Skip to main content
SpringerLink
Log in

On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings

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

Abstract

Uncertainty is a common phenomenon in our real world. Interval utility values and interval preference orderings are two of the simplest and most convenient tools to describe uncertain preferences in decision making. In this paper, we investigate consensus problems in group decision making with interval utility values and interval preference orderings. We first establish their transformation relations, and give a formula for calculating the association coefficients of individual uncertain preferences and group ones. We then develop a consensus procedure for group decision making with interval utility values and interval preference orderings, which takes interval utility values as the uniform preference representation. This procedure can be reduced to a series of processes for dealing with some special group decision making situations, such as: group decision making with utility values and preference orderings, group decision making with interval utility values, group decision making with interval preference orderings, etc. Finally, we illustrate the applications of the developed procedures with two practical examples.

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

Similar content being viewed by others

References

  • Bodily SE (1979) A delegation process for combining individual utility functions. Manag Sci 25: 1035–1041

    Article  Google Scholar 

  • Brock HW (1980) The problem of utility weights in group preference aggregation. Oper Res 28: 176–187

    Article  Google Scholar 

  • Cabrerizo FJ, Moreno JM, Pérez IJ, Herrera-Viedma E (2010) Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput 14: 451–463

    Article  Google Scholar 

  • Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making: methods and applications. Springer, Berlin

    Book  Google Scholar 

  • 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: 277–291

    Article  Google Scholar 

  • Fan ZP, Liu Y (2010) An approach to solve group decision making problems with ordinal interval numbers. IEEE Trans Syst Man Cybern Part B 40: 1413–1423

    Article  Google Scholar 

  • Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13: 613–622

    Article  Google Scholar 

  • Genc S, Boran FE, Akay D, Xu ZS (2010) Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations. Inf Sci 180: 4877–4891

    Article  Google Scholar 

  • González-Pachón J, Rodríguez-Galiano MI, Romero C (2003) Transitive approximation to pairwise comparison matrices by using interval goal programming. J Oper Res Soc 54: 532–538

    Article  Google Scholar 

  • González-Pachón J, Romero C (2001) Aggregation of partial ordinal rankings: an interval goal programming approach. Comput Oper Res 28: 823–834

    Article  Google Scholar 

  • Haines LM (1998) A statistical approach to the analytic hierarchy process with interval judgments. Eur J Oper Res 110: 112–125

    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-Viedma E, Garcia-Lapresta J, Kacprzyk J, Nurmi H, Fedrizzi M, Zadrozny S (2011) Consensual processes. Springer, Berlin

    Book  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 Part A 32: 394–402

    Article  Google Scholar 

  • Jiang HF, Xia MM, Wei CP (2010) The priority method of interval fuzzy preference relation. Appl Math Sci 4: 1681–1690

    Google Scholar 

  • Jiang YL (2007) An approach to group decision making based on interval fuzzy preference relations. Journal of Systems Science and Systems Engineering 16: 113–120

    Article  Google Scholar 

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

    Book  Google Scholar 

  • Li XM, Min M, Tan CF (2005) The functional assessment of agricultural ecosystems in Hubei Province, China. Ecol Model 187: 352–360

    Article  Google Scholar 

  • Luce RD, Suppes P et al (1965) Preferences, utility and subject probability. In: Luce RD (ed) Handbook of mathematical psychology, vol III. Wiley, New York, pp 249–410

    Google Scholar 

  • 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 36: 876–889

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ramanathan R, Ganesh LS (1994) Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members weightages. Eur J Oper Res 79: 249–265

    Article  Google Scholar 

  • Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32: 107–117

    Article  Google Scholar 

  • Schubert J (1995) On p in a decision-theoretic apparatus of Dempster–Shafer theory. Int J Approx Reason 13: 185–200

    Article  Google Scholar 

  • Seo F, Sakawa M (1985) Fuzzy multiattribute utility analysis for collective choice. IEEE Trans Syst Man Cybern 15: 45–53

    Article  Google Scholar 

  • Strat TM (1990) Decision analysis using belief functions. Int J Approx Reason 4: 391–417

    Article  Google Scholar 

  • Tanino T (1984) Fuzzy preference ordering in group decision making. Fuzzy Sets Syst 12: 117–131

    Article  Google Scholar 

  • Wang YM, Yang JB, Xu DL (2005a) A preference aggregation method through the estimation of utility intervals. Comput Oper Res 32: 2027–2049

    Article  Google Scholar 

  • Wang YM, Yang JB, Xu DL (2005b) A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst 152: 475–498

    Article  Google Scholar 

  • Wu J, Li JC, Li H, Duan WQ (2009) The induced continuous ordered weighted geometric operators and their application in group decision making. Comput Ind Eng 56: 1545–1552

    Article  Google Scholar 

  • Xia MM, Xu ZS (2011) Some issues on multiplicative consistency of interval fuzzy preference relations. Int J Inf Technol Decis Mak 10: 1043–1065

    Article  Google Scholar 

  • Xu RN, Zhai XY (1992) Extensions of the analytic hierarchy process in fuzzy environment. Fuzzy Sets Syst 52: 251–257

    Article  Google Scholar 

  • Xu ZS (2003) On compatibility of interval fuzzy preference matrices. Fuzzy Optim Decis Mak 3: 217–225

    Article  Google Scholar 

  • Xu ZS (2006) A C-OWA operator based approach to decision making with interval fuzzy preference relation. Int J Intell Syst 21: 1289–1298

    Article  Google Scholar 

  • Xu ZS (2007) Multiple attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybern Part B 37: 1500–1511

    Article  Google Scholar 

  • Xu ZS (2009) An automatic approach to reaching consensus in multiple attribute group decision making. Comput Ind Eng 56: 1369–1374

    Article  Google Scholar 

  • Xu ZS (2011) Consistency of interval fuzzy preference relations in group decision making. Appl Soft Comput 11: 3898–3909

    Article  Google Scholar 

  • Xu ZS, Cai XQ (2011) Minimizing group discordance optimization model for deriving expert weights. Group Decis Negot. doi:10.1007/s10726-011-9253-7

  • Xu ZS, Cai XQ, Liu SS (2010) Nonlinear programming model integrating different preference structures. IEEE Trans Syst Man Cybern Part A 41: 169–177

    Article  Google Scholar 

  • Xu ZS, Cai XQ (2012) Uncertain power average operators for aggregating interval fuzzy preference relations. Group Decis Negot 21: 381–397

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) MAGDM linear programming models with distinct uncertain preference structures. IEEE Trans Syst Man Cybern Part B 38: 1356–1370

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) Some models for deriving the priority weights from interval fuzzy preference relations. Eur J Oper Res 184: 266–280

    Article  Google Scholar 

  • Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17: 569–575

    Article  Google Scholar 

  • Yager RR, Xu ZS (2006) The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets Syst 157: 1393–1402

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Sciences, PLA University of Science and Technology, Nanjing, 210007, China

    Zeshui Xu

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

    Xiaoqiang Cai

Authors
  1. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoqiang Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeshui Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, Z., Cai, X. On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings. Group Decis Negot 22, 997–1019 (2013). https://doi.org/10.1007/s10726-012-9298-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10726-012-9298-2

Keywords

Search

Navigation