Group Decision Making with Heterogeneous Preference Structures: An Automatic Mechanism to Support Consensus Reaching

  • Bowen Zhang
  • Yucheng DongEmail author
  • Enrique Herrera-Viedma


In real-world decision problems, decision makers usually express their opinions with different preference structures. In order to deal with the heterogeneous preference information in group decision making, this paper presents an optimization-based consensus model for group decision making with heterogeneous preference structures (utility values, preference orderings, multiplicative preference relations and additive preference relations). This proposal seeks to minimize the information loss between decision makers’ heterogeneous preference information and individual preference vectors and also seeks the collective solution with a consensus. Meanwhile, in order to justify the consensus model, we discuss its internal aggregation operator between the obtained individual and group preference vectors, demonstrate that the proposed model satisfies the Pareto principle of social choice theory, and prove the uniqueness of the solution to the optimization model. Furthermore, based on the proposed optimization-based consensus model, we present an automatic mechanism to support consensus reaching in the group decision making with heterogeneous preference structures. In the consensus reaching process, the obtained individual and group preference vectors are considered as a decision aid which decision makers can use as a reference to adjust their preference opinions. Finally, detailed simulation experiments and comparison analysis are conducted to demonstrate the feasibility and effectiveness of our proposed model.


Group decision and negotiation Heterogeneous preference structures Consensus Information loss 



We would like to acknowledge the financial support of the grants (Nos. 71871149 and 71571124) from NSF of China, the grants (Nos. sksyl201705 and 2018hhs-58) from Sichuan University, and the grant TIN2016-75850-R supported by the Spanish Ministry of Economy and Competitiveness with FEDER funds.


  1. Altuzarra A, Moreno-Jiménez JM, Salvador M (2010) Consensus building in AHP-group decision making: a Bayesian approach. Oper Res 58(6):1755–1773CrossRefGoogle Scholar
  2. An LTH (2000) An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math Program 87(3):401–426CrossRefGoogle Scholar
  3. Arrow KJ (1963) Social choice and individual values. Wiley, New YorkGoogle Scholar
  4. Ben-Arieh D, Easton T (2007) Multi-criteria group consensus under linear cost opinion elasticity. Decis Support Syst 43:713–721CrossRefGoogle Scholar
  5. Ben-Arieh D, Easton T, Evans B (2008) Minimum cost consensus with quadratic cost functions. IEEE Trans Syst Man Cybern Part A Syst Hum 39(1):210–217CrossRefGoogle Scholar
  6. Chen X, Zhang HJ, Dong YC (2015) The fusion process with heterogeneous preference structures in group decision making: a survey. Inf Fusion 24:72–83CrossRefGoogle Scholar
  7. Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on additive preference relations. Fuzzy Sets Syst 97:33–48CrossRefGoogle Scholar
  8. Chiclana F, Herrera F, Herrera-Viedma E (2001) Integrating multiplicative preference relations in a multipurpose decision-making model based on additive preference relations. Fuzzy Sets Syst 122:277–291CrossRefGoogle Scholar
  9. Contreras I (2010) A distance-based consensus model with flexible choice of rank-position weights. Group Decis Negot 19(5):441–456CrossRefGoogle Scholar
  10. Cook WD (2006) Distance-based and ad hoc consensus models in ordinal preference ranking. Eur J Oper Res 172(2):369–385CrossRefGoogle Scholar
  11. Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(24):1721–1732CrossRefGoogle Scholar
  12. Dong YC, Zhang HJ (2014) Multiperson decision making with different preference representation structures: a direct consensus framework and its properties. Knowl Based Syst 58:45–57CrossRefGoogle Scholar
  13. 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 203:455–463CrossRefGoogle Scholar
  14. Dong YC, Li CC, Xu YF, Gu X (2015) Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decis Negot 24:217–242CrossRefGoogle Scholar
  15. Dong YC, Zhang HJ, Herrera-Viedma E (2016) Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decis Support Syst 84:1–15CrossRefGoogle Scholar
  16. Dong YC, Zha QB, Zhang HJ, Kou G, Fujita H, Chiclana F, Herrera-Viedma E (2018) Consensus reaching in social network group decision making: research paradigms and challenges. Knowl Based Syst 162:3–13CrossRefGoogle Scholar
  17. Fan ZP, Zhang Y (2010) A goal programming approach to group decision-making with three formats of incomplete preference relations. Soft Comput 14(10):1083–1090CrossRefGoogle Scholar
  18. Fan ZP, Xiao SH, Hu GF (2004) An optimization method for integrating two kinds of preference information in group decision-making. Comput Ind Eng 46:329–335CrossRefGoogle Scholar
  19. Fan ZP, Ma J, Jiang YP, Sun YH, Ma L (2006) A goal programming approach to group decision making based on multiplicative preference relations and additive preference relations. Eur J Oper Res 174:311–321CrossRefGoogle Scholar
  20. Gong ZW, Zhang HH, Forrest J, Li LS, Xu XX (2015) Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual. Eur J Oper Res 240:183–192CrossRefGoogle Scholar
  21. Gong ZW, Xu C, Chiclana F, Xu XX (2016) Consensus measure with multi-stage fluctuation utility based on china’s urban demolition negotiation. Group Decis Negot 26(2):1–29Google Scholar
  22. Herrera F, Martínez L, Sánchez PJ (2005) Managing non-homogeneous information in group decision making. Eur J Oper Res 166(1):115–132CrossRefGoogle Scholar
  23. Herrera-Viedma E, Herrera F, Chiclana F (2002) A consensus model for multiperson decision making with different preference structures. IEEE Trans Syst Man Cybern Part A Syst Hum 32:394–402CrossRefGoogle Scholar
  24. Herrera-Viedma E, Martínez 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
  25. Herrera-Viedma E, Cabrerizo FJ, Kacprzyk J, Pedrycz W (2014) A review of soft consensus models in a fuzzy environment. Inf Fusion 17:4–13CrossRefGoogle Scholar
  26. Jiang YP, Fan ZP, Ma J (2008) A method for group decision making with multi-granularity linguistic assessment information. Inf Sci 178(4):1098–1109CrossRefGoogle Scholar
  27. Kacprzyk J, Fedrizzi M (1988) A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. Eur J Oper Res 343:16–325Google Scholar
  28. Kacprzyk J, Zadrozny S (2010) Soft computing and Web intelligence for supporting consensus reaching. Soft Comput 14:833–846CrossRefGoogle Scholar
  29. Kacprzyk J, Fedrizzi M, Nurmi H (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst 49:21–31CrossRefGoogle Scholar
  30. Kacprzyk J, Fedrizzi M, Nurmi H (1997) Consensus under fuzziness. Kluwer, NorwellCrossRefGoogle Scholar
  31. Kim J (2008) A model and case for supporting participatory public decision making in edemocracy. Group Decis Negot 17:179–193CrossRefGoogle Scholar
  32. Kozierkiewicz-Hetmanska A (2017) The analysis of expert opinions’ consensus quality. Inf Fusion 34:80–86CrossRefGoogle Scholar
  33. Li CC, Dong YC, Herrera F (2018) 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 1:25. Google Scholar
  34. Liu YT, Dong YC, Liang HM, Chiclana F, Herrera-Viedma E (2018) Multiple attribute strategic weight manipulation with minimum cost in a group decision making context with interval attribute weights information. IEEE Trans Syst Man Cybern Syst. Google Scholar
  35. Ma J, Fan ZP, Jiang YP, Mao JY (2006) An optimization approach to multiperson decision making based on different formats of preference information. IEEE Trans Syst Man Cybern Part A Syst Hum 36(5):876–889CrossRefGoogle Scholar
  36. María J, Jiménez M, Joven JA, Pirla AR, Lanuza AT (2005) A spreadsheet module for consistent consensus building in AHP-group decision making. Group Decis Negot 14(2):89–108CrossRefGoogle Scholar
  37. Moreno-Jiménez JM, Joven JA, Pirla AR, Lanuza AT (2005) A spreadsheet module for consistent consensus building in AHP group decision making. Group Decis Negot 14:89–108CrossRefGoogle Scholar
  38. Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1(3):155–167CrossRefGoogle Scholar
  39. Palomares I, Estrella FJ, Martínez L, Herrera F (2014) Consensus under a fuzzy context: taxonomy, analysis framework AFRYCA and experimental case of study. Inf Fusion 20:252–271CrossRefGoogle Scholar
  40. Parreiras RO, Ekel PY, Morais DC (2012) Fuzzy set based consensus schemes for multicriteria group decision making applied to strategic planning. Group Decis Negot 21:153–183CrossRefGoogle Scholar
  41. Pérez IJ, Cabrerizo FJ, Alonso S, Herrera-Viedma E (2014) A new consensus model for group decision making problems with non-homogeneous experts. IEEE Trans Syst Man Cybern Syst 44(4):494–498CrossRefGoogle Scholar
  42. Pérez IJ, Cabrerizo FJ, Alonso S, Dong YC, Chiclana F, Herrera-Viedma E (2018) On dynamic consensus processes in group decision making problems. Inf Sci 459:20–35CrossRefGoogle Scholar
  43. Perny P, Roy B (1992) The use of fuzzy outranking relations in preference modelling. Fuzzy Sets Syst 49(1):33–53CrossRefGoogle Scholar
  44. Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281CrossRefGoogle Scholar
  45. Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New YorkGoogle Scholar
  46. Sen A (1970) Collective choice and social welfare. Holdenday, San FranciscoGoogle Scholar
  47. Seo F, Sakawa M (1985) Fuzzy multiattribute utility analysis for collective choice. IEEE Trans Syst Man Cybern 15:45–53CrossRefGoogle Scholar
  48. Srdjevic B (2007) Linking analytic hierarchy process and social choice methods to support group decision-making in water management. Decis Support Syst 42:2261–2273CrossRefGoogle Scholar
  49. Sun BZ, Ma WM (2015) An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application. Omega 51:83–92CrossRefGoogle Scholar
  50. Tanino T (1990) On group decision making under fuzzy preferences. In: Kacprzyk J, Fedrizzi M (eds) Multiperson decision making using fuzzy sets and possibility theory. Kluwer, Dordrecht, pp 172–185CrossRefGoogle Scholar
  51. Wu J, Chiclana F (2014a) Visual information feedback mechanism and attitudinal prioritisation method for group decision making with triangular fuzzy complementary preference relations. Inf Sci 279:716–734CrossRefGoogle Scholar
  52. Wu J, Chiclana F (2014b) A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions. Appl Soft Comput 22(5):272–286CrossRefGoogle Scholar
  53. Wu ZB, Xu JP (2012) A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis Support Syst 52:757–767CrossRefGoogle Scholar
  54. Xu JP, Wu ZB, Zhang Y (2014) A consensus based method for multi-criteria group decision making under uncertain linguistic setting. Group Decis Negot 23(1):127–148CrossRefGoogle Scholar
  55. Xu XH, Du ZJ, Chen XH (2015) Consensus model for multi-criteria large-group emergency decision making considering non-cooperative behaviors and minority opinions. Decis Support Syst 79:150–160CrossRefGoogle Scholar
  56. Zhang Z, Gao CH (2014) An approach to group decision making with heterogeneous incomplete uncertain preference relations. Comput Ind Eng 71:27–36CrossRefGoogle Scholar
  57. Zhang GQ, Dong YC, Xu YF, Li HY (2011) Minimum-cost consensus models under aggregation operators. IEEE Trans Syst Man Cybern Part A Syst Hum 41(6):1253–1261CrossRefGoogle Scholar
  58. Zhang BW, Dong YC, Xu YF (2014) Multiple attribute consensus rules with minimum adjustments to support consensus reaching. Knowl Based Syst 67:35–48CrossRefGoogle Scholar
  59. Zhang HJ, Dong YC, Chiclana F, Yu S (2018) Consensus efficiency in group decision making: a comprehensive comparative study and its optimal design. Eur J Oper Res. Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Bowen Zhang
    • 1
  • Yucheng Dong
    • 2
    Email author
  • Enrique Herrera-Viedma
    • 3
    • 4
  1. 1.School of Economics and ManagementXidian UniversityXi’anChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  4. 4.Department of Electrical and Computer EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations