Skip to main content

Advertisement

Springer Nature Link
Log in

Deriving priority weights from hesitant fuzzy preference relations in view of additive consistency and consensus

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Given that deriving priority weights is essential in group decision making, this study focuses on deriving priority weights from hesitant fuzzy preference relation (HFPR) in view of additive consistency and consensus. To achieve this goal, first, a new additive consistency concept of the HFPR is proposed. The main feature of the proposed additive consistency concept is that it considers all evaluation information provided by decision makers, that is, neither add values into nor remove values from hesitant fuzzy elements. Second, a programming model is constructed to verify the complete additive consistency of HFPR, an additive consistency index is suggested to validate its consistency degree, and then, a programming model is established to improve its consistency degree. Third, an algorithm is designed to derive a priority weight vector from the HFPR, and the proposed algorithm not only addresses the situation in which the HFPR is a complete and acceptable additive consistency. Fourth, a programming model is presented to determine the decision makers’ weights, and then, a consensus measure index based on extraction priority weight vectors is introduced. Moreover, a programming model is constructed to derive the priority weights that correspond to expected consensus levels. Finally, the most cost-effective car selection problems are provided to illustrate the effectiveness of the proposed method. Comparative studies with several existing methods are also provided.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Dong YC, Xu JP (2016) Consensus building in group decision making-searching the consensus path with minimum adjustments. Springer, Berlin

    Google Scholar 

  • Dong YC, Xu YF, Li HY (2008) On consistency measures of linguistic preference relations. Eur J Oper Res 189(2):430–444

    MathSciNet  MATH  Google Scholar 

  • Dong YC, Xu YF, Li HY, Feng B (2010) The OWA-based consensus operator under linguistic representation models using position indexes. Eur J Oper Res 203(2):455–463

    MATH  Google Scholar 

  • Dong YC, Li CC, Chiclana F, Herrera-Viedma E (2016) Average-case consistency measurement and analysis of interval-valued reciprocal preference relations. Knowl-Based Syst 114:108–117

    Google Scholar 

  • Dong YC, Zha QB, Zhang HJ, Kou G, Fujita H, Chiclana F, Herrera-Viedma E (2018a) Consensus reaching in social network group decision making: research paradigms and challenges. Knowl-Based Syst 162:3–13

    Google Scholar 

  • Dong YC, Zhan M, Kou G, Ding ZG, Liang HM (2018b) A survey on the fusion process in opinion dynamics. Inf Fus 43:57–65

    Google Scholar 

  • He Y, Xu ZS (2017) A consensus reaching model for hesitant information with different preference structures. Knowl-Based Syst 135:99–112

    Google Scholar 

  • He Y, Xu ZS, Gu J (2016) An approach to group decision making with hesitant information and its application in credit risk evaluation of enterprises. Appl Soft Comput 43:159–169

    Google Scholar 

  • Herrera-Viedma E, Cabrerizo FJ, Kacprzyk J, Pedrycz W (2014) A review of soft consensus models in a fuzzy environment. Inf Fus 17(1):4–13

    Google Scholar 

  • Li J, Wang JQ (2018a) Multi-criteria decision making with probabilistic hesitant fuzzy information based on expected multiplicative consistency. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3753-1

    Article  Google Scholar 

  • Li J, Wang ZX (2018b) Consensus building for probabilistic hesitant fuzzy preference relations with expected additive consistency. Int J Fuzzy Syst 20(5):1495–1510

    MathSciNet  Google Scholar 

  • Li Y, Zhang HJ, Dong YC (2017) The interactive consensus reaching process with the minimum and uncertain cost in group decision making. Appl Soft Comput 60(Supplement C):202–212

    Google Scholar 

  • Li CC, Rodríguez RM, Herrera F, Martínez L, Dong YC (2018a) Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. Inf Sci 432:361–437

    MathSciNet  Google Scholar 

  • Li CC, Rodríguez RM, Martínez L, Dong YC, Herrera F (2018b) Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions. Knowl-Based Syst 145:156–165

    Google Scholar 

  • Li CC, Dong YC, Herrera F (2019a) A consensus model for large-scale linguistic group decision making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups. IEEE Trans Fuzzy Syst. 27(2):221–233

    Google Scholar 

  • Li J, Wang JQ, Hu JH (2019b) Consensus building for hesitant fuzzy preference relations with multiplicative consistency. Comput Ind Eng 128:387–400

    Google Scholar 

  • Liu HF, Xu ZS, Liao HC (2016) The multiplicative consistency index of hesitant fuzzy preference relation. IEEE Trans Fuzzy Syst 24(1):82–93

    Google Scholar 

  • Luo SZ, Zhang HY, Wang JQ, Li L (2018) Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J Oper Res Soc. https://doi.org/10.1080/01605682.2018.1510806

    Article  Google Scholar 

  • Meng FY, An QX (2017) A new approach for group decision making method with hesitant fuzzy preference relations. Knowl-Based Syst 127(Supplement C):1–15

    Google Scholar 

  • Tang J, An QX, Meng FY, Chen XH (2017) A natural method for ranking objects from hesitant fuzzy preference relations. Int J Inf Technol Decis Making 16(6):1611–1646

    Google Scholar 

  • Thuong NTH, Zhang RC, Li ZM, Hong PTD (2018) Multi-criteria evaluation of financial statement quality based on hesitant fuzzy judgments with assessing attitude. Int J Manag Sci Eng Manag 13(4):254–264

    Google Scholar 

  • Tian ZP, Nie RX, Wang JQ, Zhang HY (2018a) A two-fold feedback mechanism to support consensus-reaching in social network group decision-making. Knowl-Based Syst 162:74–91

    Google Scholar 

  • Tian ZP, Wang JQ, Zhang HY, Wang TL (2018b) Signed distance-based consensus in multi-criteria group decision-making with multi-granular hesitant unbalanced linguistic information. Comput Ind Eng 124:125–138

    Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Ureña R, Kou G, Dong YC, Chiclana F, Herrera-Viedma E (2019) A review on trust propagation and opinion dynamics in social networks and group decision making frameworks. Inf Sci 478:461–475

    Google Scholar 

  • Wu ZB, Xu JP (2012) A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures. Fuzzy Sets Syst 206(11):58–73

    MathSciNet  MATH  Google Scholar 

  • Wu J, Dai LF, Chiclana F, Fujita H, Herrera-Viedma E (2018a) A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Inf Fus 41:232–242

    Google Scholar 

  • Wu YZ, Li CC, Chen X, Dong YC (2018b) Group decision making based on linguistic distributions and hesitant assessments: maximizing the support degree with an accuracy constraint. Inf Fus 41(Supplement C):151–160

    Google Scholar 

  • Wu ZB, Jin BM, Xu JP (2018c) Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations. Appl Soft Comput 67:691–705

    Google Scholar 

  • Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407

    MathSciNet  MATH  Google Scholar 

  • Xia MM, Xu ZS (2013) Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations. Int J Uncertain, Fuzziness Knowl-Based Syst 21(06):865–897

    MathSciNet  MATH  Google Scholar 

  • Xu YJ, Chen L, Rodríguez RM, Herrera F, Wang HM (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowl-Based Syst 99(Supplement C):71–78

    Google Scholar 

  • Xu YJ, Cabrerizo FJ, Herrera-Viedma E (2017) A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Appl Soft Comput 58(Supplement C):265–284

    Google Scholar 

  • Xu JP, Xu K, Wu ZB (2019) A consistency reaching approach for probability-interval valued hesitant fuzzy preference relations. J Comput Anal Appl 27(4):636–655

    Google Scholar 

  • Zhang GQ, Dong YC, Xu YF (2012) Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations. Expert Syst Appl 39(3):2415–2420

    Google Scholar 

  • Zhang ZM, Wang C, Tian XD (2015) A decision support model for group decision making with hesitant fuzzy preference relations. Knowl-Based Syst 86:77–101

    Google Scholar 

  • Zhang HJ, Dong YC, Herrera-Viedma E (2018a) Consensus building for the heterogeneous large-scale GDM with the individual concerns and satisfactions. IEEE Trans Fuzzy Syst 26(2):884–898

    Google Scholar 

  • Zhang XY, Wang XK, Yu SM, Wang JQ, Wang TL (2018b) Location selection of offshore wind power station by consensus decision framework using picture fuzzy modelling. J Clean Prod 202:980–992

    Google Scholar 

  • Zhang Z, Kou XY, Dong QX (2018c) Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst Appl 98:118–128

    Google Scholar 

  • Zhang Z, Kou XY, Yu WY, Guo CH (2018d) On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowl-Based Syst 141(1):115–126

    Google Scholar 

  • Zhang HJ, Dong YC, Chiclana F, Yu S (2019) Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design. Eur J Oper Res 275(2):580–598

    MathSciNet  MATH  Google Scholar 

  • Zhou W, Xu ZS (2017) Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment. Inf Sci 414(Supplement C):276–288

    Google Scholar 

  • Zhu B, Xu ZS (2013) Regression methods for hesitant fuzzy preference relations. Technol Econ Dev Econ 19(sup1):S214–S227

    Google Scholar 

  • Zhu B, Xu ZS (2014) Analytic hierarchy process-hesitant group decision making. Eur J Oper Res 239(3):794–801

    MathSciNet  MATH  Google Scholar 

  • Zhu B, Xu ZS, Xu JP (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44(8):1328–1337

    Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was supported by the Key Research and Development Program of Guangxi (Nos. 2017AB16004), Promotion project of Middle-aged and Young Teachers’ Basic Scientific Research Ability in Universities of Guangxi (No. 2019KY0963) and the Research Funds for the Guangxi University Xingjian College of Science and Liberal Arts (Nos. Y2018ZKT01).

Author information

Authors and Affiliations

  1. School of XingJian College of Science and Liberal Arts, Guangxi University, Nanning, 530005, Guangxi, People’s Republic of China

    Jian Li

  2. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, People’s Republic of China

    Zhong-Xing Wang

Authors
  1. Jian Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhong-Xing Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhong-Xing Wang.

Ethics declarations

Conflict of interest

All authors have declared that they have no conflicts of interest.

Informed consent

Informed consent was unnecessary because no human or animals were involved.

Human and animal rights

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

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Wang, ZX. Deriving priority weights from hesitant fuzzy preference relations in view of additive consistency and consensus. Soft Comput 23, 13691–13707 (2019). https://doi.org/10.1007/s00500-019-03908-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-03908-5

Keywords