Advertisement

Soft Computing

, Volume 23, Issue 2, pp 669–682 | Cite as

A consensus-based method for group decision making with incomplete uncertain linguistic preference relations

  • Yejun XuEmail author
  • Ziqiang Zhang
  • Huimin Wang
Methodologies and Application
  • 143 Downloads

Abstract

In practical group decision-making (GDM) problems, it is nature for experts to express their preference relations in uncertain linguistic pattern, due to the ambiguity of the external environments and the internal nature of human judgments. In this paper, a consensus process is introduced to deal with GDM problems with incomplete uncertain linguistic preference relations (ULPRs). Firstly, a consistency level for ULPRs is defined. Secondly, a linear goal programming model is furnished to estimate the missing uncertain linguistic preference values with respect to consistency property. Thirdly, an additively consistent ULPR is constructed. What’s more, one can obtain the collective ULPR by aggregating individual additively consistent ULPRs, where the order-inducing variable is consistency level (CL), based on the thought of more importance will be given to the larger CL. Furthermore, a consensus reaching process is presented to make experts’ opinions achieve to a predefined level. In the end, a new algorithm is proposed to solve the GDM problem with incomplete ULPR, which is further applied to the selection of best cooperator in a water conservancy project.

Keywords

Group decision making Consistency measure Incomplete uncertain linguistic preference relation (ULPR) Consensus reaching process 

Notes

Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (NSFC) (No. 71471056), the Key Project of National Natural Science Foundation of China (No. 71433003), sponsored by Qing Lan Project of Jiangsu Province.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Alonso S, Cabrerizo FJ, Chiclana F, Herrera F, Herrera-Viedma E (2009) Group decision making with incomplete fuzzy linguistic preference relations. Int J Intell Syst 24:201–222CrossRefzbMATHGoogle Scholar
  2. 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 23:155–175CrossRefzbMATHGoogle Scholar
  3. Cabrerizo FJ, Moreno JM, Pérez IJ, Herrera-Viedma E (2010a) Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput 14:451–463CrossRefGoogle Scholar
  4. Cabrerizo FJ, Pérez IJ, Herrera-Viedma E (2010b) Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowl-Based Syst 23:169–181CrossRefGoogle Scholar
  5. Chiclana F, Herrera F, Herrera-Viedma E (2001) Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277–291MathSciNetCrossRefzbMATHGoogle Scholar
  6. Cordón O, Herrera F, Zwir I (2002) Linguistic modeling by hierarchical systems of linguistic rules. IEEE Trans Fuzzy Syst 10:2–20CrossRefzbMATHGoogle Scholar
  7. Delgado M, Verdegay JL, Vila MA (1993) On aggregation operations of linguistic labels. Int J Intell Syst 8:351–370CrossRefzbMATHGoogle Scholar
  8. Dong YC, Hong WC, Xu YF (2013) Measuring consistency of linguistic preference relations: a 2-tuple linguistic approach. Soft Comput 17:2117–2130CrossRefGoogle Scholar
  9. Dong YC, Xu YF, Li HY (2008) On consistency measures of linguistic preference relations. Eur J Oper Res 189:430–444MathSciNetCrossRefzbMATHGoogle Scholar
  10. Herrera-Viedma E, Martinez L, Mata F, Chiclana F (2005) A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans Fuzzy Syst 13:644–658CrossRefGoogle Scholar
  11. Herrera F, Herrera-Viedma E, Chiclana F (2001) Multiperson decision-making based on multiplicative preference relations. Eur J Oper Res 129:372–385MathSciNetCrossRefzbMATHGoogle Scholar
  12. Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inf Sci 85:223–239CrossRefzbMATHGoogle Scholar
  13. Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8:746–752CrossRefGoogle Scholar
  14. Herrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans Syst Man Cybern Part B (Cybern) 31:227–234CrossRefGoogle Scholar
  15. Kacprzyk J (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst 18:105–118MathSciNetCrossRefzbMATHGoogle Scholar
  16. Liu F, Zhang WG (2014) TOPSIS-based consensus model for group decision making with incomplete interval fuzzy preference relations. IEEE Trans Cybern 44:1283–1294MathSciNetCrossRefGoogle Scholar
  17. Liu F, Zhang WG, Wang ZX (2012) A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. Eur J Oper Res 218:747–754MathSciNetCrossRefzbMATHGoogle Scholar
  18. Maio CD, Fenza G, Loia V, Orciuoli F, Herrera-Viedma E (2016a) A context-aware fuzzy linguistic consensus model supporting innovation processes. In: IEEE international conference on fuzzy systems, pp 1685–1692Google Scholar
  19. Maio CD, Fenza G, Loia V, Orciuoli F, Herrera-Viedma E (2016b) A framework for context-aware heterogeneous group decision making in business processes. Knowl-Based Syst 102:39–50CrossRefGoogle Scholar
  20. 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 17:279–290CrossRefGoogle Scholar
  21. Orlovsky S (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155–167MathSciNetCrossRefzbMATHGoogle Scholar
  22. Roubens M (1997) Fuzzy sets and decision analysis. Fuzzy Sets Syst 90:199–206MathSciNetCrossRefzbMATHGoogle Scholar
  23. Saaty TL (1980) The analytic hierarchy process. McGrew Hill, New YorkzbMATHGoogle Scholar
  24. Torra V (1996) Negation functions based semantics for ordered linguistic labels. Int J Intell Syst 11:975–988CrossRefGoogle Scholar
  25. Wang TC, Chen YH (2010) Incomplete fuzzy linguistic preference relations under uncertain environments. Inf Fusion 11:201–207CrossRefGoogle Scholar
  26. Xu JP, Wu ZB (2011) A discrete consensus support model for multiple attribute group decision making. Knowl-Based Syst 24:1196–1202CrossRefGoogle Scholar
  27. Xu JP, Wu ZB, Zhang Y (2014a) A consensus based method for multi-criteria group decision making under uncertain linguistic setting. Group Decis Negot 23:127–148CrossRefGoogle Scholar
  28. Xu YJ, Cabrerizo FJ, Herrera-Viedma E (2017a) A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Appl Soft Comput 58:265–284CrossRefGoogle Scholar
  29. Xu YJ, Chen L, Li KW, Wang HM (2015) A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations. Inf Sci 306:166–179CrossRefzbMATHGoogle Scholar
  30. 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 99:71–78CrossRefGoogle Scholar
  31. Xu YJ, Gupta JND, Wang HM (2014b) The ordinal consistency of an incomplete reciprocal preference relation. Fuzzy Sets Syst 246:62–77MathSciNetCrossRefzbMATHGoogle Scholar
  32. Xu YJ, Li KW, Wang HM (2014c) Consistency test and weight generation for additive interval fuzzy preference relations. Soft Comput 18:1499–1513CrossRefzbMATHGoogle Scholar
  33. Xu YJ, Li KW, Wang HM (2014d) Incomplete interval fuzzy preference relations and their applications. Comput Ind Eng 67:93–103CrossRefGoogle Scholar
  34. Xu YJ, Ma F, Tao FF, Wang HM (2014e) Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic preference relations in group decision making. Knowl-Based Syst 56:179–190CrossRefGoogle Scholar
  35. Xu YJ, Wei CP, Sun H (2017b) Distance-based nonlinear programming models to identify and adjust inconsistencies for linguistic preference relations. Soft Comput.  https://doi.org/10.1007/s00500-017-2671-y zbMATHGoogle Scholar
  36. Xu ZS (2005) An overview of methods for determining OWA weights. Int J Intell Syst 20:843–865CrossRefzbMATHGoogle Scholar
  37. Xu ZS (2006a) A direct approach to group decision making with uncertain additive linguistic preference relations. Fuzzy Optim Decis Making 5:21–32MathSciNetCrossRefzbMATHGoogle Scholar
  38. Xu ZS (2006b) Incomplete linguistic preference relations and their fusion. Inf Fusion 7:331–337CrossRefGoogle Scholar
  39. Xu ZS (2006c) Induced uncertain linguistic OWA operators applied to group decision making. Inf Fusion 7:231–238CrossRefGoogle Scholar
  40. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning–I. Inf Sci 8:199–249MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Business SchoolHohai UniversityNanjingPeople’s Republic of China

Personalised recommendations