A Consensus Model to Manage Minority Opinions and Noncooperative Behaviors in Large Group Decision Making With Probabilistic Linguistic Term Sets

Abstract

The alternative assessment and decision-making are often complicated and involve enormous decision makers (DMs), which leads to a large group decision making (LGDM) problem, and usually requires to reach consensus within a limited time. As a powerful technique in representing linguistic evaluations, the probabilistic linguistic term set is popular to express the opinions of DMs. Under this scenario, DMs who support the same linguistic term are naturally clustered into one subgroup, whereas the distance formulas are inappropriate because whether the DM supports a linguistic term is a dichotomous variable; therefore, Tanimoto coefficient is introduced to calculate the group consensus level. Additionally, an efficient consensus model is proposed to bridge the gap between the subgroup and group opinions. In particular, a weight adjustment function is proposed to process the minority opinions. A novel method including minor and major adjustment manner is proposed to manage the noncooperative behaviors. DMs are allowed to recluster into another subgroup for major adjustment manner; on the contrary, the adjustment direction and quantities are provided for minor adjustment manner. A case study of forest fire emergency decision-making is explored and a simulation is conducted to verify the proposed consensus model in the LGDM problem. The proposed consensus model is suitable for situations where the subgroup and group decision matrices are subject to preference selections and can be applied in other decision problems.