Skip to main content
SpringerLink
Log in

Method of Multiple Attribute Group Decision Making Based on 2-Dimension Interval Type-2 Fuzzy Aggregation Operators with Multi-granularity Linguistic Information

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

Abstract

This paper proposes an approach to linguistic multiple attribute group decision-making (MAGDM) problems with 2-dimension multi-granularity linguistic information by adding a subjective imprecise estimation of reliability of the linguistic assessment information for expressing fuzzy information appropriately. To avoid the drawback of traditional transformation functions of multi-granularity linguistic information (MGLI) defined in the basic linguistic term set or 2-tuple linguistic information, in this paper, decision information is fully expressed by using 2-dimension interval type-2 trapezoidal fuzzy number (2DIT2TFN) representation model under multi-granular linguistic contexts. Firstly, the definition, operational laws, and ranking method of 2DIT2TFNs are proposed. Then 2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (2DIT2TFOWA) operator and quasi-2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (quasi-2DIT2TFOWA) operator are put forward. Moreover, we apply new operators to developing approach to MAGDM problem with linguistic term set of different odd cardinalities. Finally, a numerical example related to health management is provided to illustrate the utility and effectiveness of the developed method. We also make comparisons between the methods proposed in this paper and some existing ones to confirm its feasibility and rationality. The main contribution of this paper possesses three points: (1) proposing the 2DIT2TFNs, which can reflect the evaluation on objects more reasonably; (2) developing some new aggregation operators under 2-dimension interval type-2 trapezoidal fuzzy environment; and (3) applying new operators to developing approach to MAGDM problem with MGLI.

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

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)

    Article  MathSciNet  MATH  Google Scholar 

  2. Parreiras, R.O., Ekel, P.Y., Martini, J.S.C., Palhares, R.M.: A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Inf. Sci. 180, 1075–1089 (2010)

    Article  Google Scholar 

  3. Herrera, F., Herrera-Viedma, E.: Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst. 115, 67–82 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst. 97, 33–48 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Xu, Z.S.: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf. Sci. 168, 171–184 (2004)

    Article  MATH  Google Scholar 

  7. Merigó, J.M., Casanovas, M., Palacios-Marqués, D.: Linguistic group decision making with induced aggregation operators and probabilistic information. Appl. Soft Comput. 24, 669–678 (2014)

    Article  Google Scholar 

  8. Xu, Z.S.: An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decis. Support Syst. 41, 488–499 (2006)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Herrera, F., Herrera-Viedma, E., Martínez, L.: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans. Fuzzy Syst. 16, 354–370 (2008)

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Jiang, Y.P., Fan, Z.P., Ma, J.: A method for group decision making with multi-granularity linguistic assessment information. Inf. Sci. 178, 1098–1109 (2008)

    Article  MATH  Google Scholar 

  18. Morente-Molinera, J.A., Pérez, I.J., Ureña, M.R., Herrera-Viedma, E.: On multi-granular fuzzy linguistic modeling in group decision making problems: a systematic review and future trends. Knowl.-Based Syst. 74, 49–60 (2015)

    Article  MATH  Google Scholar 

  19. Liu, S., Chan, F.T.S., Ran, W.X.: Multi-attribute group decision-making with multi-granularity linguistic assessment information: an improved approach based on deviation and TOPSIS. Appl. Math. Model. 37, 10129–10140 (2013)

    Article  MathSciNet  Google Scholar 

  20. Fan, Z.P., Liu, Y.: A method for group decision-making based on multi-granularity uncertain linguistic information. Expert Syst. Appl. 37, 4000–4008 (2010)

    Article  Google Scholar 

  21. Wu, D., Mendel, J.M., Coupland, S.: Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis. IEEE Trans. Fuzzy Syst. 20, 499–513 (2012)

    Article  Google Scholar 

  22. Wu, D., Mendel, J.M.: Enhanced Karnik–Mendel algorithms. IEEE Trans. Fuzzy Syst. 17, 923–934 (2009)

    Article  Google Scholar 

  23. Liu, F.L., Mendel, J.M.: Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans. Fuzzy Syst. 16, 1503–1521 (2008)

    Article  Google Scholar 

  24. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 808–821 (2006)

    Article  Google Scholar 

  25. Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput. Intell. Mag. 2, 20–29 (2007)

    Google Scholar 

  26. Chen, T.Y.: A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set. Know. Inf. Syst. 35, 193–231 (2013)

    Article  Google Scholar 

  27. Qin, J.D., Liu, X.W., Pedrycz, W.: An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment. Know.-Based Syst. 86, 116–130 (2015)

    Article  Google Scholar 

  28. Chen, S.M., Lee, L.W.: Fuzzy multiple criteria hierarchical group decision-making based on interval type-2 fuzzy sets. IEEE Trans. Syst. Man Cybern. 40, 1120–1128 (2010)

    Article  Google Scholar 

  29. Abdullah, L., Najib, L.: A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process. Expert Syst. Appl. 41, 3297–3305 (2014)

    Article  Google Scholar 

  30. Sari, I.U., Kahraman, C.: Interval type-2 fuzzy capital budgeting. Int. J. Fuzzy Syst. 17, 635–646 (2015)

    Article  MathSciNet  Google Scholar 

  31. Chen, S.M., Lee, L.W.: Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method. Expert Syst. Appl. 37, 2790–2798 (2010)

    Article  Google Scholar 

  32. Chen, T.Y.: A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets. Soft. Comput. 18, 923–940 (2014)

    Article  MATH  Google Scholar 

  33. Chen, T.Y.: An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets. Inf. Sci. 263, 1–21 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chen, T.Y.: A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets. Appl. Soft Comput. 13, 2735–2748 (2013)

    Article  Google Scholar 

  35. Ma, X.Y., Wu, P., Zhou, L.G., Chen, H.Y., Zheng, T., Ge, J.Q.: Approaches based on interval type-2 fuzzy aggregation operators for multiple attribute group decision making. Int. J. Fuzzy Syst. 18, 697–715 (2016)

    Article  MathSciNet  Google Scholar 

  36. Gong, Y.B.: Fuzzy multi-attribute group decision making method based on interval type-2 fuzzy sets and applications to global supplier selection. Int. J. Fuzzy Syst. 15, 392–400 (2013)

    MathSciNet  Google Scholar 

  37. Han, Z.Q., Wang, J.Q., Zhang, H.Y., Liu, X.X.: Group multi-criteria decision making method with triangular type-2 fuzzy numbers. Int. J. Fuzzy Syst. 18, 673–684 (2016)

    Article  MathSciNet  Google Scholar 

  38. 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 

  39. 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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  41. 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)

    Article  Google Scholar 

  42. Dong, Y.C., Xu, Y.F., Li, H.Y., Feng, B.: The OWA-based consensus operator under linguistic representation models using position indexes. Eur. J. Oper. Res. 203, 455–463 (2010)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  44. Zhou, L.G., Chen, H.Y.: The induced linguistic continuous ordered weighted geometric operator and its application to group decision making. Comput. Ind. Eng. 66, 222–232 (2013)

    Article  Google Scholar 

  45. Meng, D., Pei, Z.: On weighted unbalanced linguistic aggregation operators in group decision making. Inf. Sci. 223, 31–41 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  46. Park, J.H., Park, J.M., Kwun, Y.C.: 2-Tuple linguistic harmonic operators and their applications in group decision making. Knowl.-Based Syst. 44, 10–19 (2013)

    Article  Google Scholar 

  47. 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)

    Article  Google Scholar 

  48. Merigó, J.M., Gil-Lafuente, A.M.: Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf. Sci. 236, 1–16 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  49. Wang, J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information. Int. J. Fuzzy Syst. 18, 81–97 (2016)

    Article  MathSciNet  Google Scholar 

  50. Liu, P.D., Jin, F.: Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Inf. Sci. 205, 58–71 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  51. Liu, P.D.: Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl. Math. Model. 37, 2430–2444 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  52. Meng, F.Y., Chen, X.H., Zhang, Q.: Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making. Appl. Math. Model. 38, 2543–2557 (2014)

    Article  MathSciNet  Google Scholar 

  53. Wang, X.F., Wang, J.Q., Deng, S.Y.: Some geometric operators for aggregating intuitionstic linguistic information. Int. J. Fuzzy Syst. 17, 268–278 (2015)

    Article  MathSciNet  Google Scholar 

  54. Wei, G.W.: Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Int. J. Mach. Learn. Cybern. (2015). doi:10.1007/s13042-015-0433-7

    Google Scholar 

  55. Gou, X.J., Xu, Z.S., Liao, H.C.: Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft. Comput. (2016). doi:10.1007/s00500-016-2211-1

    Google Scholar 

  56. Liu, X.Y., Ju, Y.B., Yang, S.H.: Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making. Soft. Comput. 20, 495–510 (2016)

    Article  MATH  Google Scholar 

  57. Qi, X.W., Liang, C.Y., Zhang, J.L.: Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment. Int. J. Mach. Learn. Cybern. (2015). doi:10.1007/s13042-015-0445-3

    Google Scholar 

  58. Liu, P.D., He, L., Yu, X.C.: Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making. Group Decis. Negot. 25, 103–126 (2016)

    Article  Google Scholar 

  59. Li, Y., Wang, Y.M., Liu, P.D.: Multiple attribute group decision-making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators. Soft. Comput. 20, 2689–2704 (2016)

    Article  MATH  Google Scholar 

  60. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst. 79, 175–190 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  61. Qin, J.D., Liu, X.W.: Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment. Inf. Sci. 297, 293–315 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  62. Wu, D., Mendel, J.M.: Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 15, 1145–1161 (2007)

    Article  Google Scholar 

  63. Havens, T., Keller, J., Popescu, M.: Computing with words with the ontological self-organizing map. IEEE Trans. Fuzzy Syst. 18, 473–485 (2010)

    Article  Google Scholar 

  64. Kacprzyk, J., Zadrozny, S.: Computing with words is an implementable paradigm: fuzzy queries, linguistic data summaries, and natural-language generation. IEEE Trans. Fuzzy Syst. 18, 461–472 (2010)

    Article  Google Scholar 

  65. Lawry, J.: A methodology for computing with words. Int. J. Approx. Reason. 28, 51–89 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  66. Rubin, S.H.: Computing with words. IEEE Trans. Syst. Man Cybern. 29, 518–524 (1999)

    Article  Google Scholar 

  67. Niewiadomski, A.: On finity, countability, cardinalities, and cylindric extensions of type-2 fuzzy sets in linguistic summarization of databases. IEEE Trans. Fuzzy Syst. 18, 532–545 (2010)

    Article  Google Scholar 

  68. Wu, D., Mendel, J.M.: Linguistic summarization using IF–THEN rules and interval type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 19, 136–151 (2011)

    Article  Google Scholar 

  69. Mendel, J.M., Wu, D.: Perceptual Computing: Aiding People in Making Subjective Judgments. IEEE-Wiley Press, Piscataway (2010)

    Book  Google Scholar 

  70. Merigó, J.M., Casanovas, M.: The uncertain induced quasi-arithmetic OWA operator. Int. J. Intell. Syst. 26, 1–24 (2011)

    Article  MATH  Google Scholar 

  71. Liu, X.W.: The orness measure for two compound quasi-arithmetic mean aggregation operators. Int. J. Approx. Reason. 51, 305–334 (2010)

    Article  MATH  Google Scholar 

  72. Tan, C.Q., Jiang, Z.Z., Chen, X.H.: Some issues on quasi-arithmetic intuitionistic fuzzy OWA operators. Appl. Math. Inf. Sci. 7, 955–961 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  73. Xu, Y.J., Da, Q.L.: Trapezoidal fuzzy ordered weighted averaging operator and its application to decision making. J. Southeast Univ. (Nat. Sci. Edit.) 36, 1034–1038 (2006)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  76. 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)

    Article  MathSciNet  Google Scholar 

  77. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)

    Article  MATH  Google Scholar 

  78. Gong, Z.W., Zhang, H.H., Forrest, J., Li, L.S., Xu, X.X.: Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual. Eur. J. Oper. Res. 240, 183–192 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  79. Gong, Z.W., Xu, X.X., Li, L.S., Xu, C.: Consensus modeling with nonlinear utility and cost constraints: a case study. Knowl.-Based Syst. 88, 210–222 (2015)

    Article  Google Scholar 

  80. Gong, Z.W., Xu, X.X., Lu, F.L., Li, L.S., Xu, C.: On consensus models with utility preferences and limited budget. Appl. Soft Comput. 35, 840–849 (2015)

    Article  Google Scholar 

  81. 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)

    Article  Google Scholar 

  82. Gong, Z.W., Forrest, J., Zhao, Y., Yang, Y.J.: The optimal group consensus deviation measure for multiplicative preference relations. Expert Syst. Appl. 39, 11548–11555 (2012)

    Article  Google Scholar 

  83. Dong, Y.C., Zhang, H.J., Herrera-Viedma, E.: Consensus reaching model in the complex and dynamic MAGDM problem. Knowl.-Based Syst. 106, 206–219 (2016)

    Article  Google Scholar 

  84. Cavdur, F., Kose, M.: A fuzzy logic and binary-goal programming-based approach for solving the exam timetabling problem to create a balanced-exam schedule. Int. J. Fuzzy Syst. 18, 119–129 (2016)

    Article  Google Scholar 

  85. Ghaderi, A., Vasegh, N.: Input-output stabilizing controller synthesis for SISO T–S fuzzy systems by applying large gain theorem. Int. J. Fuzzy Syst. 18, 550–556 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable comments and suggestions for improving the paper. The work was supported by National Natural Science Foundation of China (Nos. 71301001, 71371011, 71501002, 71272047), Project of Anhui Province for Excellent Young Talents, the Doctoral Scientific Research Foundation of Anhui University, and Anhui provincial philosophy and social science program.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Qun Wu, Feng Wang, Ligang Zhou & Huayou Chen

  2. China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Ligang Zhou

Authors
  1. Qun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ligang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Huayou Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ligang Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, Q., Wang, F., Zhou, L. et al. Method of Multiple Attribute Group Decision Making Based on 2-Dimension Interval Type-2 Fuzzy Aggregation Operators with Multi-granularity Linguistic Information. Int. J. Fuzzy Syst. 19, 1880–1903 (2017). https://doi.org/10.1007/s40815-016-0291-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0291-9

Keywords

Search

Navigation