Skip to main content
SpringerLink
Log in

Consensus-Based Group Decision Making Under Multi-granular Unbalanced 2-Tuple Linguistic Preference Relations

  • Published:
Group Decision and Negotiation Aims and scope Submit manuscript

Abstract

In group decision making (GDM) situations, it is quite natural that the decision makers who may have different background and knowledge will provide their preferences by means of different linguistic term sets. Specifically, multi-granular linguistic term sets that are not uniformly and symmetrically distributed will be employed. To deal with this type of GDM problems, this paper proposes a consensus-based GDM model by using two existing 2-tuple linguistic representation models (i.e., the Herrera and Martínez model and the Wang and Hao model), which we called the GDM model based on multi-granular unbalanced 2-tuple linguistic preference relations. First, the framework of the GDM model with multi-granular unbalanced 2-tuple linguistic preference relations is proposed. Then, the transformation function is obtained to relate multi-granular unbalanced linguistic preference relations with uniform balanced linguistic preference relations. Further, a consensus model is presented to help the decision makers reach a consensus. This consensus model not only provides a new way to simultaneously manage individual consistency and group consensus in a linear programming model, but also minimizes information loss (or consensus cost) when reaching the established consensus level. Finally, an example is given to illustrate the feasibility and validity of the proposed model.

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

Similar content being viewed by others

References

  • Alonso S, Chiclana F, Herrera F, Herrera-Viedma E, Alcalá-Fdez J, Porcel C (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23:155–175

    Article  Google Scholar 

  • Alonso S, Herrera-Viedma E, Chiclana F, Herrera F (2010) A web based consensus support system for group decision making problems and incomplete preferences. Inf Sci 180:4477–4495

    Article  Google Scholar 

  • Ben-Arieh D, Easton T (2007) Multi-criteria group consensus under linear cost opinion elasticity. Decis Support Syst 43:713–721

    Article  Google Scholar 

  • Ben-Arieh D, Easton T, Evans B (2009) Minimum cost consensus with quadratic cost functions. IEEE Trans Syst Man Cybern A Syst Hum 39:210–217

    Article  Google Scholar 

  • Ben-Arieh D, Chen Z (2006) Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations. IEEE Trans Syst Man Cybern A Syst Hum 36:558–568

    Article  Google Scholar 

  • Cabrerizo FJ, Alonso S, Herrera-Viedma E (2009) A consensus model for group decision making problems with unbalanced fuzzy linguistic information. Int J Inf Technol Decis Mak 8:109–131

    Article  Google Scholar 

  • Cabrerizo FJ, Heradio R, Pérez IJ, Herrera-Viedma E (2010a) A selection process based on additive consistency to deal with incomplete fuzzy linguistic information. J Univ Comput Sci 16:62–81

    Google Scholar 

  • Cabrerizo FJ, López-Gijón J, Ruíz-Rodríguez AA, Herrera-Viedma E (2010b) A model based on fuzzy linguistic information to evaluate the quality of digital libraries. Int J Inf Technol Decis Mak 9:455–472

    Article  Google Scholar 

  • Cabrerizo FJ, Pérez IJ, Herrera-Viedma E (2010c) Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowl Based Syst 23:169–181

    Article  Google Scholar 

  • Chen Z, Ben-Arieh D (2006) On the fusion of multi-granularity linguistic label sets in group decision making. Comput Ind Eng 51:526–541

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Chiclana F, Mata F, Martínez L, Herrera-Viedma E, Alonso S (2008) Integration of a consistency control module within a consensus model. Int J Uncertain Fuzz Knowl Based Syst 16:35–53

    Article  Google Scholar 

  • Dantzig GB (1963) Linear programming and extensions. Princeton University Press, New York

    Google Scholar 

  • Dong Y, Hong W, Xu Y, Yu S (2011) Selecting the individual numerical scale and prioritization method in the analytic hierarchy process: a 2-tuple fuzzy linguistic approach. IEEE Trans Fuzzy Syst 19:13–26

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dong Y, Xu Y, Yu S (2009a) Linguistic multiperson decision making based on the use of multiple preference relations. Fuzzy Sets Syst 160:603–623

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dong Y, Zhang G, Hong W, Xu Y (2010b) Consensus models for AHP group decision making under row geometric mean prioritization method. Decis Support Syst 49:281–289

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fan Z, Xiao S, Hu G (2004) An optimization method for integrating two kinds of preference information in group decision-making. Comput Ind Eng 46:329–335

    Article  Google Scholar 

  • Herrera F, Herrera-Viedma E, Chiclana F (2001) Multiperson decision-making based on multiplicative preference relations. Eur J Oper Res 129:372–385

    Article  Google Scholar 

  • Herrera F, Herrera-Viedma E, Martínez L (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114:43–58

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay JL (1997) A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets Syst 88:31–49

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Herrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making. IEEE Trans Syst Man Cybern B Cybern 31:227–234

    Article  Google Scholar 

  • Herrera-Viedma E, Herrera F, Chiclana F (2002) A consensus model for multiperson decision making with different preference structures. IEEE Trans Syst Man Cybern A Syst Hum 37:176–189

    Article  Google Scholar 

  • Herrera-Viedma E, García-Lapresta JL, Kacprzyk J, Fedrizzi M, Nurmi H, Zadrozny S (eds) (2011) Consensual processes, STUDFUZZ 267. Springer, Berlin

    Google Scholar 

  • Herrera-Viedma E, López-Herrera AG (2007) A model of information retrieval system with unbalanced fuzzy linguistic information. Int J Intell Syst 22:1197–1214

    Article  Google Scholar 

  • Herrera-Viedma E, Martínez L, Mata F, Chiclana F (2005) A consensus support system model for group decision-making problems with multi-granular linguistic preference relations. IEEE Trans Fuzzy Syst 13:644–658

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kacprzyk J, Fedrizzi M, Nurmi H (1997) Consensus under fuzziness. Kluwer, Norwell

    Book  Google Scholar 

  • Martínez L (2007) Sensory evaluation based on linguistic decision analysis. Int J Approx Reason 44:148–164

    Article  Google Scholar 

  • Martínez L, Espinilla M, Liu J, Pérez LG, Sánchez PJ (2009) An evaluation model with unbalanced linguistic information applied to olive oil sensory evaluation. J Multi Valued Log Soft Comput 15:229–251

    Google Scholar 

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

    Article  Google Scholar 

  • Martínez L, Ruan D, Herrera F (2010) Computing with words in decision support systems: An overview on models and applications. Int J Comput Intell Syst 3:382–395

    Article  Google Scholar 

  • Mata F, Martínez L, Herrera-Viedma E (2009) An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. IEEE Trans Fuzzy Syst 17:279–290

    Article  Google Scholar 

  • Moreno-Jiménez JM et al (2005) A spreadsheet module for consistent consensus building in AHP group decision making. Group Decis Negot 14:89–108

    Article  Google Scholar 

  • Parreiras RO, Ekel PYa, Martini JSC, Palhares RM (2010) A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Inf Sci 180:1075–1089

    Article  Google Scholar 

  • Parreiras RO, Ekel PYa, Morais DC (2012) Fuzzy set based consensus schemes for multicriteria group decision making applied to strategic planning. Group Decis Negot 21:153–183

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rodríguez RM, Martínez L (2013) An analysis of symbolic linguistic computing models in decision making. Int J Gen Syst 42:121–136

    Article  Google Scholar 

  • Wang S (2008) Applying 2-tuple multigranularity linguistic variables to determine the supply performance in dynamic environment based on product-oriented strategy. IEEE Trans Fuzzy Syst 16:29–39

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wang JH, Hao JY (2007) Fuzzy linguistic PERT. IEEE Trans Fuzzy Syst 15:133–144

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wu ZB, Xu JP (2012) Consensus reaching models of linguistic preference relations based on distance functions. Soft Comput 16:577–589

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Xu ZS, Cai XQ, Liu SS (2011) Nonlinear programming model integrating different preference structures. IEEE Trans Syst Man Cybern A Syst Hum 41:169–177

    Article  Google Scholar 

  • Xu YJ, Wang HM (2011) Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment. Appl Soft Comput 11:3988–3997

    Article  Google Scholar 

  • Xu JP, Wu ZB, Zhang Y (2012) A consensus based method for multi-criteria group decision making under uncertain linguistic setting. Group Decis Negot. doi:10.1007/s10726-012-9310-x

    Google Scholar 

  • Yager R (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18:183–190

    Article  Google Scholar 

  • Yager R (1996) Quantifer guided aggregation using OWA operators. Int J Intell Syst 11:49–73

    Article  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  Google Scholar 

  • Zhang G, Dong Y, Xu Y, Li H (2011) Minimum-cost consensus models under aggregation operators. IEEE Trans Syst Man Cybern A Syst Hum 41:1253–1261

    Article  Google Scholar 

Download references

Acknowledgments

Yucheng Dong would like to thank Professor Francisco Herrera for his constructive comments and suggestions, which are very helpful in improving this paper. This work was supported by the grant (No. 71171160) from NSF of China, the grants (Nos. SKX201004 and skqx201308) from Sichuan University, and a grant for Changjiang Scholars and Innovative Research Team in University (IRT1173) from Ministry of Education of China.

Author information

Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610065, People’s Republic of China

    Yucheng Dong, Cong-Cong Li, Yinfeng Xu & Xin Gu

Authors
  1. Yucheng Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cong-Cong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yinfeng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yucheng Dong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dong, Y., Li, CC., Xu, Y. et al. Consensus-Based Group Decision Making Under Multi-granular Unbalanced 2-Tuple Linguistic Preference Relations. Group Decis Negot 24, 217–242 (2015). https://doi.org/10.1007/s10726-014-9387-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10726-014-9387-5

Keywords

Search

Navigation