A two-objective-optimization-driven group decision making model under the bipolarity of decision information.

When building consensus in group decision making (GDM) under uncertainty, an important yet rarely studied issue is to find the Pareto solutions of multi-objective optimization model. This paper reports a two-objective (2Ob) optimization driven consensus model in GDM by describing the bipolarity of judgements through intuitionistic multiplicative preference relations (IMPRs). First, it is realized that the inherent property of IMPRs is the hesitancy degree. A novel inconsistency index of IMPRs is proposed by combining the effects of hesitancy degree and inconsistency of boundary matrices. Second, the compatibility measure between two IMPRs is utilized to quantify the consensus level (CL) of decision makers. The threshold of acceptable group CL is found to decrease with the order of IMPRs for the first time. A 2Ob optimization model is constructed by minimizing group inconsistency degree and group CL, respectively. Third, the method of equipping two flexibility degrees to each expert is proposed for optimizing individual IMPRs. It is interesting to find that the constructed granularity matrix is different from interval-valued IMPRs. A multi-objective particle swarm optimization algorithm is adopted to obtain a set of Pareto solutions to GDM problems. Case studies are carried out to illustrate the proposed consensus reaching model. The results help to identify how to provide flexible decisions in GDM under some complexity and uncertainty of a practical problem. • The consistency degree of IMPRs is measured by proposing a novel index. • The threshold of group CL is examined to be dependent on the order of IMPRs. • Two flexibility degrees are proposed to construct a two-objective consensus model. • A MOPSO algorithm is used to derive Pareto solutions of GDM problems. [ABSTRACT FROM AUTHOR]