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Group decision making with compatibility measures of hesitant fuzzy linguistic preference relations

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Abstract

Compatibility measure is a very well-known method to deal with decision making problems with uncertain preference relations. In this paper, on the basis of generalized distance measure of hesitant fuzzy linguistic elements, we define the compatibility measures for hesitant fuzzy linguistic preference relations (HFLPRs), including compatibility degree, compatibility index, and acceptable compatibility, and some important special properties are also discussed. Furthermore, based on the compatibility measures of HFLPRs, we propose a method for determining the experts’ weights in group decision making (GDM), as well as establish an algorithm for solving the GDM problem with HFLPRs. A case study is set up to utilize the compatibility measures of HFLPRs for dealing with a practical GDM problem, which is to determine which aspect is optimal in the process of medical and health system reform. Finally, some comparisons and analyses are also discussed in detail.

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References

  • Chen HY, Gang L, Han B (2011a) On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowl Based Syst 24:816–823

    Article  Google Scholar 

  • Chen TY, Wang HP, Lu YY (2011b) A multi criteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst Appl 38(6):7647–7658

    Article  Google Scholar 

  • Gou XJ, Xu ZS (2016) Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci 372:407–427

    Article  Google Scholar 

  • Gou XJ, Xu ZS, Liao HC (2016) Multi-criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput. doi:10.1007/s00500-016-2211-1

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Herrera-Viedma E, Alonso S, Chiclana F, Herrera F (2007) A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans Fuzzy Syst 15(5):863–877

    Article  MATH  Google Scholar 

  • Jiang Y, Xu ZS, Yu XH (2013) Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations. Appl Soft Comput 13(4):2075–2086

    Article  Google Scholar 

  • Lee LW, Chen SM (2014) A new group decision making method based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets. In: IEEE international conference on systems, man, and cybernetics, pp 790–795

  • Li CC, Dong YC, Herrera F, Herrera-Viedma E, Martínez L (2017) Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching. Inf Fusion 33:29–40

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl Based Syst 76:127–138

    Article  Google Scholar 

  • Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2016) A model based on subjective linguistic preference relations for group decision making problems. Inf Sci 355–356:249–264

    Article  Google Scholar 

  • Naamani-Dery L, Kalech M, Rokach L, Shapira B (2016) Reducing preference elicitation in group decision making. Expert Syst Appl 61:246–261

    Article  MATH  Google Scholar 

  • Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci. doi:10.1016/j.ins.2016.06.021

    Article  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans Fuzzy Syst 20:109–119

    Article  Google Scholar 

  • Rodríguez RM, Martınez L, Herrera F (2013) A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf Sci 241(12):28–42

    Article  MathSciNet  MATH  Google Scholar 

  • Saaty TL, Vargas LG (2007) Dispersion of group judgments. Math Comput Modell 46:918–925

    Article  MathSciNet  MATH  Google Scholar 

  • Tao ZF, Liu X, Chen HY, Chen ZQ (2015) Group decision making with fuzzy linguistic preference relations via cooperative games method. Comput Ind Eng 83:184–192

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wang H (2015) Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int J Comput Intell Syst 8(1):14–33

    Article  Google Scholar 

  • Wang H, Xu ZS (2015) Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf Sci 297:316–331

    Article  MathSciNet  MATH  Google Scholar 

  • Wang H, Xu ZS (2016) Interactive algorithms for improving incomplete linguistic preference relations based on consistency measures. Appl Soft Comput 42(C):66–79

    Article  Google Scholar 

  • Wu ZB (2015) A consensus process for hesitant fuzzy linguistic preference relations. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), Istanbul, Turkey, pp 1–7

  • Wu ZB, Xu JP (2012) A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis Support Syst 52(3):757–767

    Article  Google Scholar 

  • Wu ZB, Xu JP (2016) Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65:28–40

    Article  Google Scholar 

  • Xu ZS (2004a) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184

    Article  MATH  Google Scholar 

  • Xu ZS (2004b) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166(1–4):19–30

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS (2005) Deviation measures of linguistic preference relations in group decision making. Omega Int J Manag 33:249–254

    Article  Google Scholar 

  • Xu ZS (2012a) A consensus reaching process under incomplete multiplicative preference relations. Int J Gen Syst 41(4):1–19

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS (2012b) Linguistic decision making. Theory and methods. Springer, Berlin

    Book  MATH  Google Scholar 

  • Xu YJ, Wang HM (2012) The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making. Appl Soft Comput 12(3):1168–1179

    Article  Google Scholar 

  • Xu ZS, Xia MM (2014) Iterative algorithms for improving consistency of intuitionistic preference relations. J Oper Res Soc 65(5):708–722

    Article  Google Scholar 

  • Xu YJ, Da QL, Liu XW (2010) Some properties of linguistic preference relation and its ranking in group decision making. J Syst Eng Electron 21(2):244–249

    Article  Google Scholar 

  • Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int J Intell Syst 26(9):787–813

    Article  Google Scholar 

  • Yu DJ (2015) Archimedean aggregation operators based on dual hesitant fuzzy set and their application to GDM. Int J Uncertain Fuzziness Knowl Based Syst 23(5):761–780

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its applications to approximate reasoning-part I. Inf Sci 8:199–249

    Article  MATH  Google Scholar 

  • Zeng SZ, Baležentis A, Weihua SU (2013) The multi-criteria hesitant fuzzy group decision making with MULTIMOORA method. Econ Comput Econ Cybern Stud Res 47(3):171–184

    Google Scholar 

  • Zhang ZM (2016) Hesitant fuzzy multi-criteria group decision making with unknown weight information. Int J Fuzzy Syst. doi:10.1007/s40815-016-0190-0

    Article  Google Scholar 

  • Zhang ZM, Wu C (2014) On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl Based Syst 72:13–27

    Article  Google Scholar 

  • Zhou LG, Chen HY (2013) On compatibility of uncertain additive linguistic preference relations based on the linguistic COWA operator. Appl Soft Comput 13(8):3668–3682

    Article  Google Scholar 

  • Zhou W, Xu ZS (2015) Optimal discrete fitting aggregation approach with hesitant fuzzy information. Knowl Based Syst 78:22–23

    Article  Google Scholar 

  • Zhou W, Xu ZS (2016a) Asymmetric fuzzy preference relations based on the generalized sigmoid scale and their application in decision making involving risk appetites. IEEE Trans Fuzzy Syst 24(3):741–756

    Article  MathSciNet  Google Scholar 

  • Zhou W, Xu ZS (2016b) Asymmetric hesitant fuzzy sigmoid preference relations in the analytic hierarchy process. Inf Sci 358–359:191–207

    Article  Google Scholar 

  • Zhou W, Xu ZS, Chen MH (2015a) Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Comput Ind Eng 87:163–175

    Article  Google Scholar 

  • Zhou LG, Zhou YY, Liu X, Chen HY (2015b) Some ILOWA operators and their applications to group decision making with additive linguistic preference relations. J Intell Fuzzy Syst 29(2):831–843

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou YY, Cheng LH, Zhou LG, Chen HY, Ge JQ (2015c) A group decision making approach for trapezoidal fuzzy preference relations with compatibility measure. Soft Comput. doi:10.1007/s00500-015-1975-z

  • Zhou LG, Merigó JM, Chen HY, Liu JP (2016) The optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the COWGA operator. Inf Sci 328:250–269

    Article  MATH  Google Scholar 

  • Zhu B, Xu ZS (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22(1):35–45

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgements

This study was funded by National Natural Science Foundation of China (Nos. 71571123, 71501135, 71171156) and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, China

    Xunjie Gou, Zeshui Xu & Huchang Liao

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  1. Xunjie Gou
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  2. Zeshui Xu
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  3. Huchang Liao
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Correspondence to Zeshui Xu.

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

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Communicated by V. Loia.

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Gou, X., Xu, Z. & Liao, H. Group decision making with compatibility measures of hesitant fuzzy linguistic preference relations. Soft Comput 23, 1511–1527 (2019). https://doi.org/10.1007/s00500-017-2871-5

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