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International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 958–969 | Cite as

On Novel Operational Laws and Aggregation Operators of Picture 2-Tuple Linguistic Information for MCDM Problems

  • Xue-yang Zhang
  • Jian-qiang WangEmail author
  • Jun-hua Hu
Article

Abstract

This paper primarily focuses on multi-criteria decision-making (MCDM) based on picture 2-tuple linguistic information. Since the picture 2-tuple linguistic set is structured by a linguistic 2-tuple and a picture fuzzy set, we first point out the inappropriateness of existing operations relating to picture fuzzy numbers and picture 2-tuple linguistic numbers. For the purpose of improving these misleading computations, we further propose novel operational laws for picture 2-tuple linguistic numbers from a correct version. Counterexamples, which are in one-to-one correspondence with the listed counterintuitive cases, are furnished to illustrate the limitations of existing operations and prove the feasibility of our newly presented operations. Moreover, by applying the novel operations, we put forward some modified aggregation operators which are further employed to a handling method for the MCDM problem with a picture 2-tuple linguistic matrix. Finally, two comparative and illustrative examples are furnished to verify the applicability and advantages of the proposed method.

Keywords

Picture 2-tuple linguistic set Inappropriateness Novel operational laws Multi-criteria decision-making Modified aggregation operator 

Notes

Acknowledgements

The authors would like to sincerely thank the editors and three anonymous reviewers for their constructive and valuable suggestions. This work was supported by the National Natural Science Foundation of China (No. 71571193).

Compliance with Ethical Standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

  1. 1.
    Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)CrossRefGoogle Scholar
  2. 2.
    Xu, Z.S.: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf. Sci. 168(1–4), 171–184 (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Zhang, X., Wang, J., Zhang, H., Hu, J.: A heterogeneous linguistic MAGDM framework to classroom teaching quality evaluation. EURASIA J. Math. Sci. Technol. Educ. 13(8), 4929–4956 (2017)CrossRefGoogle Scholar
  4. 4.
    Lin, J., Lan, J.B., Lin, Y.H.: Multi-attribute group decision-making method based on the aggregation operators of interval 2-tuple linguistic information. J. Jilin Norm. Univ. 1, 5–9 (2009)Google Scholar
  5. 5.
    Herrera, F., Herrera-Viedma, E., Martínez, L.: A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst. 114, 43–58 (2000)CrossRefzbMATHGoogle Scholar
  6. 6.
    Zhang, X.Y., Zhang, H.Y., Wang, J.Q.: Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information. Soft. Comput. (2017).  https://doi.org/10.1007/s00500-00017-02915-x Google Scholar
  7. 7.
    Rodríguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)CrossRefGoogle Scholar
  8. 8.
    Zhang, X.Y., Wang, J.Q., Hu, J.H.: A consensus approach to multi-granular linguistic MCGDM with hesitant fuzzy linguistic information by using projection. J. Intell. Fuzzy Syst. (2017).  https://doi.org/10.3233/JIFS-171629 Google Scholar
  9. 9.
    Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9, 613–626 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Meng, F.Y., Tan, C.Q., Chen, X.H.: Multiplicative consistency analysis for interval fuzzy preference relations: a comparative study. Omega 68, 17–38 (2017)CrossRefGoogle Scholar
  11. 11.
    Chen, S.M., Cheng, S.H., Chiou, C.H.: Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf. Fusion 27, 215–227 (2016)CrossRefGoogle Scholar
  12. 12.
    Wang, Z.J., Li, K.W., Xu, J.H.: A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information. Exp. Syst. Appl. 38(10), 12462–12469 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wang, J.Q., Li, H.B.: Multi-criteria decision-making method based on aggregation operators for intuitionistic linguistic fuzzy numbers. Control Decis. 25(10), 1571–1574 (2010)MathSciNetGoogle Scholar
  14. 14.
    Yu, S.M., Wang, J., Wang, J.Q.: An extended TODIM approach with intuitionistic linguistic numbers. Int. Trans. Oper. Res. (2016).  https://doi.org/10.1111/itor.12363 Google Scholar
  15. 15.
    Zhou, W., Xu, Z.S., Chen, M.H.: Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Comput. Ind. Eng. 87, 163–175 (2015)CrossRefGoogle Scholar
  16. 16.
    Yao, D., Wang, C.: Hesitant intuitionistic fuzzy entropy/cross-entropy and their applications. Soft. Comput. (2017).  https://doi.org/10.1007/s00500-017-2753-x Google Scholar
  17. 17.
    Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A.: Picture 2-tuple linguistic aggregation operators in multiple attribute decision making. Soft. Comput. (2016).  https://doi.org/10.1007/s00500-00016-02403-00508 zbMATHGoogle Scholar
  18. 18.
    Wei, G.W.: Picture 2-tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making. Int. J. Fuzzy Syst. 19(4), 997–1010 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Cuong B.C., Kreinovich V.: Picture fuzzy sets-a new concept for computational intelligence problems. In: Third World Congress on Information and Communication Technologies, Hanoi (2013)Google Scholar
  20. 20.
    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. 20, 1–18 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Rodríguez, R.M., Martínez, L.: An analysis of symbolic linguistic computing models in decision making. Int. J. Gen Syst 42(1), 121–136 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefzbMATHGoogle Scholar
  23. 23.
    Wang, J.Q., Han, Z.Q., Zhang, H.Y.: Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decis. Negot. 23(4), 715–733 (2014)CrossRefGoogle Scholar
  24. 24.
    Zhang, H.Y., Peng, H.G., Wang, J., Wang, J.Q.: An extended outranking approach for multi-criteria decision-making problems with linguistic intuitionistic fuzzy numbers. Appl. Soft Comput. 59, 462–474 (2017)CrossRefGoogle Scholar
  25. 25.
    Tian, Z.P., Wang, J., Wang, J.Q., Zhang, H.Y.: Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis. Negot. 26(3), 597–627 (2017)CrossRefGoogle Scholar
  26. 26.
    Liang, R.X., Wang, J.Q., Zhang, H.Y.: A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput. Appl. (2017).  https://doi.org/10.1007/s00521-017-2925-8 Google Scholar
  27. 27.
    Wang, J., Wang, J.Q., Tian, Z.P., Zhao, D.Y.: A multihesitant fuzzy linguistic multicriteria decision-making approach for logistics outsourcing with incomplete weight information. Int. Trans. Oper. Res. (2017).  https://doi.org/10.1111/itor.12448 Google Scholar
  28. 28.
    Zhou, H., Wang, J.Q., Zhang, H.Y.: Stochastic multicriteria decision-making approach based on SMAA-ELECTRE with extended gray numbers. Int. Trans. Oper. Res. (2017).  https://doi.org/10.1111/itor.12380 Google Scholar
  29. 29.
    Wang, J.Q., Peng, J.J., Zhang, H.Y., Liu, T., Chen, X.H.: An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis. Negot. 24(1), 171–192 (2015)CrossRefGoogle Scholar
  30. 30.
    Hu, J.H., Yang, Y., Zhang, X.L., Chen, X.H.: Similarity and entropy measures for hesitant fuzzy sets. Int. Trans. Oper. Res. (2017).  https://doi.org/10.1111/itor.12477 Google Scholar
  31. 31.
    Wan, S.P.: 2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making. Knowl. Based Syst. 45, 31–40 (2013)CrossRefGoogle Scholar
  32. 32.
    Zhang, H.M.: Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making. Appl. Math. Model. 37(6), 4269–4282 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Xu, Z.S.: Linguistic Aggregation Operators: An Overview. Fuzzy Sets and Their Extensions: Representation, Agrgegation and Models, pp. 163–181. Springer, Berlin (2008)Google Scholar
  34. 34.
    Tian, Z.P., Wang, J., Wang, J.Q., Chen, X.H.: Multicriteria decision-making approach based on gray linguistic weighted Bonferroni mean operator. Int. Trans. Oper. Res. (2015).  https://doi.org/10.1111/itor.12220 Google Scholar
  35. 35.
    Wang C.Y.: Hesitant fuzzy set and picture fuzzy set with their application research, Hunan University: Doctoral dissertation (2015)Google Scholar
  36. 36.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Yager, R.R., Filev, D.P.: Induced ordered weighted averaging operators. IEEE Trans. Syst. Man Cybern. Part B Cybern. 29(2), 141–150 (1999)CrossRefGoogle Scholar
  38. 38.
    Chiclana F., Herrera F., Herrera-Viedma E.: The ordered weighted geometric operator: Properties and application in MCDM problems. In: Proceeding of 8th International Conferrence on Information Processing and Management of Uncertainty in Knowledge based Systems, pp. 985–991 (2000)Google Scholar
  39. 39.
    Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations. Int. J. Intell. Syst. 19(3), 233–255 (2004)CrossRefzbMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaPeople’s Republic of China

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