, Fujian, 350116, China

    Zelin Wang & Ying-Ming Wang

  2. Key Laboratory of Spatial Data Mining and Information Sharing of Ministry of Education, Fuzhou University, Fujian, 350116, China

    Ying-Ming Wang

  3. Department of Computer Sciences, University of Jaén, 23071, Jaén, Spain

    Luis Martínez

Authors
  1. Zelin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying-Ming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying-Ming Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Wang, YM. & Martínez, L. A Stochastic Perspective on a Group Decision-Making Method Based on Two-Dimension 2-Tuple Linguistic Information. Int. J. Fuzzy Syst. 24, 1425–1445 (2022). https://doi.org/10.1007/s40815-021-01199-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01199-3

Keywords

Search

Navigation