Group Decision and Negotiation

, Volume 22, Issue 6, pp 997–1019 | Cite as

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

  • Zeshui Xu
  • Xiaoqiang Cai


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.


Group decision and negotiation Consensus Interval utility values Interval preference orderings 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Institute of SciencesPLA University of Science and TechnologyNanjingChina
  2. 2.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong

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